Pianotech

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074
------------------------------

Additionally, I think this could just pass an RPT tuning exam (temperament portion) as it's currently graded. Please correct me if I'm wrong.

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074

Original Message:
Sent: 01-05-2025 22:19
From: Tim Foster
Subject: Temperament experiment

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074
------------------------------

I have a device that shows 10ths of a cent. How does one demonstrate hundredths of a cent?

Additionally, I think this could just pass an RPT tuning exam (temperament portion) as it's currently graded. Please correct me if I'm wrong.

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074

Original Message:
Sent: 01-05-2025 22:19
From: Tim Foster
Subject: Temperament experiment

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074
------------------------------

My ETD does 100th of a cent, but you can just round to the nearest 10th.

I have a device that shows 10ths of a cent. How does one demonstrate hundredths of a cent?

Additionally, I think this could just pass an RPT tuning exam (temperament portion) as it's currently graded. Please correct me if I'm wrong.

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074

Original Message:
Sent: 01-05-2025 22:19
From: Tim Foster
Subject: Temperament experiment

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074
------------------------------

You can read it to a hundredth of a cent but can you manipulate the string to a hundredth of a cent?

My ETD does 100th of a cent, but you can just round to the nearest 10th.

I have a device that shows 10ths of a cent. How does one demonstrate hundredths of a cent?

Additionally, I think this could just pass an RPT tuning exam (temperament portion) as it's currently graded. Please correct me if I'm wrong.

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074

Original Message:
Sent: 01-05-2025 22:19
From: Tim Foster
Subject: Temperament experiment

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074
------------------------------

You can read it to a hundredth of a cent but can you manipulate the string to a hundredth of a cent?

My ETD does 100th of a cent, but you can just round to the nearest 10th.

I have a device that shows 10ths of a cent. How does one demonstrate hundredths of a cent?

Additionally, I think this could just pass an RPT tuning exam (temperament portion) as it's currently graded. Please correct me if I'm wrong.

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074

Original Message:
Sent: 01-05-2025 22:19
From: Tim Foster
Subject: Temperament experiment

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074
------------------------------

I have a device that shows 10ths of a cent. How does one demonstrate hundredths of a cent?

Additionally, I think this could just pass an RPT tuning exam (temperament portion) as it's currently graded. Please correct me if I'm wrong.

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074

Original Message:
Sent: 01-05-2025 22:19
From: Tim Foster
Subject: Temperament experiment

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074
------------------------------

Additionally, I think this could just pass an RPT tuning exam (temperament portion) as it's currently graded. Please correct me if I'm wrong.

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074

Original Message:
Sent: 01-05-2025 22:19
From: Tim Foster
Subject: Temperament experiment

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074
------------------------------

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

I'll give it a try this week and hear how it plays - thanks for posting.

Ron Koval

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

Maggie,

I told Tim I was going to give it a go and I will attempt it today on one or two appts. It seems to me that since the deviations from ET are all the same (1 cent) it should be a rather simple matter of tuning a good aural temperament and then raising or lowering the prescribed notes by 1 cent (which can easily be done digitally at first...once the hearing is attuned to what it's "supposed" to sound like, it should be simple enough to create your own scheme to duplicate).  This is what I do with EBVT...I know the procedure, but more importantly I know what the end goal is in general (EBVT turns out different on each piano, esp little ones) but understanding it's thought process I can tweak it as needed to come as close to the stated goal as I can. 

Tim sent me a preliminary version of this some months back. He asked for my feedback which I gave him (I didn't like it for MY music) and he has since modified it so I'm game to give it a try. If I have to the first time around I'll use the machine but once I get the sense of it (if I like it) I know I can do it in analog fashion. I'll bet you can too (without anyone telling you how)!

Peter Grey Piano Doctor 

I'll give it a try this week and hear how it plays - thanks for posting.

Ron Koval

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

Tim,

I was able to give your pattern a try yesterday. I will say that the results were mixed and here's why:

Though I was going to do it on two different instruments I ended up only doing it on one, a 1985 SS K that I had only tuned once before and that was 5 years ago, so pitch correction was in order. Anyway I was quite able to produce the temperament aurally simply by tuning a very good ET and then by following your delineation of deviation from top to bottom (the order was ideal) it was relatively easy to approximate the 1 cent alterations, with the final proof being in the placement of pure 5ths. I then descended into the bass with slightly expanded 6:3 octaves consistently, and then into the remainder above with expanded 4:2 approximating pure 12ths (which is my usual procedure). 

