Pianotech

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

Edit: I strongly agree with Patrick -- we should look into what you're using and how you're setting it up. I think this is often the biggest source of discrepancy between ear and ETD in practice.

------------------------------
Ryan Sowers RPT
Olympia WA
(360) 480-5648
------------------------------

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

I use an ETD but consider it's value only good for setting initial pitch of the first string in a unison. I, too, disagree with what the ETD may be telling me in setting unisons more often than not. The unisons I always tune by ear because I have the ability to hear what sounds correct while the ETD does not.

Inharmonicity is a crazy phenomena and I find it really interesting. If you consider only the string itself and not how it's terminated it's a bit easier to understand what's going on. As I understand it, because a string has thickness and is stiff it does not vibrate at it's harmonic divisions mathematically. In other words, the reason why A4 at 440 Hz does not have a second partial of exactly 880 Hz is because of the stiffness and the thickness of the string. It does not have absolutely defined speaking length points where the waveforms start and end because the nodes don't act like a finite point hinge. Instead, that node where the string divides itself for that second partial acts like a small curve, making the speaking length of that second partial shorter than the total length of the string by about the same length as the string is thick. On each end. When you have a string that has a first partial of 440 Hz and you measure the second partial it will wind up being a tiny bit sharp of the first partial doubled because the length of the vibrating portion of the string for that second partial is a tiny small amount shorter than the full length of the string divided by two. Every time you divide the string into it's next higher partial that happens again. Every higher partial winds up having a slightly higher frequency than pure mathematical division would suggest. 

Because of this, if you change the thickness of one string in a unison, let's say make it thinner, the partial divisions of that string will be longer, which make the partials of that thinner string divide into slightly lower frequencies than the other strings in that unison. Unisons would be very difficult to pull in, if not impossible. 

Also, increasing or decreasing the total length of one string in a unison means that the length of all the partials divisions in that string will now be longer or shorter and no longer match the divisions of the strings in the rest of the unison. Again, impossible unisons. 

Another thing that can contribute to unwanted beats could be a bridge notch that is not square with the string. If the horizontal and vertical movement of the string are not terminated at exactly the same point on the string you wind up with a string that is one length horizontally and a different length vertically. That single string winds up acting like two strings of different lengths and thus gives false beats. 

I thank Ron Nossaman for covering much of this in his three articles on false beats in the Journal in 2016. 

------------------------------
Geoff Sykes, RPT
Los Angeles CA

Original Message:
Sent: 08-07-2024 19:36
From: Ryan Sowers
Subject: ETD Discrepancies and limits of accuracy

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

------------------------------
Ryan Sowers RPT
Olympia WA
(360) 480-5648
------------------------------

Geoff wrote:

> When you have a string that has a first partial of 440 Hz and you measure the second partial it will wind up being a tiny bit sharp of the first partial doubled because the length of the vibrating portion of the string for that second partial is a tiny small amount shorter than the full length of the string divided by two. Every time you divide the string into it's next higher partial that happens again. Every higher partial winds up having a slightly higher frequency than pure mathematical division would suggest. 

Small addition: The first few partials can be a bit lower pitched than expected from the string inharmonicity forumula(e), and can even go slightly flat rather than sharp compared to their multiple of fundamental.  I've seen this attributed to bridge motion (I think that was in Physics of the Piano, but I don't have it in front of me).  Robert once mentioned that TuneLab uses a lookup table rather than a simple function, to calculate partial frequencies from the inharmonicity constant it stores...

Edit: I believe this is the reason for the discrepancies between partials that Ron Koval mentioned.  I've observed that too, although I've only seen a few tenths of a cent in either direction.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 08-08-2024 02:52
From: Geoff Sykes
Subject: ETD Discrepancies and limits of accuracy

I use an ETD but consider it's value only good for setting initial pitch of the first string in a unison. I, too, disagree with what the ETD may be telling me in setting unisons more often than not. The unisons I always tune by ear because I have the ability to hear what sounds correct while the ETD does not.

Inharmonicity is a crazy phenomena and I find it really interesting. If you consider only the string itself and not how it's terminated it's a bit easier to understand what's going on. As I understand it, because a string has thickness and is stiff it does not vibrate at it's harmonic divisions mathematically. In other words, the reason why A4 at 440 Hz does not have a second partial of exactly 880 Hz is because of the stiffness and the thickness of the string. It does not have absolutely defined speaking length points where the waveforms start and end because the nodes don't act like a finite point hinge. Instead, that node where the string divides itself for that second partial acts like a small curve, making the speaking length of that second partial shorter than the total length of the string by about the same length as the string is thick. On each end. When you have a string that has a first partial of 440 Hz and you measure the second partial it will wind up being a tiny bit sharp of the first partial doubled because the length of the vibrating portion of the string for that second partial is a tiny small amount shorter than the full length of the string divided by two. Every time you divide the string into it's next higher partial that happens again. Every higher partial winds up having a slightly higher frequency than pure mathematical division would suggest. 

Because of this, if you change the thickness of one string in a unison, let's say make it thinner, the partial divisions of that string will be longer, which make the partials of that thinner string divide into slightly lower frequencies than the other strings in that unison. Unisons would be very difficult to pull in, if not impossible. 

Also, increasing or decreasing the total length of one string in a unison means that the length of all the partials divisions in that string will now be longer or shorter and no longer match the divisions of the strings in the rest of the unison. Again, impossible unisons. 

Another thing that can contribute to unwanted beats could be a bridge notch that is not square with the string. If the horizontal and vertical movement of the string are not terminated at exactly the same point on the string you wind up with a string that is one length horizontally and a different length vertically. That single string winds up acting like two strings of different lengths and thus gives false beats. 

I thank Ron Nossaman for covering much of this in his three articles on false beats in the Journal in 2016. 

------------------------------
Geoff Sykes, RPT
Los Angeles CA

Original Message:
Sent: 08-07-2024 19:36
From: Ryan Sowers
Subject: ETD Discrepancies and limits of accuracy

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

------------------------------
Ryan Sowers RPT
Olympia WA
(360) 480-5648
------------------------------

OK I'm going to reproduce Robert's post that I referred to because it was on Facebook, and the search function there is absolute trash:

Geoff wrote:

> When you have a string that has a first partial of 440 Hz and you measure the second partial it will wind up being a tiny bit sharp of the first partial doubled because the length of the vibrating portion of the string for that second partial is a tiny small amount shorter than the full length of the string divided by two. Every time you divide the string into it's next higher partial that happens again. Every higher partial winds up having a slightly higher frequency than pure mathematical division would suggest. 

Small addition: The first few partials can be a bit lower pitched than expected from the string inharmonicity forumula(e), and can even go slightly flat rather than sharp compared to their multiple of fundamental.  I've seen this attributed to bridge motion (I think that was in Physics of the Piano, but I don't have it in front of me).  Robert once mentioned that TuneLab uses a lookup table rather than a simple function, to calculate partial frequencies from the inharmonicity constant it stores...

Edit: I believe this is the reason for the discrepancies between partials that Ron Koval mentioned.  I've observed that too, although I've only seen a few tenths of a cent in either direction.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 08-08-2024 02:52
From: Geoff Sykes
Subject: ETD Discrepancies and limits of accuracy

I use an ETD but consider it's value only good for setting initial pitch of the first string in a unison. I, too, disagree with what the ETD may be telling me in setting unisons more often than not. The unisons I always tune by ear because I have the ability to hear what sounds correct while the ETD does not.

Inharmonicity is a crazy phenomena and I find it really interesting. If you consider only the string itself and not how it's terminated it's a bit easier to understand what's going on. As I understand it, because a string has thickness and is stiff it does not vibrate at it's harmonic divisions mathematically. In other words, the reason why A4 at 440 Hz does not have a second partial of exactly 880 Hz is because of the stiffness and the thickness of the string. It does not have absolutely defined speaking length points where the waveforms start and end because the nodes don't act like a finite point hinge. Instead, that node where the string divides itself for that second partial acts like a small curve, making the speaking length of that second partial shorter than the total length of the string by about the same length as the string is thick. On each end. When you have a string that has a first partial of 440 Hz and you measure the second partial it will wind up being a tiny bit sharp of the first partial doubled because the length of the vibrating portion of the string for that second partial is a tiny small amount shorter than the full length of the string divided by two. Every time you divide the string into it's next higher partial that happens again. Every higher partial winds up having a slightly higher frequency than pure mathematical division would suggest. 

Because of this, if you change the thickness of one string in a unison, let's say make it thinner, the partial divisions of that string will be longer, which make the partials of that thinner string divide into slightly lower frequencies than the other strings in that unison. Unisons would be very difficult to pull in, if not impossible. 

Also, increasing or decreasing the total length of one string in a unison means that the length of all the partials divisions in that string will now be longer or shorter and no longer match the divisions of the strings in the rest of the unison. Again, impossible unisons. 

Another thing that can contribute to unwanted beats could be a bridge notch that is not square with the string. If the horizontal and vertical movement of the string are not terminated at exactly the same point on the string you wind up with a string that is one length horizontally and a different length vertically. That single string winds up acting like two strings of different lengths and thus gives false beats. 

I thank Ron Nossaman for covering much of this in his three articles on false beats in the Journal in 2016. 

------------------------------
Geoff Sykes, RPT
Los Angeles CA

Original Message:
Sent: 08-07-2024 19:36
From: Ryan Sowers
Subject: ETD Discrepancies and limits of accuracy

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

------------------------------
Ryan Sowers RPT
Olympia WA
(360) 480-5648
------------------------------

Replying to Nathan's post about the inharmonicity equations 

F_n = n*F₀ * sqrt(1 + B*n²)

vs. 

CentsOffset = B*n²

The two models are basically equivalent and you can get from one to the other with some log identities and the approximation:

log2(1 + x) ≈ ln(2) * x   (for small x) 

The inharmonicity constants (B) in the two models are related by a factor of 1731.2.

OK I'm going to reproduce Robert's post that I referred to because it was on Facebook, and the search function there is absolute trash:

Geoff wrote:

> When you have a string that has a first partial of 440 Hz and you measure the second partial it will wind up being a tiny bit sharp of the first partial doubled because the length of the vibrating portion of the string for that second partial is a tiny small amount shorter than the full length of the string divided by two. Every time you divide the string into it's next higher partial that happens again. Every higher partial winds up having a slightly higher frequency than pure mathematical division would suggest. 

Small addition: The first few partials can be a bit lower pitched than expected from the string inharmonicity forumula(e), and can even go slightly flat rather than sharp compared to their multiple of fundamental.  I've seen this attributed to bridge motion (I think that was in Physics of the Piano, but I don't have it in front of me).  Robert once mentioned that TuneLab uses a lookup table rather than a simple function, to calculate partial frequencies from the inharmonicity constant it stores...

Edit: I believe this is the reason for the discrepancies between partials that Ron Koval mentioned.  I've observed that too, although I've only seen a few tenths of a cent in either direction.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 08-08-2024 02:52
From: Geoff Sykes
Subject: ETD Discrepancies and limits of accuracy

I use an ETD but consider it's value only good for setting initial pitch of the first string in a unison. I, too, disagree with what the ETD may be telling me in setting unisons more often than not. The unisons I always tune by ear because I have the ability to hear what sounds correct while the ETD does not.

Inharmonicity is a crazy phenomena and I find it really interesting. If you consider only the string itself and not how it's terminated it's a bit easier to understand what's going on. As I understand it, because a string has thickness and is stiff it does not vibrate at it's harmonic divisions mathematically. In other words, the reason why A4 at 440 Hz does not have a second partial of exactly 880 Hz is because of the stiffness and the thickness of the string. It does not have absolutely defined speaking length points where the waveforms start and end because the nodes don't act like a finite point hinge. Instead, that node where the string divides itself for that second partial acts like a small curve, making the speaking length of that second partial shorter than the total length of the string by about the same length as the string is thick. On each end. When you have a string that has a first partial of 440 Hz and you measure the second partial it will wind up being a tiny bit sharp of the first partial doubled because the length of the vibrating portion of the string for that second partial is a tiny small amount shorter than the full length of the string divided by two. Every time you divide the string into it's next higher partial that happens again. Every higher partial winds up having a slightly higher frequency than pure mathematical division would suggest. 

Because of this, if you change the thickness of one string in a unison, let's say make it thinner, the partial divisions of that string will be longer, which make the partials of that thinner string divide into slightly lower frequencies than the other strings in that unison. Unisons would be very difficult to pull in, if not impossible. 

Also, increasing or decreasing the total length of one string in a unison means that the length of all the partials divisions in that string will now be longer or shorter and no longer match the divisions of the strings in the rest of the unison. Again, impossible unisons. 

Another thing that can contribute to unwanted beats could be a bridge notch that is not square with the string. If the horizontal and vertical movement of the string are not terminated at exactly the same point on the string you wind up with a string that is one length horizontally and a different length vertically. That single string winds up acting like two strings of different lengths and thus gives false beats. 

I thank Ron Nossaman for covering much of this in his three articles on false beats in the Journal in 2016. 

------------------------------
Geoff Sykes, RPT
Los Angeles CA

Original Message:
Sent: 08-07-2024 19:36
From: Ryan Sowers
Subject: ETD Discrepancies and limits of accuracy

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

------------------------------
Ryan Sowers RPT
Olympia WA
(360) 480-5648
------------------------------

Replying to Nathan's post about the inharmonicity equations 

F_n = n*F₀ * sqrt(1 + B*n²)

vs. 

CentsOffset = B*n²

The two models are basically equivalent and you can get from one to the other with some log identities and the approximation:

log2(1 + x) ≈ ln(2) * x   (for small x) 

The inharmonicity constants (B) in the two models are related by a factor of 1731.2.

OK I'm going to reproduce Robert's post that I referred to because it was on Facebook, and the search function there is absolute trash:

Geoff wrote:

> When you have a string that has a first partial of 440 Hz and you measure the second partial it will wind up being a tiny bit sharp of the first partial doubled because the length of the vibrating portion of the string for that second partial is a tiny small amount shorter than the full length of the string divided by two. Every time you divide the string into it's next higher partial that happens again. Every higher partial winds up having a slightly higher frequency than pure mathematical division would suggest. 

Small addition: The first few partials can be a bit lower pitched than expected from the string inharmonicity forumula(e), and can even go slightly flat rather than sharp compared to their multiple of fundamental.  I've seen this attributed to bridge motion (I think that was in Physics of the Piano, but I don't have it in front of me).  Robert once mentioned that TuneLab uses a lookup table rather than a simple function, to calculate partial frequencies from the inharmonicity constant it stores...

Edit: I believe this is the reason for the discrepancies between partials that Ron Koval mentioned.  I've observed that too, although I've only seen a few tenths of a cent in either direction.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 08-08-2024 02:52
From: Geoff Sykes
Subject: ETD Discrepancies and limits of accuracy

I use an ETD but consider it's value only good for setting initial pitch of the first string in a unison. I, too, disagree with what the ETD may be telling me in setting unisons more often than not. The unisons I always tune by ear because I have the ability to hear what sounds correct while the ETD does not.

