Pianotech

In piano tuning, there is a somewhat difficult concept to understand regarding "stretch tuning" and "inharmonicity".  This has come up most often when a musician measures the tuning of a piano using a basic electronic tuner suitable for guitars or other instruments.  Some of them are inexpensive "apps"for a smartphone, others such as chromatic strobe tuners seem quite impressive in their accuracy and features.  This can become a complicated subject, but let me try my best to explain in a straightforward way why piano tuning cannot be evaluated in this way.

Piano strings vibrate as a whole and in sections.  The sections are called "partial", "harmonics", or "overtones".  The pitch of a string is determined by the vibration of the whole length of string, called the fundamental.  Different notes blend together because of their combination of partials.  Octaves are uniquely related notes.  The partials of octaves are almost perfect doubles.  For instance, if a lower note has a frequency of 1000 hz (cycles per second), then the note one octave above has a frequency of 2000 hz.  They match together well because a partial from the lower note is also 2000 hz.

However, there is a problem.  Because piano strings are stiff, the length of each partial in a pianos is a bit shorter than we would expect.  Consequently, the pitch of the partials/harmonics/overtones are a bit higher than expected. Therefore, the octaves must be tuned a bit sharper than the theoretical frequencies to sound musical together.  Early electronic tuners in the 1950s got a bad reputation, because they ignored inharmonicity.  Inexpensive chromatic tuners have the same problem, no matter how accurate they measure frequency.  In measuring a well tuned piano, they will find the treble to seem sharp, and the bass to be flat.  They can be accurate in measuring a concert  pitch in the center of the keyboard.  It is, of course, important to agree on the pitch standard.  Usually A=440, but some symphonies use A=442 or 443 as their standard.

Tuning a piano aurally (by ear), naturally accommodates the problem with inharmonicity.  Expensive electronic piano tuning devices also measure inharmonicity and make the needed adjustments. Pianos that are properly tuned usually have no major problems playing with other instruments or singing voices. 

Note: I am not an engineer or piano designer. My degree is in music, but I explain this all the time, so either my clients are super bright, are lying to me to be kind as I stand there wearing a foil hat, or my explanation sort of makes sense. Slightly. 

I explain it like this:

Suppose you have a wire which is 1 meter in length, which is 100cm (we don't use the metric system here in the US commonly, but the math is easier).

That wire is vibrating 100 times per second, which we call 100hz (I the play a note in the range of 100 like A2).

As crazy as it sounds, the half length of that wire is vibrating as well, in two equal lengths. This produces a pitch which is double the value of the fundamental pitch, which is an octave.

Now play a note while touching the wire at half length to demonstrate harmonic to the client.

This division or point has no mathematical value, which is impossible, right?

This point must have some value, which varies with the weight and tension of the string. This half-length pitch should be 200hz or two hundred cycles per second, and the half length of the wire should be 50cm, right? Approving nod....hopefully. 

Now, imagine cutting a piece of wood - a 2x4 - in half. If it started out as 100cm, would the two halves be equal? Of course not, since the width of the saw blade would have to be subtracted. If the saw blade is 4mm, then each segment would be 49.8cm, and this shorter length will vibrate slightly sharp of 100hz. This discrepancy, or out of tune-ness, is called inharmonicicy. I also explain that a short piece of wood has less flexibility than a long piece - which everyone seems to understand. Hence longer string = lower inharmonicity. 

I then explain that there are many subdivisions of the string, and the each segment is more out of tune mathematically than the previous division simply because there are more "cuts" to the wire, and send them off to the source of all things good and true  - Wikipedia - so that they may mentally remove my foil hat and reclassify me as Not Quite Insane. 

I do this about 5-6 times per week, and have several apprentices I'm in the process of explaingin this to.  The thing is, intellectually it's pretty straight forward, but man, when you start trying to teach an actual musician to listen to the piano this way, you realize how little headway you've actually made. 

My ultimate goal is to explain this in 2 minutes, satisfy their curiosity, redirect them towards getting me a cup of coffee, and maintain billable hours. Perhaps a simple brochure on how this subject would be worthwhile. 

Wow, I really should stay away from the internet when I can't sleep. 

Note: I am not an engineer or piano designer. My degree is in music, but I explain this all the time, so either my clients are super bright, are lying to me to be kind as I stand there wearing a foil hat, or my explanation sort of makes sense. Slightly. 