While the piano sounded "good" (in fact I did praise the tone of the thing), there was a bit of distraction since the touch is unbelievably heavy due to excessive damper spring strength combined with very early damper pickup (clearly this way straight out of the factory). I of course pointed this out to the current owner of the piano and, though it can be improved, it would not be an easy job. However, this issue prevented me from really testing out the instrument, but also I had no way to really compare any resonance improvements (if any) under all these circumstances. Therefore I cannot attest to how much of what I heard was due to the altered tuning or if it's just the piano. Interestingly there was also a significant degree of background bass string leakage (activated worse in certain keys...which might be significant 😳) with which I had a "hmmm" moment. The jury is still out...

The second piano I realized when I got there that I have been tuning in EBVT so I decided to stick with that. Therefore no second chance on that one. 

I will do it again and try to evaluate things more objectively. 

Peter Grey Piano Doctor 

Maggie,

I told Tim I was going to give it a go and I will attempt it today on one or two appts. It seems to me that since the deviations from ET are all the same (1 cent) it should be a rather simple matter of tuning a good aural temperament and then raising or lowering the prescribed notes by 1 cent (which can easily be done digitally at first...once the hearing is attuned to what it's "supposed" to sound like, it should be simple enough to create your own scheme to duplicate).  This is what I do with EBVT...I know the procedure, but more importantly I know what the end goal is in general (EBVT turns out different on each piano, esp little ones) but understanding it's thought process I can tweak it as needed to come as close to the stated goal as I can. 

Tim sent me a preliminary version of this some months back. He asked for my feedback which I gave him (I didn't like it for MY music) and he has since modified it so I'm game to give it a try. If I have to the first time around I'll use the machine but once I get the sense of it (if I like it) I know I can do it in analog fashion. I'll bet you can too (without anyone telling you how)!

Peter Grey Piano Doctor 

I'll give it a try this week and hear how it plays - thanks for posting.

Ron Koval

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

Peter,

Thank you for your feedback! If I have to play in some semblance of ET, I would prefer this one, I feel like the clarity and resonance is improved. Historically, are you already know, C, F, and G are the "calmest" keys, and there is no way to keep the four symmetrical pure fifths without imposing a slightly wider third on one of these "calm" keys, at least with all other keys being equal.  In the current iteration, we could make it slightly more unequal which would place G-B closer to ET (14.15 cents wide, currently it's 15.65 cents wide) by raising the G-D pure fifth by half a cent and lowering the E-B pure fifth by 1 cent. This slightly improves some tempered fifths (C-G, B-F#) and slightly narrows others (D-A, A-E). Even so, both are slightly under 4 cents narrow, which is very usable in my book.

Thank again for giving it a shot! 

Tim,

I was able to give your pattern a try yesterday. I will say that the results were mixed and here's why:

Though I was going to do it on two different instruments I ended up only doing it on one, a 1985 SS K that I had only tuned once before and that was 5 years ago, so pitch correction was in order. Anyway I was quite able to produce the temperament aurally simply by tuning a very good ET and then by following your delineation of deviation from top to bottom (the order was ideal) it was relatively easy to approximate the 1 cent alterations, with the final proof being in the placement of pure 5ths. I then descended into the bass with slightly expanded 6:3 octaves consistently, and then into the remainder above with expanded 4:2 approximating pure 12ths (which is my usual procedure). 

While the piano sounded "good" (in fact I did praise the tone of the thing), there was a bit of distraction since the touch is unbelievably heavy due to excessive damper spring strength combined with very early damper pickup (clearly this way straight out of the factory). I of course pointed this out to the current owner of the piano and, though it can be improved, it would not be an easy job. However, this issue prevented me from really testing out the instrument, but also I had no way to really compare any resonance improvements (if any) under all these circumstances. Therefore I cannot attest to how much of what I heard was due to the altered tuning or if it's just the piano. Interestingly there was also a significant degree of background bass string leakage (activated worse in certain keys...which might be significant 😳) with which I had a "hmmm" moment. The jury is still out...

The second piano I realized when I got there that I have been tuning in EBVT so I decided to stick with that. Therefore no second chance on that one. 

I will do it again and try to evaluate things more objectively. 