Inharmonicity is a crazy phenomena and I find it really interesting. If you consider only the string itself and not how it's terminated it's a bit easier to understand what's going on. As I understand it, because a string has thickness and is stiff it does not vibrate at it's harmonic divisions mathematically. In other words, the reason why A4 at 440 Hz does not have a second partial of exactly 880 Hz is because of the stiffness and the thickness of the string. It does not have absolutely defined speaking length points where the waveforms start and end because the nodes don't act like a finite point hinge. Instead, that node where the string divides itself for that second partial acts like a small curve, making the speaking length of that second partial shorter than the total length of the string by about the same length as the string is thick. On each end. When you have a string that has a first partial of 440 Hz and you measure the second partial it will wind up being a tiny bit sharp of the first partial doubled because the length of the vibrating portion of the string for that second partial is a tiny small amount shorter than the full length of the string divided by two. Every time you divide the string into it's next higher partial that happens again. Every higher partial winds up having a slightly higher frequency than pure mathematical division would suggest. 

Because of this, if you change the thickness of one string in a unison, let's say make it thinner, the partial divisions of that string will be longer, which make the partials of that thinner string divide into slightly lower frequencies than the other strings in that unison. Unisons would be very difficult to pull in, if not impossible. 

Also, increasing or decreasing the total length of one string in a unison means that the length of all the partials divisions in that string will now be longer or shorter and no longer match the divisions of the strings in the rest of the unison. Again, impossible unisons. 

Another thing that can contribute to unwanted beats could be a bridge notch that is not square with the string. If the horizontal and vertical movement of the string are not terminated at exactly the same point on the string you wind up with a string that is one length horizontally and a different length vertically. That single string winds up acting like two strings of different lengths and thus gives false beats. 

I thank Ron Nossaman for covering much of this in his three articles on false beats in the Journal in 2016. 

------------------------------
Geoff Sykes, RPT
Los Angeles CA

Original Message:
Sent: 08-07-2024 19:36
From: Ryan Sowers
Subject: ETD Discrepancies and limits of accuracy

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

------------------------------
Ryan Sowers RPT
Olympia WA
(360) 480-5648
------------------------------

Geoff wrote:

> When you have a string that has a first partial of 440 Hz and you measure the second partial it will wind up being a tiny bit sharp of the first partial doubled because the length of the vibrating portion of the string for that second partial is a tiny small amount shorter than the full length of the string divided by two. Every time you divide the string into it's next higher partial that happens again. Every higher partial winds up having a slightly higher frequency than pure mathematical division would suggest. 

Small addition: The first few partials can be a bit lower pitched than expected from the string inharmonicity forumula(e), and can even go slightly flat rather than sharp compared to their multiple of fundamental.  I've seen this attributed to bridge motion (I think that was in Physics of the Piano, but I don't have it in front of me).  Robert once mentioned that TuneLab uses a lookup table rather than a simple function, to calculate partial frequencies from the inharmonicity constant it stores...

Edit: I believe this is the reason for the discrepancies between partials that Ron Koval mentioned.  I've observed that too, although I've only seen a few tenths of a cent in either direction.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com
------------------------------

Original Message:
Sent: 08-08-2024 02:52
From: Geoff Sykes
Subject: ETD Discrepancies and limits of accuracy

I use an ETD but consider it's value only good for setting initial pitch of the first string in a unison. I, too, disagree with what the ETD may be telling me in setting unisons more often than not. The unisons I always tune by ear because I have the ability to hear what sounds correct while the ETD does not.

Inharmonicity is a crazy phenomena and I find it really interesting. If you consider only the string itself and not how it's terminated it's a bit easier to understand what's going on. As I understand it, because a string has thickness and is stiff it does not vibrate at it's harmonic divisions mathematically. In other words, the reason why A4 at 440 Hz does not have a second partial of exactly 880 Hz is because of the stiffness and the thickness of the string. It does not have absolutely defined speaking length points where the waveforms start and end because the nodes don't act like a finite point hinge. Instead, that node where the string divides itself for that second partial acts like a small curve, making the speaking length of that second partial shorter than the total length of the string by about the same length as the string is thick. On each end. When you have a string that has a first partial of 440 Hz and you measure the second partial it will wind up being a tiny bit sharp of the first partial doubled because the length of the vibrating portion of the string for that second partial is a tiny small amount shorter than the full length of the string divided by two. Every time you divide the string into it's next higher partial that happens again. Every higher partial winds up having a slightly higher frequency than pure mathematical division would suggest. 

Because of this, if you change the thickness of one string in a unison, let's say make it thinner, the partial divisions of that string will be longer, which make the partials of that thinner string divide into slightly lower frequencies than the other strings in that unison. Unisons would be very difficult to pull in, if not impossible. 

Also, increasing or decreasing the total length of one string in a unison means that the length of all the partials divisions in that string will now be longer or shorter and no longer match the divisions of the strings in the rest of the unison. Again, impossible unisons. 

Another thing that can contribute to unwanted beats could be a bridge notch that is not square with the string. If the horizontal and vertical movement of the string are not terminated at exactly the same point on the string you wind up with a string that is one length horizontally and a different length vertically. That single string winds up acting like two strings of different lengths and thus gives false beats. 

I thank Ron Nossaman for covering much of this in his three articles on false beats in the Journal in 2016. 

------------------------------
Geoff Sykes, RPT
Los Angeles CA

Original Message:
Sent: 08-07-2024 19:36
From: Ryan Sowers
Subject: ETD Discrepancies and limits of accuracy

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

------------------------------
Ryan Sowers RPT
Olympia WA
(360) 480-5648
------------------------------

Geoff wrote:

> When you have a string that has a first partial of 440 Hz and you measure the second partial it will wind up being a tiny bit sharp of the first partial doubled because the length of the vibrating portion of the string for that second partial is a tiny small amount shorter than the full length of the string divided by two. Every time you divide the string into it's next higher partial that happens again. Every higher partial winds up having a slightly higher frequency than pure mathematical division would suggest. 

Small addition: The first few partials can be a bit lower pitched than expected from the string inharmonicity forumula(e), and can even go slightly flat rather than sharp compared to their multiple of fundamental.  I've seen this attributed to bridge motion (I think that was in Physics of the Piano, but I don't have it in front of me).  Robert once mentioned that TuneLab uses a lookup table rather than a simple function, to calculate partial frequencies from the inharmonicity constant it stores...

Edit: I believe this is the reason for the discrepancies between partials that Ron Koval mentioned.  I've observed that too, although I've only seen a few tenths of a cent in either direction.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com
------------------------------

Original Message:
Sent: 08-08-2024 02:52
From: Geoff Sykes
Subject: ETD Discrepancies and limits of accuracy

I use an ETD but consider it's value only good for setting initial pitch of the first string in a unison. I, too, disagree with what the ETD may be telling me in setting unisons more often than not. The unisons I always tune by ear because I have the ability to hear what sounds correct while the ETD does not.

Inharmonicity is a crazy phenomena and I find it really interesting. If you consider only the string itself and not how it's terminated it's a bit easier to understand what's going on. As I understand it, because a string has thickness and is stiff it does not vibrate at it's harmonic divisions mathematically. In other words, the reason why A4 at 440 Hz does not have a second partial of exactly 880 Hz is because of the stiffness and the thickness of the string. It does not have absolutely defined speaking length points where the waveforms start and end because the nodes don't act like a finite point hinge. Instead, that node where the string divides itself for that second partial acts like a small curve, making the speaking length of that second partial shorter than the total length of the string by about the same length as the string is thick. On each end. When you have a string that has a first partial of 440 Hz and you measure the second partial it will wind up being a tiny bit sharp of the first partial doubled because the length of the vibrating portion of the string for that second partial is a tiny small amount shorter than the full length of the string divided by two. Every time you divide the string into it's next higher partial that happens again. Every higher partial winds up having a slightly higher frequency than pure mathematical division would suggest. 

Because of this, if you change the thickness of one string in a unison, let's say make it thinner, the partial divisions of that string will be longer, which make the partials of that thinner string divide into slightly lower frequencies than the other strings in that unison. Unisons would be very difficult to pull in, if not impossible. 

Also, increasing or decreasing the total length of one string in a unison means that the length of all the partials divisions in that string will now be longer or shorter and no longer match the divisions of the strings in the rest of the unison. Again, impossible unisons. 

Another thing that can contribute to unwanted beats could be a bridge notch that is not square with the string. If the horizontal and vertical movement of the string are not terminated at exactly the same point on the string you wind up with a string that is one length horizontally and a different length vertically. That single string winds up acting like two strings of different lengths and thus gives false beats. 

I thank Ron Nossaman for covering much of this in his three articles on false beats in the Journal in 2016. 

------------------------------
Geoff Sykes, RPT
Los Angeles CA

Original Message:
Sent: 08-07-2024 19:36
From: Ryan Sowers
Subject: ETD Discrepancies and limits of accuracy

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

------------------------------
Ryan Sowers RPT
Olympia WA
(360) 480-5648
------------------------------

Geoff wrote:

> When you have a string that has a first partial of 440 Hz and you measure the second partial it will wind up being a tiny bit sharp of the first partial doubled because the length of the vibrating portion of the string for that second partial is a tiny small amount shorter than the full length of the string divided by two. Every time you divide the string into it's next higher partial that happens again. Every higher partial winds up having a slightly higher frequency than pure mathematical division would suggest. 

Small addition: The first few partials can be a bit lower pitched than expected from the string inharmonicity forumula(e), and can even go slightly flat rather than sharp compared to their multiple of fundamental.  I've seen this attributed to bridge motion (I think that was in Physics of the Piano, but I don't have it in front of me).  Robert once mentioned that TuneLab uses a lookup table rather than a simple function, to calculate partial frequencies from the inharmonicity constant it stores...

Edit: I believe this is the reason for the discrepancies between partials that Ron Koval mentioned.  I've observed that too, although I've only seen a few tenths of a cent in either direction.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 08-08-2024 02:52
From: Geoff Sykes
Subject: ETD Discrepancies and limits of accuracy

I use an ETD but consider it's value only good for setting initial pitch of the first string in a unison. I, too, disagree with what the ETD may be telling me in setting unisons more often than not. The unisons I always tune by ear because I have the ability to hear what sounds correct while the ETD does not.

Inharmonicity is a crazy phenomena and I find it really interesting. If you consider only the string itself and not how it's terminated it's a bit easier to understand what's going on. As I understand it, because a string has thickness and is stiff it does not vibrate at it's harmonic divisions mathematically. In other words, the reason why A4 at 440 Hz does not have a second partial of exactly 880 Hz is because of the stiffness and the thickness of the string. It does not have absolutely defined speaking length points where the waveforms start and end because the nodes don't act like a finite point hinge. Instead, that node where the string divides itself for that second partial acts like a small curve, making the speaking length of that second partial shorter than the total length of the string by about the same length as the string is thick. On each end. When you have a string that has a first partial of 440 Hz and you measure the second partial it will wind up being a tiny bit sharp of the first partial doubled because the length of the vibrating portion of the string for that second partial is a tiny small amount shorter than the full length of the string divided by two. Every time you divide the string into it's next higher partial that happens again. Every higher partial winds up having a slightly higher frequency than pure mathematical division would suggest. 

Because of this, if you change the thickness of one string in a unison, let's say make it thinner, the partial divisions of that string will be longer, which make the partials of that thinner string divide into slightly lower frequencies than the other strings in that unison. Unisons would be very difficult to pull in, if not impossible. 

Also, increasing or decreasing the total length of one string in a unison means that the length of all the partials divisions in that string will now be longer or shorter and no longer match the divisions of the strings in the rest of the unison. Again, impossible unisons. 

Another thing that can contribute to unwanted beats could be a bridge notch that is not square with the string. If the horizontal and vertical movement of the string are not terminated at exactly the same point on the string you wind up with a string that is one length horizontally and a different length vertically. That single string winds up acting like two strings of different lengths and thus gives false beats. 

I thank Ron Nossaman for covering much of this in his three articles on false beats in the Journal in 2016. 

------------------------------
Geoff Sykes, RPT
Los Angeles CA

Original Message:
Sent: 08-07-2024 19:36
From: Ryan Sowers
Subject: ETD Discrepancies and limits of accuracy

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

------------------------------
Ryan Sowers RPT
Olympia WA
(360) 480-5648
------------------------------

I find it amusing (at the very least) that this specific subject would come up "now" after all the related discussions over past few months (as if they never took place). Either eyes and ears have been "elsewhere" and not cognizant of relevant data presented, or perhaps it's due to eyes and ears NOT WANTING to hear it from the source it has come from. Hmmmm...LOL!

I had the same question 20 years ago. It was recently clearly answered, experimentally proven, AND a viable solution devised and made available. 

I'm still shaking my head and laughing at this. 

Peter Grey Piano Doctor 

Edit: GIGO

------------------------------
Peter Grey
Stratham NH
(603) 686-2395
pianodoctor57@gmail.com

Original Message:
Sent: 08-08-2024 13:39
From: Horace Greeley
Subject: ETD Discrepancies and limits of accuracy

Hi, Nathan,

The title of the book you mention is:

The Physics of Piano Unisons (Studies in Science and Philosophy), Capelton, Dr. Brian, Amarilli Books, 2015

The ISBN (at least on the copy I have is:

13: 9780992814168

For my money, this is required reading.

Kind regards.

Horace


  Original Message


Original Message:
Sent: 8/8/2024 11:14:00 AM
From: Nathan Monteleone
Subject: RE: ETD Discrepancies and limits of accuracy

Geoff wrote:

> When you have a string that has a first partial of 440 Hz and you measure the second partial it will wind up being a tiny bit sharp of the first partial doubled because the length of the vibrating portion of the string for that second partial is a tiny small amount shorter than the full length of the string divided by two. Every time you divide the string into it's next higher partial that happens again. Every higher partial winds up having a slightly higher frequency than pure mathematical division would suggest. 

Small addition: The first few partials can be a bit lower pitched than expected from the string inharmonicity forumula(e), and can even go slightly flat rather than sharp compared to their multiple of fundamental.  I've seen this attributed to bridge motion (I think that was in Physics of the Piano, but I don't have it in front of me).  Robert once mentioned that TuneLab uses a lookup table rather than a simple function, to calculate partial frequencies from the inharmonicity constant it stores...

Edit: I believe this is the reason for the discrepancies between partials that Ron Koval mentioned.  I've observed that too, although I've only seen a few tenths of a cent in either direction.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 08-08-2024 02:52
From: Geoff Sykes
Subject: ETD Discrepancies and limits of accuracy

I use an ETD but consider it's value only good for setting initial pitch of the first string in a unison. I, too, disagree with what the ETD may be telling me in setting unisons more often than not. The unisons I always tune by ear because I have the ability to hear what sounds correct while the ETD does not.

Inharmonicity is a crazy phenomena and I find it really interesting. If you consider only the string itself and not how it's terminated it's a bit easier to understand what's going on. As I understand it, because a string has thickness and is stiff it does not vibrate at it's harmonic divisions mathematically. In other words, the reason why A4 at 440 Hz does not have a second partial of exactly 880 Hz is because of the stiffness and the thickness of the string. It does not have absolutely defined speaking length points where the waveforms start and end because the nodes don't act like a finite point hinge. Instead, that node where the string divides itself for that second partial acts like a small curve, making the speaking length of that second partial shorter than the total length of the string by about the same length as the string is thick. On each end. When you have a string that has a first partial of 440 Hz and you measure the second partial it will wind up being a tiny bit sharp of the first partial doubled because the length of the vibrating portion of the string for that second partial is a tiny small amount shorter than the full length of the string divided by two. Every time you divide the string into it's next higher partial that happens again. Every higher partial winds up having a slightly higher frequency than pure mathematical division would suggest. 

Because of this, if you change the thickness of one string in a unison, let's say make it thinner, the partial divisions of that string will be longer, which make the partials of that thinner string divide into slightly lower frequencies than the other strings in that unison. Unisons would be very difficult to pull in, if not impossible. 