I explain it like this:

Suppose you have a wire which is 1 meter in length, which is 100cm (we don't use the metric system here in the US commonly, but the math is easier).

That wire is vibrating 100 times per second, which we call 100hz (I the play a note in the range of 100 like A2).

As crazy as it sounds, the half length of that wire is vibrating as well, in two equal lengths. This produces a pitch which is double the value of the fundamental pitch, which is an octave.

Now play a note while touching the wire at half length to demonstrate harmonic to the client.

This division or point has no mathematical value, which is impossible, right?

This point must have some value, which varies with the weight and tension of the string. This half-length pitch should be 200hz or two hundred cycles per second, and the half length of the wire should be 50cm, right? Approving nod....hopefully. 

Now, imagine cutting a piece of wood - a 2x4 - in half. If it started out as 100cm, would the two halves be equal? Of course not, since the width of the saw blade would have to be subtracted. If the saw blade is 4mm, then each segment would be 49.8cm, and this shorter length will vibrate slightly sharp of 200hz. This discrepancy, or out of tune-ness, is called inharmonicicy. I also explain that a short piece of wood has less flexibility than a long piece - which everyone seems to understand. Hence longer string = lower inharmonicity. 

I then explain that there are many subdivisions of the string, and the each segment is more out of tune mathematically than the previous division simply because there are more "cuts" to the wire, and send them off to the source of all things good and true  - Wikipedia - so that they may mentally remove my foil hat and reclassify me as Not Quite Insane. 

I do this about 5-6 times per week, and have several apprentices I'm in the process of explaingin this to.  The thing is, intellectually it's pretty straight forward, but man, when you start trying to teach an actual musician to listen to the piano this way, you realize how little headway you've actually made. 

My ultimate goal is to explain this in 2 minutes, satisfy their curiosity, redirect them towards getting me a cup of coffee, and maintain billable hours. Perhaps a simple brochure on how this subject would be worthwhile. 

Wow, I really should stay away from the internet when I can't sleep. 

Note: I am not an engineer or piano designer. My degree is in music, but I explain this all the time, so either my clients are super bright, are lying to me to be kind as I stand there wearing a foil hat, or my explanation sort of makes sense. Slightly. 

I explain it like this:

Suppose you have a wire which is 1 meter in length, which is 100cm (we don't use the metric system here in the US commonly, but the math is easier).

That wire is vibrating 100 times per second, which we call 100hz (I the play a note in the range of 100 like A2).

As crazy as it sounds, the half length of that wire is vibrating as well, in two equal lengths. This produces a pitch which is double the value of the fundamental pitch, which is an octave.

Now play a note while touching the wire at half length to demonstrate harmonic to the client.

This division or point has no mathematical value, which is impossible, right?

This point must have some value, which varies with the weight and tension of the string. This half-length pitch should be 200hz or two hundred cycles per second, and the half length of the wire should be 50cm, right? Approving nod....hopefully. 

Now, imagine cutting a piece of wood - a 2x4 - in half. If it started out as 100cm, would the two halves be equal? Of course not, since the width of the saw blade would have to be subtracted. If the saw blade is 4mm, then each segment would be 49.8cm, and this shorter length will vibrate slightly sharp of 200hz. This discrepancy, or out of tune-ness, is called inharmonicicy. I also explain that a short piece of wood has less flexibility than a long piece - which everyone seems to understand. Hence longer string = lower inharmonicity. 

I then explain that there are many subdivisions of the string, and the each segment is more out of tune mathematically than the previous division simply because there are more "cuts" to the wire, and send them off to the source of all things good and true  - Wikipedia - so that they may mentally remove my foil hat and reclassify me as Not Quite Insane. 

I do this about 5-6 times per week, and have several apprentices I'm in the process of explaingin this to.  The thing is, intellectually it's pretty straight forward, but man, when you start trying to teach an actual musician to listen to the piano this way, you realize how little headway you've actually made. 

My ultimate goal is to explain this in 2 minutes, satisfy their curiosity, redirect them towards getting me a cup of coffee, and maintain billable hours. Perhaps a simple brochure on how this subject would be worthwhile. 

Wow, I really should stay away from the internet when I can't sleep. 

Note: I am not an engineer or piano designer. My degree is in music, but I explain this all the time, so either my clients are super bright, are lying to me to be kind as I stand there wearing a foil hat, or my explanation sort of makes sense. Slightly. 