Peter Grey Piano Doctor 

Maggie,

I told Tim I was going to give it a go and I will attempt it today on one or two appts. It seems to me that since the deviations from ET are all the same (1 cent) it should be a rather simple matter of tuning a good aural temperament and then raising or lowering the prescribed notes by 1 cent (which can easily be done digitally at first...once the hearing is attuned to what it's "supposed" to sound like, it should be simple enough to create your own scheme to duplicate).  This is what I do with EBVT...I know the procedure, but more importantly I know what the end goal is in general (EBVT turns out different on each piano, esp little ones) but understanding it's thought process I can tweak it as needed to come as close to the stated goal as I can. 

Tim sent me a preliminary version of this some months back. He asked for my feedback which I gave him (I didn't like it for MY music) and he has since modified it so I'm game to give it a try. If I have to the first time around I'll use the machine but once I get the sense of it (if I like it) I know I can do it in analog fashion. I'll bet you can too (without anyone telling you how)!

Peter Grey Piano Doctor 

I'll give it a try this week and hear how it plays - thanks for posting.

Ron Koval

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

Tim,

I noticed that fast G-B 3rd straight away. As you know, I'm not going to write this off. It needs more trials on several more pianos (particularly those I know well totally so as to compare). I don't think I'll bother on PSO since ET cannot even be accomplished anyway so it would be useless (I'll stick with EBVT on those), but on an instrument I know and usually do ET I'll play with it. The goal (as I see it) is an attempt to improve vibrational resonance without roo much departure from ET. (a.k.a. another alternative). 

Peter Grey Piano Doctor 

Peter,

Thank you for your feedback! If I have to play in some semblance of ET, I would prefer this one, I feel like the clarity and resonance is improved. Historically, are you already know, C, F, and G are the "calmest" keys, and there is no way to keep the four symmetrical pure fifths without imposing a slightly wider third on one of these "calm" keys, at least with all other keys being equal.  In the current iteration, we could make it slightly more unequal which would place G-B closer to ET (14.15 cents wide, currently it's 15.65 cents wide) by raising the G-D pure fifth by half a cent and lowering the E-B pure fifth by 1 cent. This slightly improves some tempered fifths (C-G, B-F#) and slightly narrows others (D-A, A-E). Even so, both are slightly under 4 cents narrow, which is very usable in my book.

Thank again for giving it a shot! 

Tim,

I was able to give your pattern a try yesterday. I will say that the results were mixed and here's why:

Though I was going to do it on two different instruments I ended up only doing it on one, a 1985 SS K that I had only tuned once before and that was 5 years ago, so pitch correction was in order. Anyway I was quite able to produce the temperament aurally simply by tuning a very good ET and then by following your delineation of deviation from top to bottom (the order was ideal) it was relatively easy to approximate the 1 cent alterations, with the final proof being in the placement of pure 5ths. I then descended into the bass with slightly expanded 6:3 octaves consistently, and then into the remainder above with expanded 4:2 approximating pure 12ths (which is my usual procedure). 

While the piano sounded "good" (in fact I did praise the tone of the thing), there was a bit of distraction since the touch is unbelievably heavy due to excessive damper spring strength combined with very early damper pickup (clearly this way straight out of the factory). I of course pointed this out to the current owner of the piano and, though it can be improved, it would not be an easy job. However, this issue prevented me from really testing out the instrument, but also I had no way to really compare any resonance improvements (if any) under all these circumstances. Therefore I cannot attest to how much of what I heard was due to the altered tuning or if it's just the piano. Interestingly there was also a significant degree of background bass string leakage (activated worse in certain keys...which might be significant 😳) with which I had a "hmmm" moment. The jury is still out...

The second piano I realized when I got there that I have been tuning in EBVT so I decided to stick with that. Therefore no second chance on that one. 

I will do it again and try to evaluate things more objectively. 

Peter Grey Piano Doctor 

Maggie,

I told Tim I was going to give it a go and I will attempt it today on one or two appts. It seems to me that since the deviations from ET are all the same (1 cent) it should be a rather simple matter of tuning a good aural temperament and then raising or lowering the prescribed notes by 1 cent (which can easily be done digitally at first...once the hearing is attuned to what it's "supposed" to sound like, it should be simple enough to create your own scheme to duplicate).  This is what I do with EBVT...I know the procedure, but more importantly I know what the end goal is in general (EBVT turns out different on each piano, esp little ones) but understanding it's thought process I can tweak it as needed to come as close to the stated goal as I can. 