Also, increasing or decreasing the total length of one string in a unison means that the length of all the partials divisions in that string will now be longer or shorter and no longer match the divisions of the strings in the rest of the unison. Again, impossible unisons. 

Another thing that can contribute to unwanted beats could be a bridge notch that is not square with the string. If the horizontal and vertical movement of the string are not terminated at exactly the same point on the string you wind up with a string that is one length horizontally and a different length vertically. That single string winds up acting like two strings of different lengths and thus gives false beats. 

I thank Ron Nossaman for covering much of this in his three articles on false beats in the Journal in 2016. 

------------------------------
Geoff Sykes, RPT
Los Angeles CA

Original Message:
Sent: 08-07-2024 19:36
From: Ryan Sowers
Subject: ETD Discrepancies and limits of accuracy

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

------------------------------
Ryan Sowers RPT
Olympia WA
(360) 480-5648
------------------------------

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

I'll agree that there is way more variation between the results of tuning apps than tech may first realize...

Another thing for you to research is the precision of using an inharmonicity constant, which seems to be standard for many of the apps. While the partial "locations" fall close to the line projected by the constants, there seems to be a bit of wiggle room in some of the testing I've seen. If your app allows for stepping through partials of a tuned note and the display moves, that shows that the calculations which should be able to predict the location of each partial isn't quite right. Multipartial tuning can help smooth this out a bit.

I know Veritune uses a different model which claims to do a better job of predicting the exact location of one partial based on the location of another. I believe that is one reason for a much slower measuring time.

Then there is the noise in the system - how repeatable (using what ever input) using the app are the tuning target results. They should be very close on repeated measures, but for those claiming absolut precision, they might be surprised to see .1 or .5 or 1 cent differences between multiple measures of the same piano. I believe this tends to actually be more apparent in apps that measure many notes. The ones that only measure a few can be more repeatable, but miss closely matching the piano scale because of having to 'fill in the blanks'.

Like my mentors reminded me - unisons are the most important intervals in having clients happy with the tuning.

Ron Koval 

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

I'll agree that there is way more variation between the results of tuning apps than tech may first realize...

Another thing for you to research is the precision of using an inharmonicity constant, which seems to be standard for many of the apps. While the partial "locations" fall close to the line projected by the constants, there seems to be a bit of wiggle room in some of the testing I've seen. If your app allows for stepping through partials of a tuned note and the display moves, that shows that the calculations which should be able to predict the location of each partial isn't quite right. Multipartial tuning can help smooth this out a bit.

I know Veritune uses a different model which claims to do a better job of predicting the exact location of one partial based on the location of another. I believe that is one reason for a much slower measuring time.

Then there is the noise in the system - how repeatable (using what ever input) using the app are the tuning target results. They should be very close on repeated measures, but for those claiming absolut precision, they might be surprised to see .1 or .5 or 1 cent differences between multiple measures of the same piano. I believe this tends to actually be more apparent in apps that measure many notes. The ones that only measure a few can be more repeatable, but miss closely matching the piano scale because of having to 'fill in the blanks'.

Like my mentors reminded me - unisons are the most important intervals in having clients happy with the tuning.

Ron Koval 

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

Just yesterday in an online conversation with a colleague, I commented...

I'll agree that there is way more variation between the results of tuning apps than tech may first realize...

Another thing for you to research is the precision of using an inharmonicity constant, which seems to be standard for many of the apps. While the partial "locations" fall close to the line projected by the constants, there seems to be a bit of wiggle room in some of the testing I've seen. If your app allows for stepping through partials of a tuned note and the display moves, that shows that the calculations which should be able to predict the location of each partial isn't quite right. Multipartial tuning can help smooth this out a bit.

I know Veritune uses a different model which claims to do a better job of predicting the exact location of one partial based on the location of another. I believe that is one reason for a much slower measuring time.

Then there is the noise in the system - how repeatable (using what ever input) using the app are the tuning target results. They should be very close on repeated measures, but for those claiming absolut precision, they might be surprised to see .1 or .5 or 1 cent differences between multiple measures of the same piano. I believe this tends to actually be more apparent in apps that measure many notes. The ones that only measure a few can be more repeatable, but miss closely matching the piano scale because of having to 'fill in the blanks'.

Like my mentors reminded me - unisons are the most important intervals in having clients happy with the tuning.

Ron Koval 

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

Just yesterday in an online conversation with a colleague, I commented...

I'll agree that there is way more variation between the results of tuning apps than tech may first realize...

Another thing for you to research is the precision of using an inharmonicity constant, which seems to be standard for many of the apps. While the partial "locations" fall close to the line projected by the constants, there seems to be a bit of wiggle room in some of the testing I've seen. If your app allows for stepping through partials of a tuned note and the display moves, that shows that the calculations which should be able to predict the location of each partial isn't quite right. Multipartial tuning can help smooth this out a bit.

I know Veritune uses a different model which claims to do a better job of predicting the exact location of one partial based on the location of another. I believe that is one reason for a much slower measuring time.

Then there is the noise in the system - how repeatable (using what ever input) using the app are the tuning target results. They should be very close on repeated measures, but for those claiming absolut precision, they might be surprised to see .1 or .5 or 1 cent differences between multiple measures of the same piano. I believe this tends to actually be more apparent in apps that measure many notes. The ones that only measure a few can be more repeatable, but miss closely matching the piano scale because of having to 'fill in the blanks'.

Like my mentors reminded me - unisons are the most important intervals in having clients happy with the tuning.

Ron Koval 

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

Just yesterday in an online conversation with a colleague, I commented...

I'll agree that there is way more variation between the results of tuning apps than tech may first realize...

Another thing for you to research is the precision of using an inharmonicity constant, which seems to be standard for many of the apps. While the partial "locations" fall close to the line projected by the constants, there seems to be a bit of wiggle room in some of the testing I've seen. If your app allows for stepping through partials of a tuned note and the display moves, that shows that the calculations which should be able to predict the location of each partial isn't quite right. Multipartial tuning can help smooth this out a bit.

I know Veritune uses a different model which claims to do a better job of predicting the exact location of one partial based on the location of another. I believe that is one reason for a much slower measuring time.

Then there is the noise in the system - how repeatable (using what ever input) using the app are the tuning target results. They should be very close on repeated measures, but for those claiming absolut precision, they might be surprised to see .1 or .5 or 1 cent differences between multiple measures of the same piano. I believe this tends to actually be more apparent in apps that measure many notes. The ones that only measure a few can be more repeatable, but miss closely matching the piano scale because of having to 'fill in the blanks'.

Like my mentors reminded me - unisons are the most important intervals in having clients happy with the tuning.

Ron Koval 

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

Peter, you've got that right! 

I took a seminar with Dr. Sanderson on interval checks. No Act tuner in sight, he knew the checks backwards and forwards and could tune with them.

And a real gentleman.

Just yesterday in an online conversation with a colleague, I commented...

I'll agree that there is way more variation between the results of tuning apps than tech may first realize...

Another thing for you to research is the precision of using an inharmonicity constant, which seems to be standard for many of the apps. While the partial "locations" fall close to the line projected by the constants, there seems to be a bit of wiggle room in some of the testing I've seen. If your app allows for stepping through partials of a tuned note and the display moves, that shows that the calculations which should be able to predict the location of each partial isn't quite right. Multipartial tuning can help smooth this out a bit.

I know Veritune uses a different model which claims to do a better job of predicting the exact location of one partial based on the location of another. I believe that is one reason for a much slower measuring time.

Then there is the noise in the system - how repeatable (using what ever input) using the app are the tuning target results. They should be very close on repeated measures, but for those claiming absolut precision, they might be surprised to see .1 or .5 or 1 cent differences between multiple measures of the same piano. I believe this tends to actually be more apparent in apps that measure many notes. The ones that only measure a few can be more repeatable, but miss closely matching the piano scale because of having to 'fill in the blanks'.

Like my mentors reminded me - unisons are the most important intervals in having clients happy with the tuning.

Ron Koval 

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

Peter, you've got that right! 

I took a seminar with Dr. Sanderson on interval checks. No Act tuner in sight, he knew the checks backwards and forwards and could tune with them.

And a real gentleman.

Just yesterday in an online conversation with a colleague, I commented...

I'll agree that there is way more variation between the results of tuning apps than tech may first realize...

Another thing for you to research is the precision of using an inharmonicity constant, which seems to be standard for many of the apps. While the partial "locations" fall close to the line projected by the constants, there seems to be a bit of wiggle room in some of the testing I've seen. If your app allows for stepping through partials of a tuned note and the display moves, that shows that the calculations which should be able to predict the location of each partial isn't quite right. Multipartial tuning can help smooth this out a bit.

I know Veritune uses a different model which claims to do a better job of predicting the exact location of one partial based on the location of another. I believe that is one reason for a much slower measuring time.

Then there is the noise in the system - how repeatable (using what ever input) using the app are the tuning target results. They should be very close on repeated measures, but for those claiming absolut precision, they might be surprised to see .1 or .5 or 1 cent differences between multiple measures of the same piano. I believe this tends to actually be more apparent in apps that measure many notes. The ones that only measure a few can be more repeatable, but miss closely matching the piano scale because of having to 'fill in the blanks'.

Like my mentors reminded me - unisons are the most important intervals in having clients happy with the tuning.

Ron Koval 

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

------------------------------
Ryan Sowers RPT
Olympia WA
(360) 480-5648
------------------------------

What is wrong with a simple tone generator that produces the middle or only a few middle octaves and tuning to a pitch?  If the temperament is good then wouldn't we automatically apply appropriate stretch when we tune to the pitch, whether as a unison pitch or within one or two octaves?  It seems that every one of our current ETDs should be able to incorporate this as a new feature very easily.

------------------------------
Blaine Hebert RPT
Duarte CA
(626) 390-0512
------------------------------

Original Message:
Sent: 08-07-2024 19:36
From: Ryan Sowers
Subject: ETD Discrepancies and limits of accuracy

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

------------------------------
Ryan Sowers RPT
Olympia WA
(360) 480-5648
------------------------------

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

------------------------------
Ryan Sowers RPT
Olympia WA
(360) 480-5648
------------------------------

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

Ryan (responding directly to the original post),

You posit experience where you disagree aurally with what you believe to be the "decision" of the ETD. This is pretty amorphous stuff. I can't really respond to your questions based on your personal experience without being there, observing you tune a piano with an ETD, and then checking with you, comparing notes.

What I CAN do is share my own initial experience tuning with an ETD, 30 years ago (following 15 years of purely aural tuning). I got an SAT so that I would be able to give tuning tests, and decided to try it out, though I was very skeptical. I tuned a couple midrange octaves with SAT, then checked that aurally, and found "errors." But then I looked at each of the error notes, with the ETD, and found that they were not zeroed. (I had just been through lots of CTE training on zeroing the display, so I was well aware of what I was seeing). When I zeroed the notes, all the errors went away. (This kind of experience was repeated time and time again).

So as a first response, not wishing to cause offense, I would first ask you to do precisely the same thing. Recheck the notes you object to. What does "zeroed" mean on your device? I don't know, not knowing what device you are using. To be successful at tuning with an ETD you need to figure out what zeroed means, how to see through any "junk" in the display (in many cases, use the strobe emulator, moving gray rectangles, as the most reliable factor), and then execute to zero out. As an exercise. take a note, zero the ETD on it, set an offset to plus or minus 0.5¢. Now tune to that new, slightly changed pitch target. Can you zero to it? Try again with 0.3¢. If you can't match the ETD's template to that degree of accuracy, how can you judge what the ETD has calculated?

As I took up the SAT, and very rapidly decided not to tune without it (for reasons I'll describe later), I certainly had quarrels with it, particularly with respect to stretch. I won't bother going into details, but I found ways to make it do what I wanted to do for that purpose. But there were inharmonic gaps to get past, particularly on my fleet of Hamilton studios. Nasty gaps of inharmonicity. I had never been able to be satisfied with how intervals progressed across them.

So I analyzed them, and realized that if I wanted smooth M3s I would need to lower the plain wire pitches and raise the wrapped for the notes involved in the M3s across the break. So I experimented with that, and found that if I did enough to get good beat rate progression of M3s, all kinds of other things fell apart, and they were magnified when I expanded outwards into bass and treble. I came to the conclusion that the algorithm of the ETD actually was better in the long run when I was looking at wider intervals like 19ths and triple octaves. And the piano didn't really sound better with improved beat rate progressions.

I could write more along these lines, but I think this much provides some pertinent ideas.

More to the point, the reason I have used an ETD for all my tunings for 30 years comes down to unisons and stability. Pitch isn't all that important. Violins, voices, clarinets, oboes, full orchestras are all over the place, even the very best. All over the place relative to our cents and fractional cents. And that's if they aren't intentionally bending pitch, which they are doing all the time.

For the piano, timbre is entirely dependent on unisons. (Yes, lots of other factors, but even if they are all perfect, including mating, bad unisons will overcome them). And a perfect unison is nothing if it doesn't last. Use of an ETD enables me to focus on the feel of the pin moving in the wood, the sound of the result, and the movement of pitch, simultaneously. When homing in on the pitch of each string, it is possible to make tiny, real-time manipulations of the tuning pin that don't move it in the block, and find out whether the pitch is solid or not. This is more complex than I care to go into, but in a nutshell, if you can make minute motions of twist and flex of the pin in both directions, and see (in the ETD display) the pitch move slightly sharp and flat evenly in response to those moves, and if playing the note a few times results in no pitch change, you know you have nailed it. (Bearing friction means that it ain't that simple :-)) That's the most important reason I use an ETD: ability to achieve stability efficiently.

Bottom line, I'm guessing you are coming at your question from the point of view that ETDs really don't work that well, that aural is better, and wanting to justify that position. I also have the impression that you haven't done a lot of ETD assisted tuning, just fooled with it a bit and didn't like it. Am I wrong?

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

Interesting that Ryan's only post is the first one.

------------------------------
Larry Messerly, RPT
Bringing Harmony to Homes
www.lacrossepianotuning.com
ljmesserly@gmail.com
928-899-7292

Original Message:
Sent: 08-15-2024 16:05
From: Fred Sturm
Subject: ETD Discrepancies and limits of accuracy

Ryan (responding directly to the original post),

You posit experience where you disagree aurally with what you believe to be the "decision" of the ETD. This is pretty amorphous stuff. I can't really respond to your questions based on your personal experience without being there, observing you tune a piano with an ETD, and then checking with you, comparing notes.

What I CAN do is share my own initial experience tuning with an ETD, 30 years ago (following 15 years of purely aural tuning). I got an SAT so that I would be able to give tuning tests, and decided to try it out, though I was very skeptical. I tuned a couple midrange octaves with SAT, then checked that aurally, and found "errors." But then I looked at each of the error notes, with the ETD, and found that they were not zeroed. (I had just been through lots of CTE training on zeroing the display, so I was well aware of what I was seeing). When I zeroed the notes, all the errors went away. (This kind of experience was repeated time and time again).

So as a first response, not wishing to cause offense, I would first ask you to do precisely the same thing. Recheck the notes you object to. What does "zeroed" mean on your device? I don't know, not knowing what device you are using. To be successful at tuning with an ETD you need to figure out what zeroed means, how to see through any "junk" in the display (in many cases, use the strobe emulator, moving gray rectangles, as the most reliable factor), and then execute to zero out. As an exercise. take a note, zero the ETD on it, set an offset to plus or minus 0.5¢. Now tune to that new, slightly changed pitch target. Can you zero to it? Try again with 0.3¢. If you can't match the ETD's template to that degree of accuracy, how can you judge what the ETD has calculated?