I explain it like this:

Suppose you have a wire which is 1 meter in length, which is 100cm (we don't use the metric system here in the US commonly, but the math is easier).

That wire is vibrating 100 times per second, which we call 100hz (I the play a note in the range of 100 like A2).

As crazy as it sounds, the half length of that wire is vibrating as well, in two equal lengths. This produces a pitch which is double the value of the fundamental pitch, which is an octave.

Now play a note while touching the wire at half length to demonstrate harmonic to the client.

This division or point has no mathematical value, which is impossible, right?

This point must have some value, which varies with the weight and tension of the string. This half-length pitch should be 200hz or two hundred cycles per second, and the half length of the wire should be 50cm, right? Approving nod....hopefully. 

Now, imagine cutting a piece of wood - a 2x4 - in half. If it started out as 100cm, would the two halves be equal? Of course not, since the width of the saw blade would have to be subtracted. If the saw blade is 4mm, then each segment would be 49.8cm, and this shorter length will vibrate slightly sharp of 200hz. This discrepancy, or out of tune-ness, is called inharmonicicy. I also explain that a short piece of wood has less flexibility than a long piece - which everyone seems to understand. Hence longer string = lower inharmonicity. 

I then explain that there are many subdivisions of the string, and the each segment is more out of tune mathematically than the previous division simply because there are more "cuts" to the wire, and send them off to the source of all things good and true  - Wikipedia - so that they may mentally remove my foil hat and reclassify me as Not Quite Insane. 

I do this about 5-6 times per week, and have several apprentices I'm in the process of explaingin this to.  The thing is, intellectually it's pretty straight forward, but man, when you start trying to teach an actual musician to listen to the piano this way, you realize how little headway you've actually made. 

My ultimate goal is to explain this in 2 minutes, satisfy their curiosity, redirect them towards getting me a cup of coffee, and maintain billable hours. Perhaps a simple brochure on how this subject would be worthwhile. 

Wow, I really should stay away from the internet when I can't sleep. 

Note: I am not an engineer or piano designer. My degree is in music, but I explain this all the time, so either my clients are super bright, are lying to me to be kind as I stand there wearing a foil hat, or my explanation sort of makes sense. Slightly. 

I explain it like this:

Suppose you have a wire which is 1 meter in length, which is 100cm (we don't use the metric system here in the US commonly, but the math is easier).

That wire is vibrating 100 times per second, which we call 100hz (I the play a note in the range of 100 like A2).

As crazy as it sounds, the half length of that wire is vibrating as well, in two equal lengths. This produces a pitch which is double the value of the fundamental pitch, which is an octave.

Now play a note while touching the wire at half length to demonstrate harmonic to the client.

This division or point has no mathematical value, which is impossible, right?

This point must have some value, which varies with the weight and tension of the string. This half-length pitch should be 200hz or two hundred cycles per second, and the half length of the wire should be 50cm, right? Approving nod....hopefully. 

Now, imagine cutting a piece of wood - a 2x4 - in half. If it started out as 100cm, would the two halves be equal? Of course not, since the width of the saw blade would have to be subtracted. If the saw blade is 4mm, then each segment would be 49.8cm, and this shorter length will vibrate slightly sharp of 200hz. This discrepancy, or out of tune-ness, is called inharmonicicy. I also explain that a short piece of wood has less flexibility than a long piece - which everyone seems to understand. Hence longer string = lower inharmonicity. 

I then explain that there are many subdivisions of the string, and the each segment is more out of tune mathematically than the previous division simply because there are more "cuts" to the wire, and send them off to the source of all things good and true  - Wikipedia - so that they may mentally remove my foil hat and reclassify me as Not Quite Insane. 

I do this about 5-6 times per week, and have several apprentices I'm in the process of explaingin this to.  The thing is, intellectually it's pretty straight forward, but man, when you start trying to teach an actual musician to listen to the piano this way, you realize how little headway you've actually made. 

My ultimate goal is to explain this in 2 minutes, satisfy their curiosity, redirect them towards getting me a cup of coffee, and maintain billable hours. Perhaps a simple brochure on how this subject would be worthwhile. 

Wow, I really should stay away from the internet when I can't sleep. 