Tim sent me a preliminary version of this some months back. He asked for my feedback which I gave him (I didn't like it for MY music) and he has since modified it so I'm game to give it a try. If I have to the first time around I'll use the machine but once I get the sense of it (if I like it) I know I can do it in analog fashion. I'll bet you can too (without anyone telling you how)!

Peter Grey Piano Doctor 

I'll give it a try this week and hear how it plays - thanks for posting.

Ron Koval

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

Tim,

I noticed that fast G-B 3rd straight away. As you know, I'm not going to write this off. It needs more trials on several more pianos (particularly those I know well totally so as to compare). I don't think I'll bother on PSO since ET cannot even be accomplished anyway so it would be useless (I'll stick with EBVT on those), but on an instrument I know and usually do ET I'll play with it. The goal (as I see it) is an attempt to improve vibrational resonance without roo much departure from ET. (a.k.a. another alternative). 

Peter Grey Piano Doctor 

Peter,

Thank you for your feedback! If I have to play in some semblance of ET, I would prefer this one, I feel like the clarity and resonance is improved. Historically, are you already know, C, F, and G are the "calmest" keys, and there is no way to keep the four symmetrical pure fifths without imposing a slightly wider third on one of these "calm" keys, at least with all other keys being equal.  In the current iteration, we could make it slightly more unequal which would place G-B closer to ET (14.15 cents wide, currently it's 15.65 cents wide) by raising the G-D pure fifth by half a cent and lowering the E-B pure fifth by 1 cent. This slightly improves some tempered fifths (C-G, B-F#) and slightly narrows others (D-A, A-E). Even so, both are slightly under 4 cents narrow, which is very usable in my book.

Thank again for giving it a shot! 

Tim,

I was able to give your pattern a try yesterday. I will say that the results were mixed and here's why:

Though I was going to do it on two different instruments I ended up only doing it on one, a 1985 SS K that I had only tuned once before and that was 5 years ago, so pitch correction was in order. Anyway I was quite able to produce the temperament aurally simply by tuning a very good ET and then by following your delineation of deviation from top to bottom (the order was ideal) it was relatively easy to approximate the 1 cent alterations, with the final proof being in the placement of pure 5ths. I then descended into the bass with slightly expanded 6:3 octaves consistently, and then into the remainder above with expanded 4:2 approximating pure 12ths (which is my usual procedure). 

While the piano sounded "good" (in fact I did praise the tone of the thing), there was a bit of distraction since the touch is unbelievably heavy due to excessive damper spring strength combined with very early damper pickup (clearly this way straight out of the factory). I of course pointed this out to the current owner of the piano and, though it can be improved, it would not be an easy job. However, this issue prevented me from really testing out the instrument, but also I had no way to really compare any resonance improvements (if any) under all these circumstances. Therefore I cannot attest to how much of what I heard was due to the altered tuning or if it's just the piano. Interestingly there was also a significant degree of background bass string leakage (activated worse in certain keys...which might be significant 😳) with which I had a "hmmm" moment. The jury is still out...

The second piano I realized when I got there that I have been tuning in EBVT so I decided to stick with that. Therefore no second chance on that one. 

I will do it again and try to evaluate things more objectively. 

Peter Grey Piano Doctor 

Maggie,

I told Tim I was going to give it a go and I will attempt it today on one or two appts. It seems to me that since the deviations from ET are all the same (1 cent) it should be a rather simple matter of tuning a good aural temperament and then raising or lowering the prescribed notes by 1 cent (which can easily be done digitally at first...once the hearing is attuned to what it's "supposed" to sound like, it should be simple enough to create your own scheme to duplicate).  This is what I do with EBVT...I know the procedure, but more importantly I know what the end goal is in general (EBVT turns out different on each piano, esp little ones) but understanding it's thought process I can tweak it as needed to come as close to the stated goal as I can. 

Tim sent me a preliminary version of this some months back. He asked for my feedback which I gave him (I didn't like it for MY music) and he has since modified it so I'm game to give it a try. If I have to the first time around I'll use the machine but once I get the sense of it (if I like it) I know I can do it in analog fashion. I'll bet you can too (without anyone telling you how)!

Peter Grey Piano Doctor 

I'll give it a try this week and hear how it plays - thanks for posting.