As I took up the SAT, and very rapidly decided not to tune without it (for reasons I'll describe later), I certainly had quarrels with it, particularly with respect to stretch. I won't bother going into details, but I found ways to make it do what I wanted to do for that purpose. But there were inharmonic gaps to get past, particularly on my fleet of Hamilton studios. Nasty gaps of inharmonicity. I had never been able to be satisfied with how intervals progressed across them.

So I analyzed them, and realized that if I wanted smooth M3s I would need to lower the plain wire pitches and raise the wrapped for the notes involved in the M3s across the break. So I experimented with that, and found that if I did enough to get good beat rate progression of M3s, all kinds of other things fell apart, and they were magnified when I expanded outwards into bass and treble. I came to the conclusion that the algorithm of the ETD actually was better in the long run when I was looking at wider intervals like 19ths and triple octaves. And the piano didn't really sound better with improved beat rate progressions.

I could write more along these lines, but I think this much provides some pertinent ideas.

More to the point, the reason I have used an ETD for all my tunings for 30 years comes down to unisons and stability. Pitch isn't all that important. Violins, voices, clarinets, oboes, full orchestras are all over the place, even the very best. All over the place relative to our cents and fractional cents. And that's if they aren't intentionally bending pitch, which they are doing all the time.

For the piano, timbre is entirely dependent on unisons. (Yes, lots of other factors, but even if they are all perfect, including mating, bad unisons will overcome them). And a perfect unison is nothing if it doesn't last. Use of an ETD enables me to focus on the feel of the pin moving in the wood, the sound of the result, and the movement of pitch, simultaneously. When homing in on the pitch of each string, it is possible to make tiny, real-time manipulations of the tuning pin that don't move it in the block, and find out whether the pitch is solid or not. This is more complex than I care to go into, but in a nutshell, if you can make minute motions of twist and flex of the pin in both directions, and see (in the ETD display) the pitch move slightly sharp and flat evenly in response to those moves, and if playing the note a few times results in no pitch change, you know you have nailed it. (Bearing friction means that it ain't that simple :-)) That's the most important reason I use an ETD: ability to achieve stability efficiently.

Bottom line, I'm guessing you are coming at your question from the point of view that ETDs really don't work that well, that aural is better, and wanting to justify that position. I also have the impression that you haven't done a lot of ETD assisted tuning, just fooled with it a bit and didn't like it. Am I wrong?

------------------------------
Fred Sturm
University of New Mexico
fssturm@unm.edu
http://fredsturm.net
http://www.artoftuning.com
"We either make ourselves happy or miserable. The amount of work is the same." - Carlos Casteneda

Original Message:
Sent: 08-07-2024 19:36
From: Ryan Sowers
Subject: ETD Discrepancies and limits of accuracy

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

------------------------------
Ryan Sowers RPT
Olympia WA
(360) 480-5648
------------------------------

Ryan (responding directly to the original post),

You posit experience where you disagree aurally with what you believe to be the "decision" of the ETD. This is pretty amorphous stuff. I can't really respond to your questions based on your personal experience without being there, observing you tune a piano with an ETD, and then checking with you, comparing notes.

What I CAN do is share my own initial experience tuning with an ETD, 30 years ago (following 15 years of purely aural tuning). I got an SAT so that I would be able to give tuning tests, and decided to try it out, though I was very skeptical. I tuned a couple midrange octaves with SAT, then checked that aurally, and found "errors." But then I looked at each of the error notes, with the ETD, and found that they were not zeroed. (I had just been through lots of CTE training on zeroing the display, so I was well aware of what I was seeing). When I zeroed the notes, all the errors went away. (This kind of experience was repeated time and time again).

So as a first response, not wishing to cause offense, I would first ask you to do precisely the same thing. Recheck the notes you object to. What does "zeroed" mean on your device? I don't know, not knowing what device you are using. To be successful at tuning with an ETD you need to figure out what zeroed means, how to see through any "junk" in the display (in many cases, use the strobe emulator, moving gray rectangles, as the most reliable factor), and then execute to zero out. As an exercise. take a note, zero the ETD on it, set an offset to plus or minus 0.5¢. Now tune to that new, slightly changed pitch target. Can you zero to it? Try again with 0.3¢. If you can't match the ETD's template to that degree of accuracy, how can you judge what the ETD has calculated?

As I took up the SAT, and very rapidly decided not to tune without it (for reasons I'll describe later), I certainly had quarrels with it, particularly with respect to stretch. I won't bother going into details, but I found ways to make it do what I wanted to do for that purpose. But there were inharmonic gaps to get past, particularly on my fleet of Hamilton studios. Nasty gaps of inharmonicity. I had never been able to be satisfied with how intervals progressed across them.

So I analyzed them, and realized that if I wanted smooth M3s I would need to lower the plain wire pitches and raise the wrapped for the notes involved in the M3s across the break. So I experimented with that, and found that if I did enough to get good beat rate progression of M3s, all kinds of other things fell apart, and they were magnified when I expanded outwards into bass and treble. I came to the conclusion that the algorithm of the ETD actually was better in the long run when I was looking at wider intervals like 19ths and triple octaves. And the piano didn't really sound better with improved beat rate progressions.

I could write more along these lines, but I think this much provides some pertinent ideas.

More to the point, the reason I have used an ETD for all my tunings for 30 years comes down to unisons and stability. Pitch isn't all that important. Violins, voices, clarinets, oboes, full orchestras are all over the place, even the very best. All over the place relative to our cents and fractional cents. And that's if they aren't intentionally bending pitch, which they are doing all the time.

For the piano, timbre is entirely dependent on unisons. (Yes, lots of other factors, but even if they are all perfect, including mating, bad unisons will overcome them). And a perfect unison is nothing if it doesn't last. Use of an ETD enables me to focus on the feel of the pin moving in the wood, the sound of the result, and the movement of pitch, simultaneously. When homing in on the pitch of each string, it is possible to make tiny, real-time manipulations of the tuning pin that don't move it in the block, and find out whether the pitch is solid or not. This is more complex than I care to go into, but in a nutshell, if you can make minute motions of twist and flex of the pin in both directions, and see (in the ETD display) the pitch move slightly sharp and flat evenly in response to those moves, and if playing the note a few times results in no pitch change, you know you have nailed it. (Bearing friction means that it ain't that simple :-)) That's the most important reason I use an ETD: ability to achieve stability efficiently.

Bottom line, I'm guessing you are coming at your question from the point of view that ETDs really don't work that well, that aural is better, and wanting to justify that position. I also have the impression that you haven't done a lot of ETD assisted tuning, just fooled with it a bit and didn't like it. Am I wrong?

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

Ryan (responding directly to the original post),

You posit experience where you disagree aurally with what you believe to be the "decision" of the ETD. This is pretty amorphous stuff. I can't really respond to your questions based on your personal experience without being there, observing you tune a piano with an ETD, and then checking with you, comparing notes.

What I CAN do is share my own initial experience tuning with an ETD, 30 years ago (following 15 years of purely aural tuning). I got an SAT so that I would be able to give tuning tests, and decided to try it out, though I was very skeptical. I tuned a couple midrange octaves with SAT, then checked that aurally, and found "errors." But then I looked at each of the error notes, with the ETD, and found that they were not zeroed. (I had just been through lots of CTE training on zeroing the display, so I was well aware of what I was seeing). When I zeroed the notes, all the errors went away. (This kind of experience was repeated time and time again).

So as a first response, not wishing to cause offense, I would first ask you to do precisely the same thing. Recheck the notes you object to. What does "zeroed" mean on your device? I don't know, not knowing what device you are using. To be successful at tuning with an ETD you need to figure out what zeroed means, how to see through any "junk" in the display (in many cases, use the strobe emulator, moving gray rectangles, as the most reliable factor), and then execute to zero out. As an exercise. take a note, zero the ETD on it, set an offset to plus or minus 0.5¢. Now tune to that new, slightly changed pitch target. Can you zero to it? Try again with 0.3¢. If you can't match the ETD's template to that degree of accuracy, how can you judge what the ETD has calculated?

As I took up the SAT, and very rapidly decided not to tune without it (for reasons I'll describe later), I certainly had quarrels with it, particularly with respect to stretch. I won't bother going into details, but I found ways to make it do what I wanted to do for that purpose. But there were inharmonic gaps to get past, particularly on my fleet of Hamilton studios. Nasty gaps of inharmonicity. I had never been able to be satisfied with how intervals progressed across them.

So I analyzed them, and realized that if I wanted smooth M3s I would need to lower the plain wire pitches and raise the wrapped for the notes involved in the M3s across the break. So I experimented with that, and found that if I did enough to get good beat rate progression of M3s, all kinds of other things fell apart, and they were magnified when I expanded outwards into bass and treble. I came to the conclusion that the algorithm of the ETD actually was better in the long run when I was looking at wider intervals like 19ths and triple octaves. And the piano didn't really sound better with improved beat rate progressions.

I could write more along these lines, but I think this much provides some pertinent ideas.

More to the point, the reason I have used an ETD for all my tunings for 30 years comes down to unisons and stability. Pitch isn't all that important. Violins, voices, clarinets, oboes, full orchestras are all over the place, even the very best. All over the place relative to our cents and fractional cents. And that's if they aren't intentionally bending pitch, which they are doing all the time.

For the piano, timbre is entirely dependent on unisons. (Yes, lots of other factors, but even if they are all perfect, including mating, bad unisons will overcome them). And a perfect unison is nothing if it doesn't last. Use of an ETD enables me to focus on the feel of the pin moving in the wood, the sound of the result, and the movement of pitch, simultaneously. When homing in on the pitch of each string, it is possible to make tiny, real-time manipulations of the tuning pin that don't move it in the block, and find out whether the pitch is solid or not. This is more complex than I care to go into, but in a nutshell, if you can make minute motions of twist and flex of the pin in both directions, and see (in the ETD display) the pitch move slightly sharp and flat evenly in response to those moves, and if playing the note a few times results in no pitch change, you know you have nailed it. (Bearing friction means that it ain't that simple :-)) That's the most important reason I use an ETD: ability to achieve stability efficiently.

Bottom line, I'm guessing you are coming at your question from the point of view that ETDs really don't work that well, that aural is better, and wanting to justify that position. I also have the impression that you haven't done a lot of ETD assisted tuning, just fooled with it a bit and didn't like it. Am I wrong?

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

Thanks for the thoughtful reply Fred, and everybody else as well. I originally posted right before I got caught up in flurry of activity and am now trying to catch up.

You said: "You posit experience where you disagree aurally with what you believe to be the "decision" of the ETD. This is pretty amorphous stuff." The decisions don't feel amorphous - a fifth should be almost pure but not exactly. Octaves in the midrange need to be reigned in by the faster beating intervals so they don't get to "edgy" sounding. It's  pretty straightforward. But I'll have to agree that if you aren't in the room when I'm going through my temperament and midrange, then my claims are pretty much heresay. 

You said: Bottom line, I'm guessing you are coming at your question from the point of view that ETDs really don't work that well, that aural is better, and wanting to justify that position. I also have the impression that you haven't done a lot of ETD assisted tuning, just fooled with it a bit and didn't like it. Am I wrong?

You are only partially right (no pun intended).  ETDs work extremely well at measuring pitch. They do a reasonable job at temperament and stretch if you know how to keep them on track. But I find that as unisons are pulled in, it is always important to keep checking and rechecking the intonation of the intervals. I have not found I can rely on it, and constantly second-guessing the ETD interupts my work flow.

I also wouldn't say aural is better: I have a thought experiment that goes like this: For some reason I am no longer able to tune my piano and have to choose between two other tuners in my area. Tuner one, is not an RPT because he failed the aural midrange portion of the exam but scored 100% on everything else including unisons and stability. The other tuner is an RPT who squeaked by with scores in the 80's including unisons and stability. Which do you think I would choose? It's not a difficult decision at all. 

My orignal post mentioned that I'm working on a hybrid tuning class. "Aural tuners without an ETD are lacking a valuable tool, ETD users who lack strong aural abilities are lacking an invaluable skill" is the subititle. I'm trying to figure out where the best of both worlds is. What are the strengths of the ear and where can ETDs serve us best? So I'm certainly not "anti-ETD". But I'm also a little heartbroken to see talented young tuners who have become dependent on their ETD and are failing to learn how powerful aural tuning techniques can be. 

My first use of ETDs was when I was in CTE training back in the late 1990's when the Accutuner II was the standard. I know exactly what you are saying about "zeroing out" the machine being a leaned skill that requires a somewhat nuanced technique and plenty of practice. Different examiners may have different interpretations of the display when the rotating lights did not give a steady signal. It's particularly tricky when one or two tenths of a cent can be the final straw for that examinees score. 

I purposfully did not disclose what ETD I've been using because I'm not entirely sure how relevent it is. But for full disclosure, I mainly use Tunelab as my ETD assist. I also have an upgraded version of Pianometer that I've played with as well. 

One thing I'm very curious about is how ETDs are being used in Master Tuning exam pianos these days. Is anyone able to use a stock ETD midrange as a mastertuning without having to make a few tweaks here and there? If tweaks have to be made: why?

You also made an interesting point in your post that "When I zeroed the notes, all the errors went away. (This kind of experience was repeated time and time again)." Yet, how did you know the errors went away unless you could aurally verify? One of my points about aural tuning, is that it make you better at interpreting the display. 

I've been meaning to borrow cybertuner and a SAT IV to compare the results I get from Tunelab. I've heard Cybertunings that I thought were overstretched - yet that can be largly a matter of taste and the stretch settings. Which begs the question: What's the best way to develop taste from a tuning perspective? 

Of course you are absolutely right that it comes down to unisons and stabilty. This is the reason why I currently prefer open string tuning and mostly just use one mute when tuning grands. It forces you to be picky about unisons, and it puts you in "unison headspace" much more frequently than other approaches. Unison shimming because extremely useful and important in addition to being very effecient. I now percieve the single string of a note to be like the "course adjust" on an old shortwave radio and the "shim method" as the "fine adjust". I have to thank David Anderson and Rick Butler for the "one mute" tuning advice. I resisted for many years, but am now a believer. 

I find the most powerful use of an ETD is in "direct interval tuning" which it turns out goes back to site-o-tuner days. For example: When tuning F7, have the machine listen to F7 but play F6 and F5 and A#5 to see how the display behaves with the single octave, double-octave, and twelth. It's very educational to see how these things line up and to observe inharmonicy somewhat directly.

We will definietly have to get together in Iowa, Fred, and work some of this out on a real piano! 

Ryan (responding directly to the original post),

You posit experience where you disagree aurally with what you believe to be the "decision" of the ETD. This is pretty amorphous stuff. I can't really respond to your questions based on your personal experience without being there, observing you tune a piano with an ETD, and then checking with you, comparing notes.

What I CAN do is share my own initial experience tuning with an ETD, 30 years ago (following 15 years of purely aural tuning). I got an SAT so that I would be able to give tuning tests, and decided to try it out, though I was very skeptical. I tuned a couple midrange octaves with SAT, then checked that aurally, and found "errors." But then I looked at each of the error notes, with the ETD, and found that they were not zeroed. (I had just been through lots of CTE training on zeroing the display, so I was well aware of what I was seeing). When I zeroed the notes, all the errors went away. (This kind of experience was repeated time and time again).