Note: I am not an engineer or piano designer. My degree is in music, but I explain this all the time, so either my clients are super bright, are lying to me to be kind as I stand there wearing a foil hat, or my explanation sort of makes sense. Slightly. 

I explain it like this:

Suppose you have a wire which is 1 meter in length, which is 100cm (we don't use the metric system here in the US commonly, but the math is easier).

That wire is vibrating 100 times per second, which we call 100hz (I the play a note in the range of 100 like A2).

As crazy as it sounds, the half length of that wire is vibrating as well, in two equal lengths. This produces a pitch which is double the value of the fundamental pitch, which is an octave.

Now play a note while touching the wire at half length to demonstrate harmonic to the client.

This division or point has no mathematical value, which is impossible, right?

This point must have some value, which varies with the weight and tension of the string. This half-length pitch should be 200hz or two hundred cycles per second, and the half length of the wire should be 50cm, right? Approving nod....hopefully. 

Now, imagine cutting a piece of wood - a 2x4 - in half. If it started out as 100cm, would the two halves be equal? Of course not, since the width of the saw blade would have to be subtracted. If the saw blade is 4mm, then each segment would be 49.8cm, and this shorter length will vibrate slightly sharp of 200hz. This discrepancy, or out of tune-ness, is called inharmonicicy. I also explain that a short piece of wood has less flexibility than a long piece - which everyone seems to understand. Hence longer string = lower inharmonicity. 

I then explain that there are many subdivisions of the string, and the each segment is more out of tune mathematically than the previous division simply because there are more "cuts" to the wire, and send them off to the source of all things good and true  - Wikipedia - so that they may mentally remove my foil hat and reclassify me as Not Quite Insane. 

I do this about 5-6 times per week, and have several apprentices I'm in the process of explaingin this to.  The thing is, intellectually it's pretty straight forward, but man, when you start trying to teach an actual musician to listen to the piano this way, you realize how little headway you've actually made. 

My ultimate goal is to explain this in 2 minutes, satisfy their curiosity, redirect them towards getting me a cup of coffee, and maintain billable hours. Perhaps a simple brochure on how this subject would be worthwhile. 

Wow, I really should stay away from the internet when I can't sleep. 

Note: I am not an engineer or piano designer. My degree is in music, but I explain this all the time, so either my clients are super bright, are lying to me to be kind as I stand there wearing a foil hat, or my explanation sort of makes sense. Slightly. 

I explain it like this:

Suppose you have a wire which is 1 meter in length, which is 100cm (we don't use the metric system here in the US commonly, but the math is easier).

That wire is vibrating 100 times per second, which we call 100hz (I the play a note in the range of 100 like A2).

As crazy as it sounds, the half length of that wire is vibrating as well, in two equal lengths. This produces a pitch which is double the value of the fundamental pitch, which is an octave.

Now play a note while touching the wire at half length to demonstrate harmonic to the client.

This division or point has no mathematical value, which is impossible, right?

This point must have some value, which varies with the weight and tension of the string. This half-length pitch should be 200hz or two hundred cycles per second, and the half length of the wire should be 50cm, right? Approving nod....hopefully. 

Now, imagine cutting a piece of wood - a 2x4 - in half. If it started out as 100cm, would the two halves be equal? Of course not, since the width of the saw blade would have to be subtracted. If the saw blade is 4mm, then each segment would be 49.8cm, and this shorter length will vibrate slightly sharp of 200hz. This discrepancy, or out of tune-ness, is called inharmonicicy. I also explain that a short piece of wood has less flexibility than a long piece - which everyone seems to understand. Hence longer string = lower inharmonicity. 

I then explain that there are many subdivisions of the string, and the each segment is more out of tune mathematically than the previous division simply because there are more "cuts" to the wire, and send them off to the source of all things good and true  - Wikipedia - so that they may mentally remove my foil hat and reclassify me as Not Quite Insane. 

I do this about 5-6 times per week, and have several apprentices I'm in the process of explaingin this to.  The thing is, intellectually it's pretty straight forward, but man, when you start trying to teach an actual musician to listen to the piano this way, you realize how little headway you've actually made. 

My ultimate goal is to explain this in 2 minutes, satisfy their curiosity, redirect them towards getting me a cup of coffee, and maintain billable hours. Perhaps a simple brochure on how this subject would be worthwhile. 

Wow, I really should stay away from the internet when I can't sleep. 