Ron Koval

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

Hi Nicolas,

Thanks for including your offsets! I did chart your temperament and it's a really nice mild "Victorian" temperament with a good shape.  It looks similar to Ron Koval's Equal Well 1.3. My current interest is finding or creating circular temperaments that utilize pure fifths. EBVT III has 2, Young has 4, Vallotti 6, Kellner and Kirnberger III have 7. Large well scaled pianos can handle the stronger temperaments well and resonate unbelievably well. My interest is trying to find something that makes smaller pianos more settled and sound larger. I like Wendall's Natural Synchronous Well for small pianos (6 pure fifths and synchronizes all M/m 3rds), but I'm trying to find something that gives me the greatest "bang for the buck" on smaller pianos, since even ET fifths often sound noisy on small pianos. The Symmetrical Unequal in the OP is an attempt to experiment on how we can get greater resonance with very little deviation from the standard ET. I also just developed an more historical unequal temperament that utilizes the symmetry of my temperament in the OP. 

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074

Original Message:
Sent: 01-12-2025 15:39
From: Nicolas Lessard
Subject: Temperament experiment

Tim,

Did you have a chance to try the deviation I presented in a different thread several weeks ago?

It is in fact very similar to yours!

Here it is again:

A: 0
A#: +1
B: -1
C: +1
C#: -1
D: +1
D#: 0
E: -1
F: +1
F#: -1
G: +1
G#: 0

Cheers!


Original Message:
Sent: 1/11/2025 12:37:00 PM
From: Peter Grey
Subject: RE: Temperament experiment

Tim,

I noticed that fast G-B 3rd straight away. As you know, I'm not going to write this off. It needs more trials on several more pianos (particularly those I know well totally so as to compare). I don't think I'll bother on PSO since ET cannot even be accomplished anyway so it would be useless (I'll stick with EBVT on those), but on an instrument I know and usually do ET I'll play with it. The goal (as I see it) is an attempt to improve vibrational resonance without roo much departure from ET. (a.k.a. another alternative). 

Peter Grey Piano Doctor 

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

Original Message:
Sent: 01-11-2025 11:00
From: Tim Foster
Subject: Temperament experiment

Peter,

Thank you for your feedback! If I have to play in some semblance of ET, I would prefer this one, I feel like the clarity and resonance is improved. Historically, are you already know, C, F, and G are the "calmest" keys, and there is no way to keep the four symmetrical pure fifths without imposing a slightly wider third on one of these "calm" keys, at least with all other keys being equal.  In the current iteration, we could make it slightly more unequal which would place G-B closer to ET (14.15 cents wide, currently it's 15.65 cents wide) by raising the G-D pure fifth by half a cent and lowering the E-B pure fifth by 1 cent. This slightly improves some tempered fifths (C-G, B-F#) and slightly narrows others (D-A, A-E). Even so, both are slightly under 4 cents narrow, which is very usable in my book.

Thank again for giving it a shot! 

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074

Original Message:
Sent: 01-11-2025 08:36
From: Peter Grey
Subject: Temperament experiment

Tim,

I was able to give your pattern a try yesterday. I will say that the results were mixed and here's why:

Though I was going to do it on two different instruments I ended up only doing it on one, a 1985 SS K that I had only tuned once before and that was 5 years ago, so pitch correction was in order. Anyway I was quite able to produce the temperament aurally simply by tuning a very good ET and then by following your delineation of deviation from top to bottom (the order was ideal) it was relatively easy to approximate the 1 cent alterations, with the final proof being in the placement of pure 5ths. I then descended into the bass with slightly expanded 6:3 octaves consistently, and then into the remainder above with expanded 4:2 approximating pure 12ths (which is my usual procedure). 

While the piano sounded "good" (in fact I did praise the tone of the thing), there was a bit of distraction since the touch is unbelievably heavy due to excessive damper spring strength combined with very early damper pickup (clearly this way straight out of the factory). I of course pointed this out to the current owner of the piano and, though it can be improved, it would not be an easy job. However, this issue prevented me from really testing out the instrument, but also I had no way to really compare any resonance improvements (if any) under all these circumstances. Therefore I cannot attest to how much of what I heard was due to the altered tuning or if it's just the piano. Interestingly there was also a significant degree of background bass string leakage (activated worse in certain keys...which might be significant 😳) with which I had a "hmmm" moment. The jury is still out...