So as a first response, not wishing to cause offense, I would first ask you to do precisely the same thing. Recheck the notes you object to. What does "zeroed" mean on your device? I don't know, not knowing what device you are using. To be successful at tuning with an ETD you need to figure out what zeroed means, how to see through any "junk" in the display (in many cases, use the strobe emulator, moving gray rectangles, as the most reliable factor), and then execute to zero out. As an exercise. take a note, zero the ETD on it, set an offset to plus or minus 0.5¢. Now tune to that new, slightly changed pitch target. Can you zero to it? Try again with 0.3¢. If you can't match the ETD's template to that degree of accuracy, how can you judge what the ETD has calculated?

As I took up the SAT, and very rapidly decided not to tune without it (for reasons I'll describe later), I certainly had quarrels with it, particularly with respect to stretch. I won't bother going into details, but I found ways to make it do what I wanted to do for that purpose. But there were inharmonic gaps to get past, particularly on my fleet of Hamilton studios. Nasty gaps of inharmonicity. I had never been able to be satisfied with how intervals progressed across them.

So I analyzed them, and realized that if I wanted smooth M3s I would need to lower the plain wire pitches and raise the wrapped for the notes involved in the M3s across the break. So I experimented with that, and found that if I did enough to get good beat rate progression of M3s, all kinds of other things fell apart, and they were magnified when I expanded outwards into bass and treble. I came to the conclusion that the algorithm of the ETD actually was better in the long run when I was looking at wider intervals like 19ths and triple octaves. And the piano didn't really sound better with improved beat rate progressions.

I could write more along these lines, but I think this much provides some pertinent ideas.

More to the point, the reason I have used an ETD for all my tunings for 30 years comes down to unisons and stability. Pitch isn't all that important. Violins, voices, clarinets, oboes, full orchestras are all over the place, even the very best. All over the place relative to our cents and fractional cents. And that's if they aren't intentionally bending pitch, which they are doing all the time.

For the piano, timbre is entirely dependent on unisons. (Yes, lots of other factors, but even if they are all perfect, including mating, bad unisons will overcome them). And a perfect unison is nothing if it doesn't last. Use of an ETD enables me to focus on the feel of the pin moving in the wood, the sound of the result, and the movement of pitch, simultaneously. When homing in on the pitch of each string, it is possible to make tiny, real-time manipulations of the tuning pin that don't move it in the block, and find out whether the pitch is solid or not. This is more complex than I care to go into, but in a nutshell, if you can make minute motions of twist and flex of the pin in both directions, and see (in the ETD display) the pitch move slightly sharp and flat evenly in response to those moves, and if playing the note a few times results in no pitch change, you know you have nailed it. (Bearing friction means that it ain't that simple :-)) That's the most important reason I use an ETD: ability to achieve stability efficiently.

Bottom line, I'm guessing you are coming at your question from the point of view that ETDs really don't work that well, that aural is better, and wanting to justify that position. I also have the impression that you haven't done a lot of ETD assisted tuning, just fooled with it a bit and didn't like it. Am I wrong?

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

Ryan, would you please explain "shimming"? 

Also, am I to understand that you are aurally laying in temperaments without a temperament strip?

Thanks.

Thanks for the thoughtful reply Fred, and everybody else as well. I originally posted right before I got caught up in flurry of activity and am now trying to catch up.

You said: "You posit experience where you disagree aurally with what you believe to be the "decision" of the ETD. This is pretty amorphous stuff." The decisions don't feel amorphous - a fifth should be almost pure but not exactly. Octaves in the midrange need to be reigned in by the faster beating intervals so they don't get to "edgy" sounding. It's  pretty straightforward. But I'll have to agree that if you aren't in the room when I'm going through my temperament and midrange, then my claims are pretty much heresay. 

You said: Bottom line, I'm guessing you are coming at your question from the point of view that ETDs really don't work that well, that aural is better, and wanting to justify that position. I also have the impression that you haven't done a lot of ETD assisted tuning, just fooled with it a bit and didn't like it. Am I wrong?

You are only partially right (no pun intended).  ETDs work extremely well at measuring pitch. They do a reasonable job at temperament and stretch if you know how to keep them on track. But I find that as unisons are pulled in, it is always important to keep checking and rechecking the intonation of the intervals. I have not found I can rely on it, and constantly second-guessing the ETD interupts my work flow.

I also wouldn't say aural is better: I have a thought experiment that goes like this: For some reason I am no longer able to tune my piano and have to choose between two other tuners in my area. Tuner one, is not an RPT because he failed the aural midrange portion of the exam but scored 100% on everything else including unisons and stability. The other tuner is an RPT who squeaked by with scores in the 80's including unisons and stability. Which do you think I would choose? It's not a difficult decision at all. 

My orignal post mentioned that I'm working on a hybrid tuning class. "Aural tuners without an ETD are lacking a valuable tool, ETD users who lack strong aural abilities are lacking an invaluable skill" is the subititle. I'm trying to figure out where the best of both worlds is. What are the strengths of the ear and where can ETDs serve us best? So I'm certainly not "anti-ETD". But I'm also a little heartbroken to see talented young tuners who have become dependent on their ETD and are failing to learn how powerful aural tuning techniques can be. 

My first use of ETDs was when I was in CTE training back in the late 1990's when the Accutuner II was the standard. I know exactly what you are saying about "zeroing out" the machine being a leaned skill that requires a somewhat nuanced technique and plenty of practice. Different examiners may have different interpretations of the display when the rotating lights did not give a steady signal. It's particularly tricky when one or two tenths of a cent can be the final straw for that examinees score. 

I purposfully did not disclose what ETD I've been using because I'm not entirely sure how relevent it is. But for full disclosure, I mainly use Tunelab as my ETD assist. I also have an upgraded version of Pianometer that I've played with as well. 

One thing I'm very curious about is how ETDs are being used in Master Tuning exam pianos these days. Is anyone able to use a stock ETD midrange as a mastertuning without having to make a few tweaks here and there? If tweaks have to be made: why?

You also made an interesting point in your post that "When I zeroed the notes, all the errors went away. (This kind of experience was repeated time and time again)." Yet, how did you know the errors went away unless you could aurally verify? One of my points about aural tuning, is that it make you better at interpreting the display. 

I've been meaning to borrow cybertuner and a SAT IV to compare the results I get from Tunelab. I've heard Cybertunings that I thought were overstretched - yet that can be largly a matter of taste and the stretch settings. Which begs the question: What's the best way to develop taste from a tuning perspective? 

Of course you are absolutely right that it comes down to unisons and stabilty. This is the reason why I currently prefer open string tuning and mostly just use one mute when tuning grands. It forces you to be picky about unisons, and it puts you in "unison headspace" much more frequently than other approaches. Unison shimming because extremely useful and important in addition to being very effecient. I now percieve the single string of a note to be like the "course adjust" on an old shortwave radio and the "shim method" as the "fine adjust". I have to thank David Anderson and Rick Butler for the "one mute" tuning advice. I resisted for many years, but am now a believer. 

I find the most powerful use of an ETD is in "direct interval tuning" which it turns out goes back to site-o-tuner days. For example: When tuning F7, have the machine listen to F7 but play F6 and F5 and A#5 to see how the display behaves with the single octave, double-octave, and twelth. It's very educational to see how these things line up and to observe inharmonicy somewhat directly.

We will definietly have to get together in Iowa, Fred, and work some of this out on a real piano! 

Ryan (responding directly to the original post),

You posit experience where you disagree aurally with what you believe to be the "decision" of the ETD. This is pretty amorphous stuff. I can't really respond to your questions based on your personal experience without being there, observing you tune a piano with an ETD, and then checking with you, comparing notes.

What I CAN do is share my own initial experience tuning with an ETD, 30 years ago (following 15 years of purely aural tuning). I got an SAT so that I would be able to give tuning tests, and decided to try it out, though I was very skeptical. I tuned a couple midrange octaves with SAT, then checked that aurally, and found "errors." But then I looked at each of the error notes, with the ETD, and found that they were not zeroed. (I had just been through lots of CTE training on zeroing the display, so I was well aware of what I was seeing). When I zeroed the notes, all the errors went away. (This kind of experience was repeated time and time again).

So as a first response, not wishing to cause offense, I would first ask you to do precisely the same thing. Recheck the notes you object to. What does "zeroed" mean on your device? I don't know, not knowing what device you are using. To be successful at tuning with an ETD you need to figure out what zeroed means, how to see through any "junk" in the display (in many cases, use the strobe emulator, moving gray rectangles, as the most reliable factor), and then execute to zero out. As an exercise. take a note, zero the ETD on it, set an offset to plus or minus 0.5¢. Now tune to that new, slightly changed pitch target. Can you zero to it? Try again with 0.3¢. If you can't match the ETD's template to that degree of accuracy, how can you judge what the ETD has calculated?

As I took up the SAT, and very rapidly decided not to tune without it (for reasons I'll describe later), I certainly had quarrels with it, particularly with respect to stretch. I won't bother going into details, but I found ways to make it do what I wanted to do for that purpose. But there were inharmonic gaps to get past, particularly on my fleet of Hamilton studios. Nasty gaps of inharmonicity. I had never been able to be satisfied with how intervals progressed across them.

So I analyzed them, and realized that if I wanted smooth M3s I would need to lower the plain wire pitches and raise the wrapped for the notes involved in the M3s across the break. So I experimented with that, and found that if I did enough to get good beat rate progression of M3s, all kinds of other things fell apart, and they were magnified when I expanded outwards into bass and treble. I came to the conclusion that the algorithm of the ETD actually was better in the long run when I was looking at wider intervals like 19ths and triple octaves. And the piano didn't really sound better with improved beat rate progressions.

I could write more along these lines, but I think this much provides some pertinent ideas.

More to the point, the reason I have used an ETD for all my tunings for 30 years comes down to unisons and stability. Pitch isn't all that important. Violins, voices, clarinets, oboes, full orchestras are all over the place, even the very best. All over the place relative to our cents and fractional cents. And that's if they aren't intentionally bending pitch, which they are doing all the time.

For the piano, timbre is entirely dependent on unisons. (Yes, lots of other factors, but even if they are all perfect, including mating, bad unisons will overcome them). And a perfect unison is nothing if it doesn't last. Use of an ETD enables me to focus on the feel of the pin moving in the wood, the sound of the result, and the movement of pitch, simultaneously. When homing in on the pitch of each string, it is possible to make tiny, real-time manipulations of the tuning pin that don't move it in the block, and find out whether the pitch is solid or not. This is more complex than I care to go into, but in a nutshell, if you can make minute motions of twist and flex of the pin in both directions, and see (in the ETD display) the pitch move slightly sharp and flat evenly in response to those moves, and if playing the note a few times results in no pitch change, you know you have nailed it. (Bearing friction means that it ain't that simple :-)) That's the most important reason I use an ETD: ability to achieve stability efficiently.

Bottom line, I'm guessing you are coming at your question from the point of view that ETDs really don't work that well, that aural is better, and wanting to justify that position. I also have the impression that you haven't done a lot of ETD assisted tuning, just fooled with it a bit and didn't like it. Am I wrong?

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

Ryan, would you please explain "shimming"? 

Also, am I to understand that you are aurally laying in temperaments without a temperament strip?

Thanks.

Thanks for the thoughtful reply Fred, and everybody else as well. I originally posted right before I got caught up in flurry of activity and am now trying to catch up.

You said: "You posit experience where you disagree aurally with what you believe to be the "decision" of the ETD. This is pretty amorphous stuff." The decisions don't feel amorphous - a fifth should be almost pure but not exactly. Octaves in the midrange need to be reigned in by the faster beating intervals so they don't get to "edgy" sounding. It's  pretty straightforward. But I'll have to agree that if you aren't in the room when I'm going through my temperament and midrange, then my claims are pretty much heresay. 

You said: Bottom line, I'm guessing you are coming at your question from the point of view that ETDs really don't work that well, that aural is better, and wanting to justify that position. I also have the impression that you haven't done a lot of ETD assisted tuning, just fooled with it a bit and didn't like it. Am I wrong?

You are only partially right (no pun intended).  ETDs work extremely well at measuring pitch. They do a reasonable job at temperament and stretch if you know how to keep them on track. But I find that as unisons are pulled in, it is always important to keep checking and rechecking the intonation of the intervals. I have not found I can rely on it, and constantly second-guessing the ETD interupts my work flow.

I also wouldn't say aural is better: I have a thought experiment that goes like this: For some reason I am no longer able to tune my piano and have to choose between two other tuners in my area. Tuner one, is not an RPT because he failed the aural midrange portion of the exam but scored 100% on everything else including unisons and stability. The other tuner is an RPT who squeaked by with scores in the 80's including unisons and stability. Which do you think I would choose? It's not a difficult decision at all. 

My orignal post mentioned that I'm working on a hybrid tuning class. "Aural tuners without an ETD are lacking a valuable tool, ETD users who lack strong aural abilities are lacking an invaluable skill" is the subititle. I'm trying to figure out where the best of both worlds is. What are the strengths of the ear and where can ETDs serve us best? So I'm certainly not "anti-ETD". But I'm also a little heartbroken to see talented young tuners who have become dependent on their ETD and are failing to learn how powerful aural tuning techniques can be. 

My first use of ETDs was when I was in CTE training back in the late 1990's when the Accutuner II was the standard. I know exactly what you are saying about "zeroing out" the machine being a leaned skill that requires a somewhat nuanced technique and plenty of practice. Different examiners may have different interpretations of the display when the rotating lights did not give a steady signal. It's particularly tricky when one or two tenths of a cent can be the final straw for that examinees score. 

I purposfully did not disclose what ETD I've been using because I'm not entirely sure how relevent it is. But for full disclosure, I mainly use Tunelab as my ETD assist. I also have an upgraded version of Pianometer that I've played with as well. 

One thing I'm very curious about is how ETDs are being used in Master Tuning exam pianos these days. Is anyone able to use a stock ETD midrange as a mastertuning without having to make a few tweaks here and there? If tweaks have to be made: why?

You also made an interesting point in your post that "When I zeroed the notes, all the errors went away. (This kind of experience was repeated time and time again)." Yet, how did you know the errors went away unless you could aurally verify? One of my points about aural tuning, is that it make you better at interpreting the display. 

I've been meaning to borrow cybertuner and a SAT IV to compare the results I get from Tunelab. I've heard Cybertunings that I thought were overstretched - yet that can be largly a matter of taste and the stretch settings. Which begs the question: What's the best way to develop taste from a tuning perspective? 

Of course you are absolutely right that it comes down to unisons and stabilty. This is the reason why I currently prefer open string tuning and mostly just use one mute when tuning grands. It forces you to be picky about unisons, and it puts you in "unison headspace" much more frequently than other approaches. Unison shimming because extremely useful and important in addition to being very effecient. I now percieve the single string of a note to be like the "course adjust" on an old shortwave radio and the "shim method" as the "fine adjust". I have to thank David Anderson and Rick Butler for the "one mute" tuning advice. I resisted for many years, but am now a believer. 

I find the most powerful use of an ETD is in "direct interval tuning" which it turns out goes back to site-o-tuner days. For example: When tuning F7, have the machine listen to F7 but play F6 and F5 and A#5 to see how the display behaves with the single octave, double-octave, and twelth. It's very educational to see how these things line up and to observe inharmonicy somewhat directly.

We will definietly have to get together in Iowa, Fred, and work some of this out on a real piano! 

Ryan (responding directly to the original post),

You posit experience where you disagree aurally with what you believe to be the "decision" of the ETD. This is pretty amorphous stuff. I can't really respond to your questions based on your personal experience without being there, observing you tune a piano with an ETD, and then checking with you, comparing notes.