Note: I am not an engineer or piano designer. My degree is in music, but I explain this all the time, so either my clients are super bright, are lying to me to be kind as I stand there wearing a foil hat, or my explanation sort of makes sense. Slightly. 

I explain it like this:

Suppose you have a wire which is 1 meter in length, which is 100cm (we don't use the metric system here in the US commonly, but the math is easier).

That wire is vibrating 100 times per second, which we call 100hz (I the play a note in the range of 100 like A2).

As crazy as it sounds, the half length of that wire is vibrating as well, in two equal lengths. This produces a pitch which is double the value of the fundamental pitch, which is an octave.

Now play a note while touching the wire at half length to demonstrate harmonic to the client.

This division or point has no mathematical value, which is impossible, right?

This point must have some value, which varies with the weight and tension of the string. This half-length pitch should be 200hz or two hundred cycles per second, and the half length of the wire should be 50cm, right? Approving nod....hopefully. 

Now, imagine cutting a piece of wood - a 2x4 - in half. If it started out as 100cm, would the two halves be equal? Of course not, since the width of the saw blade would have to be subtracted. If the saw blade is 4mm, then each segment would be 49.8cm, and this shorter length will vibrate slightly sharp of 200hz. This discrepancy, or out of tune-ness, is called inharmonicicy. I also explain that a short piece of wood has less flexibility than a long piece - which everyone seems to understand. Hence longer string = lower inharmonicity. 

I then explain that there are many subdivisions of the string, and the each segment is more out of tune mathematically than the previous division simply because there are more "cuts" to the wire, and send them off to the source of all things good and true  - Wikipedia - so that they may mentally remove my foil hat and reclassify me as Not Quite Insane. 

I do this about 5-6 times per week, and have several apprentices I'm in the process of explaingin this to.  The thing is, intellectually it's pretty straight forward, but man, when you start trying to teach an actual musician to listen to the piano this way, you realize how little headway you've actually made. 

My ultimate goal is to explain this in 2 minutes, satisfy their curiosity, redirect them towards getting me a cup of coffee, and maintain billable hours. Perhaps a simple brochure on how this subject would be worthwhile. 

Wow, I really should stay away from the internet when I can't sleep. 

Note: I am not an engineer or piano designer. My degree is in music, but I explain this all the time, so either my clients are super bright, are lying to me to be kind as I stand there wearing a foil hat, or my explanation sort of makes sense. Slightly. 

I explain it like this:

Suppose you have a wire which is 1 meter in length, which is 100cm (we don't use the metric system here in the US commonly, but the math is easier).

That wire is vibrating 100 times per second, which we call 100hz (I the play a note in the range of 100 like A2).

As crazy as it sounds, the half length of that wire is vibrating as well, in two equal lengths. This produces a pitch which is double the value of the fundamental pitch, which is an octave.

Now play a note while touching the wire at half length to demonstrate harmonic to the client.

This division or point has no mathematical value, which is impossible, right?

This point must have some value, which varies with the weight and tension of the string. This half-length pitch should be 200hz or two hundred cycles per second, and the half length of the wire should be 50cm, right? Approving nod....hopefully. 

Now, imagine cutting a piece of wood - a 2x4 - in half. If it started out as 100cm, would the two halves be equal? Of course not, since the width of the saw blade would have to be subtracted. If the saw blade is 4mm, then each segment would be 49.8cm, and this shorter length will vibrate slightly sharp of 200hz. This discrepancy, or out of tune-ness, is called inharmonicicy. I also explain that a short piece of wood has less flexibility than a long piece - which everyone seems to understand. Hence longer string = lower inharmonicity. 

I then explain that there are many subdivisions of the string, and the each segment is more out of tune mathematically than the previous division simply because there are more "cuts" to the wire, and send them off to the source of all things good and true  - Wikipedia - so that they may mentally remove my foil hat and reclassify me as Not Quite Insane. 

I do this about 5-6 times per week, and have several apprentices I'm in the process of explaingin this to.  The thing is, intellectually it's pretty straight forward, but man, when you start trying to teach an actual musician to listen to the piano this way, you realize how little headway you've actually made. 

My ultimate goal is to explain this in 2 minutes, satisfy their curiosity, redirect them towards getting me a cup of coffee, and maintain billable hours. Perhaps a simple brochure on how this subject would be worthwhile. 

Wow, I really should stay away from the internet when I can't sleep.