The second piano I realized when I got there that I have been tuning in EBVT so I decided to stick with that. Therefore no second chance on that one. 

I will do it again and try to evaluate things more objectively. 

Peter Grey Piano Doctor 

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

Original Message:
Sent: 01-10-2025 08:47
From: Peter Grey
Subject: Temperament experiment

Maggie,

I told Tim I was going to give it a go and I will attempt it today on one or two appts. It seems to me that since the deviations from ET are all the same (1 cent) it should be a rather simple matter of tuning a good aural temperament and then raising or lowering the prescribed notes by 1 cent (which can easily be done digitally at first...once the hearing is attuned to what it's "supposed" to sound like, it should be simple enough to create your own scheme to duplicate).  This is what I do with EBVT...I know the procedure, but more importantly I know what the end goal is in general (EBVT turns out different on each piano, esp little ones) but understanding it's thought process I can tweak it as needed to come as close to the stated goal as I can. 

Tim sent me a preliminary version of this some months back. He asked for my feedback which I gave him (I didn't like it for MY music) and he has since modified it so I'm game to give it a try. If I have to the first time around I'll use the machine but once I get the sense of it (if I like it) I know I can do it in analog fashion. I'll bet you can too (without anyone telling you how)!

Peter Grey Piano Doctor 

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

Original Message:
Sent: 01-06-2025 23:34
From: Ron Koval
Subject: Temperament experiment

I'll give it a try this week and hear how it plays - thanks for posting.

Ron Koval

------------------------------
Ron Koval
CHICAGO IL

Original Message:
Sent: 01-05-2025 22:19
From: Tim Foster
Subject: Temperament experiment

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074
------------------------------

Tim, 

Have you tried charting EBVT 1? It seems to me that it could be tweaked to have 1 or 2 more pure 5ths. Of course then it wouldn't be EBVT anymore, but hey...all UT's allow some personal expression. 

Peter Grey Piano Doctor 

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

Original Message:
Sent: 01-12-2025 17:27
From: Tim Foster
Subject: Temperament experiment

Hi Nicolas,

Thanks for including your offsets! I did chart your temperament and it's a really nice mild "Victorian" temperament with a good shape.  It looks similar to Ron Koval's Equal Well 1.3. My current interest is finding or creating circular temperaments that utilize pure fifths. EBVT III has 2, Young has 4, Vallotti 6, Kellner and Kirnberger III have 7. Large well scaled pianos can handle the stronger temperaments well and resonate unbelievably well. My interest is trying to find something that makes smaller pianos more settled and sound larger. I like Wendall's Natural Synchronous Well for small pianos (6 pure fifths and synchronizes all M/m 3rds), but I'm trying to find something that gives me the greatest "bang for the buck" on smaller pianos, since even ET fifths often sound noisy on small pianos. The Symmetrical Unequal in the OP is an attempt to experiment on how we can get greater resonance with very little deviation from the standard ET. I also just developed an more historical unequal temperament that utilizes the symmetry of my temperament in the OP. 

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074

Original Message:
Sent: 01-12-2025 15:39
From: Nicolas Lessard
Subject: Temperament experiment

Tim,

Did you have a chance to try the deviation I presented in a different thread several weeks ago?

It is in fact very similar to yours!

Here it is again:

A: 0
A#: +1
B: -1
C: +1
C#: -1
D: +1
D#: 0
E: -1
F: +1
F#: -1
G: +1
G#: 0

Cheers!


Original Message:
Sent: 1/11/2025 12:37:00 PM
From: Peter Grey
Subject: RE: Temperament experiment

Tim,

I noticed that fast G-B 3rd straight away. As you know, I'm not going to write this off. It needs more trials on several more pianos (particularly those I know well totally so as to compare). I don't think I'll bother on PSO since ET cannot even be accomplished anyway so it would be useless (I'll stick with EBVT on those), but on an instrument I know and usually do ET I'll play with it. The goal (as I see it) is an attempt to improve vibrational resonance without roo much departure from ET. (a.k.a. another alternative). 