What I CAN do is share my own initial experience tuning with an ETD, 30 years ago (following 15 years of purely aural tuning). I got an SAT so that I would be able to give tuning tests, and decided to try it out, though I was very skeptical. I tuned a couple midrange octaves with SAT, then checked that aurally, and found "errors." But then I looked at each of the error notes, with the ETD, and found that they were not zeroed. (I had just been through lots of CTE training on zeroing the display, so I was well aware of what I was seeing). When I zeroed the notes, all the errors went away. (This kind of experience was repeated time and time again).

So as a first response, not wishing to cause offense, I would first ask you to do precisely the same thing. Recheck the notes you object to. What does "zeroed" mean on your device? I don't know, not knowing what device you are using. To be successful at tuning with an ETD you need to figure out what zeroed means, how to see through any "junk" in the display (in many cases, use the strobe emulator, moving gray rectangles, as the most reliable factor), and then execute to zero out. As an exercise. take a note, zero the ETD on it, set an offset to plus or minus 0.5¢. Now tune to that new, slightly changed pitch target. Can you zero to it? Try again with 0.3¢. If you can't match the ETD's template to that degree of accuracy, how can you judge what the ETD has calculated?

As I took up the SAT, and very rapidly decided not to tune without it (for reasons I'll describe later), I certainly had quarrels with it, particularly with respect to stretch. I won't bother going into details, but I found ways to make it do what I wanted to do for that purpose. But there were inharmonic gaps to get past, particularly on my fleet of Hamilton studios. Nasty gaps of inharmonicity. I had never been able to be satisfied with how intervals progressed across them.

So I analyzed them, and realized that if I wanted smooth M3s I would need to lower the plain wire pitches and raise the wrapped for the notes involved in the M3s across the break. So I experimented with that, and found that if I did enough to get good beat rate progression of M3s, all kinds of other things fell apart, and they were magnified when I expanded outwards into bass and treble. I came to the conclusion that the algorithm of the ETD actually was better in the long run when I was looking at wider intervals like 19ths and triple octaves. And the piano didn't really sound better with improved beat rate progressions.

I could write more along these lines, but I think this much provides some pertinent ideas.

More to the point, the reason I have used an ETD for all my tunings for 30 years comes down to unisons and stability. Pitch isn't all that important. Violins, voices, clarinets, oboes, full orchestras are all over the place, even the very best. All over the place relative to our cents and fractional cents. And that's if they aren't intentionally bending pitch, which they are doing all the time.

For the piano, timbre is entirely dependent on unisons. (Yes, lots of other factors, but even if they are all perfect, including mating, bad unisons will overcome them). And a perfect unison is nothing if it doesn't last. Use of an ETD enables me to focus on the feel of the pin moving in the wood, the sound of the result, and the movement of pitch, simultaneously. When homing in on the pitch of each string, it is possible to make tiny, real-time manipulations of the tuning pin that don't move it in the block, and find out whether the pitch is solid or not. This is more complex than I care to go into, but in a nutshell, if you can make minute motions of twist and flex of the pin in both directions, and see (in the ETD display) the pitch move slightly sharp and flat evenly in response to those moves, and if playing the note a few times results in no pitch change, you know you have nailed it. (Bearing friction means that it ain't that simple :-)) That's the most important reason I use an ETD: ability to achieve stability efficiently.

Bottom line, I'm guessing you are coming at your question from the point of view that ETDs really don't work that well, that aural is better, and wanting to justify that position. I also have the impression that you haven't done a lot of ETD assisted tuning, just fooled with it a bit and didn't like it. Am I wrong?

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

Thanks for the thoughtful reply Fred, and everybody else as well. I originally posted right before I got caught up in flurry of activity and am now trying to catch up.

You said: "You posit experience where you disagree aurally with what you believe to be the "decision" of the ETD. This is pretty amorphous stuff." The decisions don't feel amorphous - a fifth should be almost pure but not exactly. Octaves in the midrange need to be reigned in by the faster beating intervals so they don't get to "edgy" sounding. It's  pretty straightforward. But I'll have to agree that if you aren't in the room when I'm going through my temperament and midrange, then my claims are pretty much heresay. 

You said: Bottom line, I'm guessing you are coming at your question from the point of view that ETDs really don't work that well, that aural is better, and wanting to justify that position. I also have the impression that you haven't done a lot of ETD assisted tuning, just fooled with it a bit and didn't like it. Am I wrong?

You are only partially right (no pun intended).  ETDs work extremely well at measuring pitch. They do a reasonable job at temperament and stretch if you know how to keep them on track. But I find that as unisons are pulled in, it is always important to keep checking and rechecking the intonation of the intervals. I have not found I can rely on it, and constantly second-guessing the ETD interupts my work flow.

I also wouldn't say aural is better: I have a thought experiment that goes like this: For some reason I am no longer able to tune my piano and have to choose between two other tuners in my area. Tuner one, is not an RPT because he failed the aural midrange portion of the exam but scored 100% on everything else including unisons and stability. The other tuner is an RPT who squeaked by with scores in the 80's including unisons and stability. Which do you think I would choose? It's not a difficult decision at all. 

My orignal post mentioned that I'm working on a hybrid tuning class. "Aural tuners without an ETD are lacking a valuable tool, ETD users who lack strong aural abilities are lacking an invaluable skill" is the subititle. I'm trying to figure out where the best of both worlds is. What are the strengths of the ear and where can ETDs serve us best? So I'm certainly not "anti-ETD". But I'm also a little heartbroken to see talented young tuners who have become dependent on their ETD and are failing to learn how powerful aural tuning techniques can be. 

My first use of ETDs was when I was in CTE training back in the late 1990's when the Accutuner II was the standard. I know exactly what you are saying about "zeroing out" the machine being a leaned skill that requires a somewhat nuanced technique and plenty of practice. Different examiners may have different interpretations of the display when the rotating lights did not give a steady signal. It's particularly tricky when one or two tenths of a cent can be the final straw for that examinees score. 

I purposfully did not disclose what ETD I've been using because I'm not entirely sure how relevent it is. But for full disclosure, I mainly use Tunelab as my ETD assist. I also have an upgraded version of Pianometer that I've played with as well. 

One thing I'm very curious about is how ETDs are being used in Master Tuning exam pianos these days. Is anyone able to use a stock ETD midrange as a mastertuning without having to make a few tweaks here and there? If tweaks have to be made: why?

You also made an interesting point in your post that "When I zeroed the notes, all the errors went away. (This kind of experience was repeated time and time again)." Yet, how did you know the errors went away unless you could aurally verify? One of my points about aural tuning, is that it make you better at interpreting the display. 

I've been meaning to borrow cybertuner and a SAT IV to compare the results I get from Tunelab. I've heard Cybertunings that I thought were overstretched - yet that can be largly a matter of taste and the stretch settings. Which begs the question: What's the best way to develop taste from a tuning perspective? 

Of course you are absolutely right that it comes down to unisons and stabilty. This is the reason why I currently prefer open string tuning and mostly just use one mute when tuning grands. It forces you to be picky about unisons, and it puts you in "unison headspace" much more frequently than other approaches. Unison shimming because extremely useful and important in addition to being very effecient. I now percieve the single string of a note to be like the "course adjust" on an old shortwave radio and the "shim method" as the "fine adjust". I have to thank David Anderson and Rick Butler for the "one mute" tuning advice. I resisted for many years, but am now a believer. 

I find the most powerful use of an ETD is in "direct interval tuning" which it turns out goes back to site-o-tuner days. For example: When tuning F7, have the machine listen to F7 but play F6 and F5 and A#5 to see how the display behaves with the single octave, double-octave, and twelth. It's very educational to see how these things line up and to observe inharmonicy somewhat directly.

We will definietly have to get together in Iowa, Fred, and work some of this out on a real piano! 

Ryan (responding directly to the original post),

You posit experience where you disagree aurally with what you believe to be the "decision" of the ETD. This is pretty amorphous stuff. I can't really respond to your questions based on your personal experience without being there, observing you tune a piano with an ETD, and then checking with you, comparing notes.

What I CAN do is share my own initial experience tuning with an ETD, 30 years ago (following 15 years of purely aural tuning). I got an SAT so that I would be able to give tuning tests, and decided to try it out, though I was very skeptical. I tuned a couple midrange octaves with SAT, then checked that aurally, and found "errors." But then I looked at each of the error notes, with the ETD, and found that they were not zeroed. (I had just been through lots of CTE training on zeroing the display, so I was well aware of what I was seeing). When I zeroed the notes, all the errors went away. (This kind of experience was repeated time and time again).

So as a first response, not wishing to cause offense, I would first ask you to do precisely the same thing. Recheck the notes you object to. What does "zeroed" mean on your device? I don't know, not knowing what device you are using. To be successful at tuning with an ETD you need to figure out what zeroed means, how to see through any "junk" in the display (in many cases, use the strobe emulator, moving gray rectangles, as the most reliable factor), and then execute to zero out. As an exercise. take a note, zero the ETD on it, set an offset to plus or minus 0.5¢. Now tune to that new, slightly changed pitch target. Can you zero to it? Try again with 0.3¢. If you can't match the ETD's template to that degree of accuracy, how can you judge what the ETD has calculated?

As I took up the SAT, and very rapidly decided not to tune without it (for reasons I'll describe later), I certainly had quarrels with it, particularly with respect to stretch. I won't bother going into details, but I found ways to make it do what I wanted to do for that purpose. But there were inharmonic gaps to get past, particularly on my fleet of Hamilton studios. Nasty gaps of inharmonicity. I had never been able to be satisfied with how intervals progressed across them.

So I analyzed them, and realized that if I wanted smooth M3s I would need to lower the plain wire pitches and raise the wrapped for the notes involved in the M3s across the break. So I experimented with that, and found that if I did enough to get good beat rate progression of M3s, all kinds of other things fell apart, and they were magnified when I expanded outwards into bass and treble. I came to the conclusion that the algorithm of the ETD actually was better in the long run when I was looking at wider intervals like 19ths and triple octaves. And the piano didn't really sound better with improved beat rate progressions.

I could write more along these lines, but I think this much provides some pertinent ideas.

More to the point, the reason I have used an ETD for all my tunings for 30 years comes down to unisons and stability. Pitch isn't all that important. Violins, voices, clarinets, oboes, full orchestras are all over the place, even the very best. All over the place relative to our cents and fractional cents. And that's if they aren't intentionally bending pitch, which they are doing all the time.

For the piano, timbre is entirely dependent on unisons. (Yes, lots of other factors, but even if they are all perfect, including mating, bad unisons will overcome them). And a perfect unison is nothing if it doesn't last. Use of an ETD enables me to focus on the feel of the pin moving in the wood, the sound of the result, and the movement of pitch, simultaneously. When homing in on the pitch of each string, it is possible to make tiny, real-time manipulations of the tuning pin that don't move it in the block, and find out whether the pitch is solid or not. This is more complex than I care to go into, but in a nutshell, if you can make minute motions of twist and flex of the pin in both directions, and see (in the ETD display) the pitch move slightly sharp and flat evenly in response to those moves, and if playing the note a few times results in no pitch change, you know you have nailed it. (Bearing friction means that it ain't that simple :-)) That's the most important reason I use an ETD: ability to achieve stability efficiently.

Bottom line, I'm guessing you are coming at your question from the point of view that ETDs really don't work that well, that aural is better, and wanting to justify that position. I also have the impression that you haven't done a lot of ETD assisted tuning, just fooled with it a bit and didn't like it. Am I wrong?

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

Original Message:
Sent: 8/15/2024 11:18:00 PM
From: Ryan Sowers
Subject: RE: ETD Discrepancies and limits of accuracy

Thanks for the thoughtful reply Fred, and everybody else as well. I originally posted right before I got caught up in flurry of activity and am now trying to catch up.

You said: "You posit experience where you disagree aurally with what you believe to be the "decision" of the ETD. This is pretty amorphous stuff." The decisions don't feel amorphous - a fifth should be almost pure but not exactly. Octaves in the midrange need to be reigned in by the faster beating intervals so they don't get to "edgy" sounding. It's  pretty straightforward. But I'll have to agree that if you aren't in the room when I'm going through my temperament and midrange, then my claims are pretty much heresay. 

You said: Bottom line, I'm guessing you are coming at your question from the point of view that ETDs really don't work that well, that aural is better, and wanting to justify that position. I also have the impression that you haven't done a lot of ETD assisted tuning, just fooled with it a bit and didn't like it. Am I wrong?

You are only partially right (no pun intended).  ETDs work extremely well at measuring pitch. They do a reasonable job at temperament and stretch if you know how to keep them on track. But I find that as unisons are pulled in, it is always important to keep checking and rechecking the intonation of the intervals. I have not found I can rely on it, and constantly second-guessing the ETD interupts my work flow.

I also wouldn't say aural is better: I have a thought experiment that goes like this: For some reason I am no longer able to tune my piano and have to choose between two other tuners in my area. Tuner one, is not an RPT because he failed the aural midrange portion of the exam but scored 100% on everything else including unisons and stability. The other tuner is an RPT who squeaked by with scores in the 80's including unisons and stability. Which do you think I would choose? It's not a difficult decision at all. 

My orignal post mentioned that I'm working on a hybrid tuning class. "Aural tuners without an ETD are lacking a valuable tool, ETD users who lack strong aural abilities are lacking an invaluable skill" is the subititle. I'm trying to figure out where the best of both worlds is. What are the strengths of the ear and where can ETDs serve us best? So I'm certainly not "anti-ETD". But I'm also a little heartbroken to see talented young tuners who have become dependent on their ETD and are failing to learn how powerful aural tuning techniques can be. 

My first use of ETDs was when I was in CTE training back in the late 1990's when the Accutuner II was the standard. I know exactly what you are saying about "zeroing out" the machine being a leaned skill that requires a somewhat nuanced technique and plenty of practice. Different examiners may have different interpretations of the display when the rotating lights did not give a steady signal. It's particularly tricky when one or two tenths of a cent can be the final straw for that examinees score. 

I purposfully did not disclose what ETD I've been using because I'm not entirely sure how relevent it is. But for full disclosure, I mainly use Tunelab as my ETD assist. I also have an upgraded version of Pianometer that I've played with as well. 

One thing I'm very curious about is how ETDs are being used in Master Tuning exam pianos these days. Is anyone able to use a stock ETD midrange as a mastertuning without having to make a few tweaks here and there? If tweaks have to be made: why?

You also made an interesting point in your post that "When I zeroed the notes, all the errors went away. (This kind of experience was repeated time and time again)." Yet, how did you know the errors went away unless you could aurally verify? One of my points about aural tuning, is that it make you better at interpreting the display. 

I've been meaning to borrow cybertuner and a SAT IV to compare the results I get from Tunelab. I've heard Cybertunings that I thought were overstretched - yet that can be largly a matter of taste and the stretch settings. Which begs the question: What's the best way to develop taste from a tuning perspective? 

Of course you are absolutely right that it comes down to unisons and stabilty. This is the reason why I currently prefer open string tuning and mostly just use one mute when tuning grands. It forces you to be picky about unisons, and it puts you in "unison headspace" much more frequently than other approaches. Unison shimming because extremely useful and important in addition to being very effecient. I now percieve the single string of a note to be like the "course adjust" on an old shortwave radio and the "shim method" as the "fine adjust". I have to thank David Anderson and Rick Butler for the "one mute" tuning advice. I resisted for many years, but am now a believer. 

I find the most powerful use of an ETD is in "direct interval tuning" which it turns out goes back to site-o-tuner days. For example: When tuning F7, have the machine listen to F7 but play F6 and F5 and A#5 to see how the display behaves with the single octave, double-octave, and twelth. It's very educational to see how these things line up and to observe inharmonicy somewhat directly.

We will definietly have to get together in Iowa, Fred, and work some of this out on a real piano! 

------------------------------
Ryan Sowers RPT
Olympia WA
(360) 480-5648

Original Message:
Sent: 08-15-2024 16:05
From: Fred Sturm
Subject: ETD Discrepancies and limits of accuracy

Ryan (responding directly to the original post),

You posit experience where you disagree aurally with what you believe to be the "decision" of the ETD. This is pretty amorphous stuff. I can't really respond to your questions based on your personal experience without being there, observing you tune a piano with an ETD, and then checking with you, comparing notes.

What I CAN do is share my own initial experience tuning with an ETD, 30 years ago (following 15 years of purely aural tuning). I got an SAT so that I would be able to give tuning tests, and decided to try it out, though I was very skeptical. I tuned a couple midrange octaves with SAT, then checked that aurally, and found "errors." But then I looked at each of the error notes, with the ETD, and found that they were not zeroed. (I had just been through lots of CTE training on zeroing the display, so I was well aware of what I was seeing). When I zeroed the notes, all the errors went away. (This kind of experience was repeated time and time again).

So as a first response, not wishing to cause offense, I would first ask you to do precisely the same thing. Recheck the notes you object to. What does "zeroed" mean on your device? I don't know, not knowing what device you are using. To be successful at tuning with an ETD you need to figure out what zeroed means, how to see through any "junk" in the display (in many cases, use the strobe emulator, moving gray rectangles, as the most reliable factor), and then execute to zero out. As an exercise. take a note, zero the ETD on it, set an offset to plus or minus 0.5¢. Now tune to that new, slightly changed pitch target. Can you zero to it? Try again with 0.3¢. If you can't match the ETD's template to that degree of accuracy, how can you judge what the ETD has calculated?

As I took up the SAT, and very rapidly decided not to tune without it (for reasons I'll describe later), I certainly had quarrels with it, particularly with respect to stretch. I won't bother going into details, but I found ways to make it do what I wanted to do for that purpose. But there were inharmonic gaps to get past, particularly on my fleet of Hamilton studios. Nasty gaps of inharmonicity. I had never been able to be satisfied with how intervals progressed across them.

So I analyzed them, and realized that if I wanted smooth M3s I would need to lower the plain wire pitches and raise the wrapped for the notes involved in the M3s across the break. So I experimented with that, and found that if I did enough to get good beat rate progression of M3s, all kinds of other things fell apart, and they were magnified when I expanded outwards into bass and treble. I came to the conclusion that the algorithm of the ETD actually was better in the long run when I was looking at wider intervals like 19ths and triple octaves. And the piano didn't really sound better with improved beat rate progressions.

I could write more along these lines, but I think this much provides some pertinent ideas.

More to the point, the reason I have used an ETD for all my tunings for 30 years comes down to unisons and stability. Pitch isn't all that important. Violins, voices, clarinets, oboes, full orchestras are all over the place, even the very best. All over the place relative to our cents and fractional cents. And that's if they aren't intentionally bending pitch, which they are doing all the time.

For the piano, timbre is entirely dependent on unisons. (Yes, lots of other factors, but even if they are all perfect, including mating, bad unisons will overcome them). And a perfect unison is nothing if it doesn't last. Use of an ETD enables me to focus on the feel of the pin moving in the wood, the sound of the result, and the movement of pitch, simultaneously. When homing in on the pitch of each string, it is possible to make tiny, real-time manipulations of the tuning pin that don't move it in the block, and find out whether the pitch is solid or not. This is more complex than I care to go into, but in a nutshell, if you can make minute motions of twist and flex of the pin in both directions, and see (in the ETD display) the pitch move slightly sharp and flat evenly in response to those moves, and if playing the note a few times results in no pitch change, you know you have nailed it. (Bearing friction means that it ain't that simple :-)) That's the most important reason I use an ETD: ability to achieve stability efficiently.

Bottom line, I'm guessing you are coming at your question from the point of view that ETDs really don't work that well, that aural is better, and wanting to justify that position. I also have the impression that you haven't done a lot of ETD assisted tuning, just fooled with it a bit and didn't like it. Am I wrong?

------------------------------
Fred Sturm
University of New Mexico
fssturm@unm.edu
http://fredsturm.net
http://www.artoftuning.com
"We either make ourselves happy or miserable. The amount of work is the same." - Carlos Casteneda

Original Message:
Sent: 08-07-2024 19:36
From: Ryan Sowers
Subject: ETD Discrepancies and limits of accuracy

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

------------------------------
Ryan Sowers RPT
Olympia WA
(360) 480-5648
------------------------------

Thanks for the thoughtful reply Fred, and everybody else as well. I originally posted right before I got caught up in flurry of activity and am now trying to catch up.

You said: "You posit experience where you disagree aurally with what you believe to be the "decision" of the ETD. This is pretty amorphous stuff." The decisions don't feel amorphous - a fifth should be almost pure but not exactly. Octaves in the midrange need to be reigned in by the faster beating intervals so they don't get to "edgy" sounding. It's  pretty straightforward. But I'll have to agree that if you aren't in the room when I'm going through my temperament and midrange, then my claims are pretty much heresay. 

You said: Bottom line, I'm guessing you are coming at your question from the point of view that ETDs really don't work that well, that aural is better, and wanting to justify that position. I also have the impression that you haven't done a lot of ETD assisted tuning, just fooled with it a bit and didn't like it. Am I wrong?

You are only partially right (no pun intended).  ETDs work extremely well at measuring pitch. They do a reasonable job at temperament and stretch if you know how to keep them on track. But I find that as unisons are pulled in, it is always important to keep checking and rechecking the intonation of the intervals. I have not found I can rely on it, and constantly second-guessing the ETD interupts my work flow.

I also wouldn't say aural is better: I have a thought experiment that goes like this: For some reason I am no longer able to tune my piano and have to choose between two other tuners in my area. Tuner one, is not an RPT because he failed the aural midrange portion of the exam but scored 100% on everything else including unisons and stability. The other tuner is an RPT who squeaked by with scores in the 80's including unisons and stability. Which do you think I would choose? It's not a difficult decision at all. 

My orignal post mentioned that I'm working on a hybrid tuning class. "Aural tuners without an ETD are lacking a valuable tool, ETD users who lack strong aural abilities are lacking an invaluable skill" is the subititle. I'm trying to figure out where the best of both worlds is. What are the strengths of the ear and where can ETDs serve us best? So I'm certainly not "anti-ETD". But I'm also a little heartbroken to see talented young tuners who have become dependent on their ETD and are failing to learn how powerful aural tuning techniques can be. 

My first use of ETDs was when I was in CTE training back in the late 1990's when the Accutuner II was the standard. I know exactly what you are saying about "zeroing out" the machine being a leaned skill that requires a somewhat nuanced technique and plenty of practice. Different examiners may have different interpretations of the display when the rotating lights did not give a steady signal. It's particularly tricky when one or two tenths of a cent can be the final straw for that examinees score. 

I purposfully did not disclose what ETD I've been using because I'm not entirely sure how relevent it is. But for full disclosure, I mainly use Tunelab as my ETD assist. I also have an upgraded version of Pianometer that I've played with as well. 

One thing I'm very curious about is how ETDs are being used in Master Tuning exam pianos these days. Is anyone able to use a stock ETD midrange as a mastertuning without having to make a few tweaks here and there? If tweaks have to be made: why?

You also made an interesting point in your post that "When I zeroed the notes, all the errors went away. (This kind of experience was repeated time and time again)." Yet, how did you know the errors went away unless you could aurally verify? One of my points about aural tuning, is that it make you better at interpreting the display. 

I've been meaning to borrow cybertuner and a SAT IV to compare the results I get from Tunelab. I've heard Cybertunings that I thought were overstretched - yet that can be largly a matter of taste and the stretch settings. Which begs the question: What's the best way to develop taste from a tuning perspective? 

Of course you are absolutely right that it comes down to unisons and stabilty. This is the reason why I currently prefer open string tuning and mostly just use one mute when tuning grands. It forces you to be picky about unisons, and it puts you in "unison headspace" much more frequently than other approaches. Unison shimming because extremely useful and important in addition to being very effecient. I now percieve the single string of a note to be like the "course adjust" on an old shortwave radio and the "shim method" as the "fine adjust". I have to thank David Anderson and Rick Butler for the "one mute" tuning advice. I resisted for many years, but am now a believer. 

I find the most powerful use of an ETD is in "direct interval tuning" which it turns out goes back to site-o-tuner days. For example: When tuning F7, have the machine listen to F7 but play F6 and F5 and A#5 to see how the display behaves with the single octave, double-octave, and twelth. It's very educational to see how these things line up and to observe inharmonicy somewhat directly.

We will definietly have to get together in Iowa, Fred, and work some of this out on a real piano! 

Ryan (responding directly to the original post),

You posit experience where you disagree aurally with what you believe to be the "decision" of the ETD. This is pretty amorphous stuff. I can't really respond to your questions based on your personal experience without being there, observing you tune a piano with an ETD, and then checking with you, comparing notes.

What I CAN do is share my own initial experience tuning with an ETD, 30 years ago (following 15 years of purely aural tuning). I got an SAT so that I would be able to give tuning tests, and decided to try it out, though I was very skeptical. I tuned a couple midrange octaves with SAT, then checked that aurally, and found "errors." But then I looked at each of the error notes, with the ETD, and found that they were not zeroed. (I had just been through lots of CTE training on zeroing the display, so I was well aware of what I was seeing). When I zeroed the notes, all the errors went away. (This kind of experience was repeated time and time again).

So as a first response, not wishing to cause offense, I would first ask you to do precisely the same thing. Recheck the notes you object to. What does "zeroed" mean on your device? I don't know, not knowing what device you are using. To be successful at tuning with an ETD you need to figure out what zeroed means, how to see through any "junk" in the display (in many cases, use the strobe emulator, moving gray rectangles, as the most reliable factor), and then execute to zero out. As an exercise. take a note, zero the ETD on it, set an offset to plus or minus 0.5¢. Now tune to that new, slightly changed pitch target. Can you zero to it? Try again with 0.3¢. If you can't match the ETD's template to that degree of accuracy, how can you judge what the ETD has calculated?

As I took up the SAT, and very rapidly decided not to tune without it (for reasons I'll describe later), I certainly had quarrels with it, particularly with respect to stretch. I won't bother going into details, but I found ways to make it do what I wanted to do for that purpose. But there were inharmonic gaps to get past, particularly on my fleet of Hamilton studios. Nasty gaps of inharmonicity. I had never been able to be satisfied with how intervals progressed across them.

So I analyzed them, and realized that if I wanted smooth M3s I would need to lower the plain wire pitches and raise the wrapped for the notes involved in the M3s across the break. So I experimented with that, and found that if I did enough to get good beat rate progression of M3s, all kinds of other things fell apart, and they were magnified when I expanded outwards into bass and treble. I came to the conclusion that the algorithm of the ETD actually was better in the long run when I was looking at wider intervals like 19ths and triple octaves. And the piano didn't really sound better with improved beat rate progressions.

I could write more along these lines, but I think this much provides some pertinent ideas.

More to the point, the reason I have used an ETD for all my tunings for 30 years comes down to unisons and stability. Pitch isn't all that important. Violins, voices, clarinets, oboes, full orchestras are all over the place, even the very best. All over the place relative to our cents and fractional cents. And that's if they aren't intentionally bending pitch, which they are doing all the time.

For the piano, timbre is entirely dependent on unisons. (Yes, lots of other factors, but even if they are all perfect, including mating, bad unisons will overcome them). And a perfect unison is nothing if it doesn't last. Use of an ETD enables me to focus on the feel of the pin moving in the wood, the sound of the result, and the movement of pitch, simultaneously. When homing in on the pitch of each string, it is possible to make tiny, real-time manipulations of the tuning pin that don't move it in the block, and find out whether the pitch is solid or not. This is more complex than I care to go into, but in a nutshell, if you can make minute motions of twist and flex of the pin in both directions, and see (in the ETD display) the pitch move slightly sharp and flat evenly in response to those moves, and if playing the note a few times results in no pitch change, you know you have nailed it. (Bearing friction means that it ain't that simple :-)) That's the most important reason I use an ETD: ability to achieve stability efficiently.

Bottom line, I'm guessing you are coming at your question from the point of view that ETDs really don't work that well, that aural is better, and wanting to justify that position. I also have the impression that you haven't done a lot of ETD assisted tuning, just fooled with it a bit and didn't like it. Am I wrong?

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

Thanks for the thoughtful reply Fred, and everybody else as well. I originally posted right before I got caught up in flurry of activity and am now trying to catch up.

You said: "You posit experience where you disagree aurally with what you believe to be the "decision" of the ETD. This is pretty amorphous stuff." The decisions don't feel amorphous - a fifth should be almost pure but not exactly. Octaves in the midrange need to be reigned in by the faster beating intervals so they don't get to "edgy" sounding. It's  pretty straightforward. But I'll have to agree that if you aren't in the room when I'm going through my temperament and midrange, then my claims are pretty much heresay. 

You said: Bottom line, I'm guessing you are coming at your question from the point of view that ETDs really don't work that well, that aural is better, and wanting to justify that position. I also have the impression that you haven't done a lot of ETD assisted tuning, just fooled with it a bit and didn't like it. Am I wrong?

You are only partially right (no pun intended).  ETDs work extremely well at measuring pitch. They do a reasonable job at temperament and stretch if you know how to keep them on track. But I find that as unisons are pulled in, it is always important to keep checking and rechecking the intonation of the intervals. I have not found I can rely on it, and constantly second-guessing the ETD interupts my work flow.

I also wouldn't say aural is better: I have a thought experiment that goes like this: For some reason I am no longer able to tune my piano and have to choose between two other tuners in my area. Tuner one, is not an RPT because he failed the aural midrange portion of the exam but scored 100% on everything else including unisons and stability. The other tuner is an RPT who squeaked by with scores in the 80's including unisons and stability. Which do you think I would choose? It's not a difficult decision at all. 

My orignal post mentioned that I'm working on a hybrid tuning class. "Aural tuners without an ETD are lacking a valuable tool, ETD users who lack strong aural abilities are lacking an invaluable skill" is the subititle. I'm trying to figure out where the best of both worlds is. What are the strengths of the ear and where can ETDs serve us best? So I'm certainly not "anti-ETD". But I'm also a little heartbroken to see talented young tuners who have become dependent on their ETD and are failing to learn how powerful aural tuning techniques can be. 

My first use of ETDs was when I was in CTE training back in the late 1990's when the Accutuner II was the standard. I know exactly what you are saying about "zeroing out" the machine being a leaned skill that requires a somewhat nuanced technique and plenty of practice. Different examiners may have different interpretations of the display when the rotating lights did not give a steady signal. It's particularly tricky when one or two tenths of a cent can be the final straw for that examinees score. 

I purposfully did not disclose what ETD I've been using because I'm not entirely sure how relevent it is. But for full disclosure, I mainly use Tunelab as my ETD assist. I also have an upgraded version of Pianometer that I've played with as well. 

One thing I'm very curious about is how ETDs are being used in Master Tuning exam pianos these days. Is anyone able to use a stock ETD midrange as a mastertuning without having to make a few tweaks here and there? If tweaks have to be made: why?

You also made an interesting point in your post that "When I zeroed the notes, all the errors went away. (This kind of experience was repeated time and time again)." Yet, how did you know the errors went away unless you could aurally verify? One of my points about aural tuning, is that it make you better at interpreting the display. 

I've been meaning to borrow cybertuner and a SAT IV to compare the results I get from Tunelab. I've heard Cybertunings that I thought were overstretched - yet that can be largly a matter of taste and the stretch settings. Which begs the question: What's the best way to develop taste from a tuning perspective? 

Of course you are absolutely right that it comes down to unisons and stabilty. This is the reason why I currently prefer open string tuning and mostly just use one mute when tuning grands. It forces you to be picky about unisons, and it puts you in "unison headspace" much more frequently than other approaches. Unison shimming because extremely useful and important in addition to being very effecient. I now percieve the single string of a note to be like the "course adjust" on an old shortwave radio and the "shim method" as the "fine adjust". I have to thank David Anderson and Rick Butler for the "one mute" tuning advice. I resisted for many years, but am now a believer. 

I find the most powerful use of an ETD is in "direct interval tuning" which it turns out goes back to site-o-tuner days. For example: When tuning F7, have the machine listen to F7 but play F6 and F5 and A#5 to see how the display behaves with the single octave, double-octave, and twelth. It's very educational to see how these things line up and to observe inharmonicy somewhat directly.

We will definietly have to get together in Iowa, Fred, and work some of this out on a real piano! 

Ryan (responding directly to the original post),

You posit experience where you disagree aurally with what you believe to be the "decision" of the ETD. This is pretty amorphous stuff. I can't really respond to your questions based on your personal experience without being there, observing you tune a piano with an ETD, and then checking with you, comparing notes.

What I CAN do is share my own initial experience tuning with an ETD, 30 years ago (following 15 years of purely aural tuning). I got an SAT so that I would be able to give tuning tests, and decided to try it out, though I was very skeptical. I tuned a couple midrange octaves with SAT, then checked that aurally, and found "errors." But then I looked at each of the error notes, with the ETD, and found that they were not zeroed. (I had just been through lots of CTE training on zeroing the display, so I was well aware of what I was seeing). When I zeroed the notes, all the errors went away. (This kind of experience was repeated time and time again).

So as a first response, not wishing to cause offense, I would first ask you to do precisely the same thing. Recheck the notes you object to. What does "zeroed" mean on your device? I don't know, not knowing what device you are using. To be successful at tuning with an ETD you need to figure out what zeroed means, how to see through any "junk" in the display (in many cases, use the strobe emulator, moving gray rectangles, as the most reliable factor), and then execute to zero out. As an exercise. take a note, zero the ETD on it, set an offset to plus or minus 0.5¢. Now tune to that new, slightly changed pitch target. Can you zero to it? Try again with 0.3¢. If you can't match the ETD's template to that degree of accuracy, how can you judge what the ETD has calculated?

As I took up the SAT, and very rapidly decided not to tune without it (for reasons I'll describe later), I certainly had quarrels with it, particularly with respect to stretch. I won't bother going into details, but I found ways to make it do what I wanted to do for that purpose. But there were inharmonic gaps to get past, particularly on my fleet of Hamilton studios. Nasty gaps of inharmonicity. I had never been able to be satisfied with how intervals progressed across them.

So I analyzed them, and realized that if I wanted smooth M3s I would need to lower the plain wire pitches and raise the wrapped for the notes involved in the M3s across the break. So I experimented with that, and found that if I did enough to get good beat rate progression of M3s, all kinds of other things fell apart, and they were magnified when I expanded outwards into bass and treble. I came to the conclusion that the algorithm of the ETD actually was better in the long run when I was looking at wider intervals like 19ths and triple octaves. And the piano didn't really sound better with improved beat rate progressions.

I could write more along these lines, but I think this much provides some pertinent ideas.

More to the point, the reason I have used an ETD for all my tunings for 30 years comes down to unisons and stability. Pitch isn't all that important. Violins, voices, clarinets, oboes, full orchestras are all over the place, even the very best. All over the place relative to our cents and fractional cents. And that's if they aren't intentionally bending pitch, which they are doing all the time.

For the piano, timbre is entirely dependent on unisons. (Yes, lots of other factors, but even if they are all perfect, including mating, bad unisons will overcome them). And a perfect unison is nothing if it doesn't last. Use of an ETD enables me to focus on the feel of the pin moving in the wood, the sound of the result, and the movement of pitch, simultaneously. When homing in on the pitch of each string, it is possible to make tiny, real-time manipulations of the tuning pin that don't move it in the block, and find out whether the pitch is solid or not. This is more complex than I care to go into, but in a nutshell, if you can make minute motions of twist and flex of the pin in both directions, and see (in the ETD display) the pitch move slightly sharp and flat evenly in response to those moves, and if playing the note a few times results in no pitch change, you know you have nailed it. (Bearing friction means that it ain't that simple :-)) That's the most important reason I use an ETD: ability to achieve stability efficiently.

Bottom line, I'm guessing you are coming at your question from the point of view that ETDs really don't work that well, that aural is better, and wanting to justify that position. I also have the impression that you haven't done a lot of ETD assisted tuning, just fooled with it a bit and didn't like it. Am I wrong?

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.

To Fred's point in the first paragraph ("there is a good possibility that the pitch of the first string shifts a bit during the process of pulling the unison, especially if there is any pitch change involved"): this is exactly my experience with using an ETD to measure open unisons, a good 95% of the time at least.  In particular, when I use the overpull function in TuneLab, I find the greater part of the pitch drop that it's compensating for, has already happened by the time I tune the rest of the unison.

Thanks for the thoughtful reply Fred, and everybody else as well. I originally posted right before I got caught up in flurry of activity and am now trying to catch up.

You said: "You posit experience where you disagree aurally with what you believe to be the "decision" of the ETD. This is pretty amorphous stuff." The decisions don't feel amorphous - a fifth should be almost pure but not exactly. Octaves in the midrange need to be reigned in by the faster beating intervals so they don't get to "edgy" sounding. It's  pretty straightforward. But I'll have to agree that if you aren't in the room when I'm going through my temperament and midrange, then my claims are pretty much heresay. 

You said: Bottom line, I'm guessing you are coming at your question from the point of view that ETDs really don't work that well, that aural is better, and wanting to justify that position. I also have the impression that you haven't done a lot of ETD assisted tuning, just fooled with it a bit and didn't like it. Am I wrong?

You are only partially right (no pun intended).  ETDs work extremely well at measuring pitch. They do a reasonable job at temperament and stretch if you know how to keep them on track. But I find that as unisons are pulled in, it is always important to keep checking and rechecking the intonation of the intervals. I have not found I can rely on it, and constantly second-guessing the ETD interupts my work flow.

I also wouldn't say aural is better: I have a thought experiment that goes like this: For some reason I am no longer able to tune my piano and have to choose between two other tuners in my area. Tuner one, is not an RPT because he failed the aural midrange portion of the exam but scored 100% on everything else including unisons and stability. The other tuner is an RPT who squeaked by with scores in the 80's including unisons and stability. Which do you think I would choose? It's not a difficult decision at all. 

My orignal post mentioned that I'm working on a hybrid tuning class. "Aural tuners without an ETD are lacking a valuable tool, ETD users who lack strong aural abilities are lacking an invaluable skill" is the subititle. I'm trying to figure out where the best of both worlds is. What are the strengths of the ear and where can ETDs serve us best? So I'm certainly not "anti-ETD". But I'm also a little heartbroken to see talented young tuners who have become dependent on their ETD and are failing to learn how powerful aural tuning techniques can be. 

My first use of ETDs was when I was in CTE training back in the late 1990's when the Accutuner II was the standard. I know exactly what you are saying about "zeroing out" the machine being a leaned skill that requires a somewhat nuanced technique and plenty of practice. Different examiners may have different interpretations of the display when the rotating lights did not give a steady signal. It's particularly tricky when one or two tenths of a cent can be the final straw for that examinees score. 

I purposfully did not disclose what ETD I've been using because I'm not entirely sure how relevent it is. But for full disclosure, I mainly use Tunelab as my ETD assist. I also have an upgraded version of Pianometer that I've played with as well. 

One thing I'm very curious about is how ETDs are being used in Master Tuning exam pianos these days. Is anyone able to use a stock ETD midrange as a mastertuning without having to make a few tweaks here and there? If tweaks have to be made: why?

You also made an interesting point in your post that "When I zeroed the notes, all the errors went away. (This kind of experience was repeated time and time again)." Yet, how did you know the errors went away unless you could aurally verify? One of my points about aural tuning, is that it make you better at interpreting the display. 

I've been meaning to borrow cybertuner and a SAT IV to compare the results I get from Tunelab. I've heard Cybertunings that I thought were overstretched - yet that can be largly a matter of taste and the stretch settings. Which begs the question: What's the best way to develop taste from a tuning perspective? 

Of course you are absolutely right that it comes down to unisons and stabilty. This is the reason why I currently prefer open string tuning and mostly just use one mute when tuning grands. It forces you to be picky about unisons, and it puts you in "unison headspace" much more frequently than other approaches. Unison shimming because extremely useful and important in addition to being very effecient. I now percieve the single string of a note to be like the "course adjust" on an old shortwave radio and the "shim method" as the "fine adjust". I have to thank David Anderson and Rick Butler for the "one mute" tuning advice. I resisted for many years, but am now a believer. 

I find the most powerful use of an ETD is in "direct interval tuning" which it turns out goes back to site-o-tuner days. For example: When tuning F7, have the machine listen to F7 but play F6 and F5 and A#5 to see how the display behaves with the single octave, double-octave, and twelth. It's very educational to see how these things line up and to observe inharmonicy somewhat directly.

We will definietly have to get together in Iowa, Fred, and work some of this out on a real piano! 

Ryan (responding directly to the original post),

You posit experience where you disagree aurally with what you believe to be the "decision" of the ETD. This is pretty amorphous stuff. I can't really respond to your questions based on your personal experience without being there, observing you tune a piano with an ETD, and then checking with you, comparing notes.

What I CAN do is share my own initial experience tuning with an ETD, 30 years ago (following 15 years of purely aural tuning). I got an SAT so that I would be able to give tuning tests, and decided to try it out, though I was very skeptical. I tuned a couple midrange octaves with SAT, then checked that aurally, and found "errors." But then I looked at each of the error notes, with the ETD, and found that they were not zeroed. (I had just been through lots of CTE training on zeroing the display, so I was well aware of what I was seeing). When I zeroed the notes, all the errors went away. (This kind of experience was repeated time and time again).

So as a first response, not wishing to cause offense, I would first ask you to do precisely the same thing. Recheck the notes you object to. What does "zeroed" mean on your device? I don't know, not knowing what device you are using. To be successful at tuning with an ETD you need to figure out what zeroed means, how to see through any "junk" in the display (in many cases, use the strobe emulator, moving gray rectangles, as the most reliable factor), and then execute to zero out. As an exercise. take a note, zero the ETD on it, set an offset to plus or minus 0.5¢. Now tune to that new, slightly changed pitch target. Can you zero to it? Try again with 0.3¢. If you can't match the ETD's template to that degree of accuracy, how can you judge what the ETD has calculated?

As I took up the SAT, and very rapidly decided not to tune without it (for reasons I'll describe later), I certainly had quarrels with it, particularly with respect to stretch. I won't bother going into details, but I found ways to make it do what I wanted to do for that purpose. But there were inharmonic gaps to get past, particularly on my fleet of Hamilton studios. Nasty gaps of inharmonicity. I had never been able to be satisfied with how intervals progressed across them.

So I analyzed them, and realized that if I wanted smooth M3s I would need to lower the plain wire pitches and raise the wrapped for the notes involved in the M3s across the break. So I experimented with that, and found that if I did enough to get good beat rate progression of M3s, all kinds of other things fell apart, and they were magnified when I expanded outwards into bass and treble. I came to the conclusion that the algorithm of the ETD actually was better in the long run when I was looking at wider intervals like 19ths and triple octaves. And the piano didn't really sound better with improved beat rate progressions.

I could write more along these lines, but I think this much provides some pertinent ideas.

More to the point, the reason I have used an ETD for all my tunings for 30 years comes down to unisons and stability. Pitch isn't all that important. Violins, voices, clarinets, oboes, full orchestras are all over the place, even the very best. All over the place relative to our cents and fractional cents. And that's if they aren't intentionally bending pitch, which they are doing all the time.

For the piano, timbre is entirely dependent on unisons. (Yes, lots of other factors, but even if they are all perfect, including mating, bad unisons will overcome them). And a perfect unison is nothing if it doesn't last. Use of an ETD enables me to focus on the feel of the pin moving in the wood, the sound of the result, and the movement of pitch, simultaneously. When homing in on the pitch of each string, it is possible to make tiny, real-time manipulations of the tuning pin that don't move it in the block, and find out whether the pitch is solid or not. This is more complex than I care to go into, but in a nutshell, if you can make minute motions of twist and flex of the pin in both directions, and see (in the ETD display) the pitch move slightly sharp and flat evenly in response to those moves, and if playing the note a few times results in no pitch change, you know you have nailed it. (Bearing friction means that it ain't that simple :-)) That's the most important reason I use an ETD: ability to achieve stability efficiently.

Bottom line, I'm guessing you are coming at your question from the point of view that ETDs really don't work that well, that aural is better, and wanting to justify that position. I also have the impression that you haven't done a lot of ETD assisted tuning, just fooled with it a bit and didn't like it. Am I wrong?

I've been developing a presentation on hybrid tuning. Something I've been wanting to understand, but am too lazy and mathematically dumb to figure out is this:

Why does my ear disagree with the ETD? I have a few hypotheses that I'll run by you.

1. The ETD assumes a perfectly smooth inharmonicity curve between sample points. 

2. Imperfections in bridge notching means the speaking lengths don't increase at a perfectly smooth rate. 

3. Straightness of the speaking portion of the wire and condition of termination points could affect the actual speaking length. 

4. ETDs don't know exactly where the wire diameters change. A wire change introduces an abrupt step in the smoothness of the inharmonicity. 

5. Having all three strings of a unison open, often creates slightly different beat speeds than a single string. ETD's are not reliable when listening to open strings. 

How much do small changes in speaking lengths and wire diameters affect the actual real-world pitches of the harmonics, since this is ultimately what affects the beat speeds? Also which has a more dramatic effect: diameter change or a 1 mm speaking length change?

Take the F3-A3 Major third, for example. If it's beating at 6.8 bps, how much would the beat rate change if you were to:

1.  increase or decrease the wire diameter of the bottom or top note by one size?

2. Increase or decrease the speaking length by 1 mm of either the top note or the bottom note. 

About 75-80 percent of my tuning is aural because I have not found that the ETD can give me the results I'm looking for, especially when I'm setting up the middle two octaves. I often disagree with the machine, especially once the unison is tuned. Having to second guess the display can interrupt my work flow. 

Generally, I strive to always tune unisons as I go, with the final string of each unison being tuned with no mutes in play. 

Since ETD's (I believe) can only accurately measure the pitch of one single string, I question how that translates to the actual intonation of an interval once all 6 strings are in play. We also have to accept that the pitch target is only an "educated guess" (albeit a highly educated one) based on samples. The target accuracy itself may be slightly off due to above mentioned discrepancies caused by wire diameter and speaking length changes. 

This is why I think the perception of accuracy of ETDs is somewhat of an illusion.