Peter Grey Piano Doctor 

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

Original Message:
Sent: 01-11-2025 11:00
From: Tim Foster
Subject: Temperament experiment

Peter,

Thank you for your feedback! If I have to play in some semblance of ET, I would prefer this one, I feel like the clarity and resonance is improved. Historically, are you already know, C, F, and G are the "calmest" keys, and there is no way to keep the four symmetrical pure fifths without imposing a slightly wider third on one of these "calm" keys, at least with all other keys being equal.  In the current iteration, we could make it slightly more unequal which would place G-B closer to ET (14.15 cents wide, currently it's 15.65 cents wide) by raising the G-D pure fifth by half a cent and lowering the E-B pure fifth by 1 cent. This slightly improves some tempered fifths (C-G, B-F#) and slightly narrows others (D-A, A-E). Even so, both are slightly under 4 cents narrow, which is very usable in my book.

Thank again for giving it a shot! 

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074

Original Message:
Sent: 01-11-2025 08:36
From: Peter Grey
Subject: Temperament experiment

Tim,

I was able to give your pattern a try yesterday. I will say that the results were mixed and here's why:

Though I was going to do it on two different instruments I ended up only doing it on one, a 1985 SS K that I had only tuned once before and that was 5 years ago, so pitch correction was in order. Anyway I was quite able to produce the temperament aurally simply by tuning a very good ET and then by following your delineation of deviation from top to bottom (the order was ideal) it was relatively easy to approximate the 1 cent alterations, with the final proof being in the placement of pure 5ths. I then descended into the bass with slightly expanded 6:3 octaves consistently, and then into the remainder above with expanded 4:2 approximating pure 12ths (which is my usual procedure). 

While the piano sounded "good" (in fact I did praise the tone of the thing), there was a bit of distraction since the touch is unbelievably heavy due to excessive damper spring strength combined with very early damper pickup (clearly this way straight out of the factory). I of course pointed this out to the current owner of the piano and, though it can be improved, it would not be an easy job. However, this issue prevented me from really testing out the instrument, but also I had no way to really compare any resonance improvements (if any) under all these circumstances. Therefore I cannot attest to how much of what I heard was due to the altered tuning or if it's just the piano. Interestingly there was also a significant degree of background bass string leakage (activated worse in certain keys...which might be significant 😳) with which I had a "hmmm" moment. The jury is still out...

The second piano I realized when I got there that I have been tuning in EBVT so I decided to stick with that. Therefore no second chance on that one. 

I will do it again and try to evaluate things more objectively. 

Peter Grey Piano Doctor 

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

Original Message:
Sent: 01-10-2025 08:47
From: Peter Grey
Subject: Temperament experiment

Maggie,

I told Tim I was going to give it a go and I will attempt it today on one or two appts. It seems to me that since the deviations from ET are all the same (1 cent) it should be a rather simple matter of tuning a good aural temperament and then raising or lowering the prescribed notes by 1 cent (which can easily be done digitally at first...once the hearing is attuned to what it's "supposed" to sound like, it should be simple enough to create your own scheme to duplicate).  This is what I do with EBVT...I know the procedure, but more importantly I know what the end goal is in general (EBVT turns out different on each piano, esp little ones) but understanding it's thought process I can tweak it as needed to come as close to the stated goal as I can. 

Tim sent me a preliminary version of this some months back. He asked for my feedback which I gave him (I didn't like it for MY music) and he has since modified it so I'm game to give it a try. If I have to the first time around I'll use the machine but once I get the sense of it (if I like it) I know I can do it in analog fashion. I'll bet you can too (without anyone telling you how)!

Peter Grey Piano Doctor 

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

Original Message:
Sent: 01-06-2025 23:34
From: Ron Koval
Subject: Temperament experiment

I'll give it a try this week and hear how it plays - thanks for posting.

Ron Koval

------------------------------
Ron Koval
CHICAGO IL

Original Message:
Sent: 01-05-2025 22:19
From: Tim Foster
Subject: Temperament experiment

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

------------------------------
Tim Foster RPT
New Oxford PA
(470) 231-6074
------------------------------

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

Tim, thanks for sharing this.

As many know, I've been using very mild well temperaments as equal substitutes for many years. I've always come from the "focus on the thirds" design of temperaments, so this focus on the fifths as well as the symmetry of design resuting in a two-tier width of thirds is interesting. Even the EBVT variants are too strong for my ear. I've had a chance to tune a yet milder version due to the above mentioned G-B M3rd - I simply changed all of positive and negative offsets to .8 or -.8 which results in the same number of  "apparently pure" 5ths (Less than 0.2 beats/second) with a very slightly less jarring G-B. I appreciate subtle differences so really enjoy working with the milder changes that 'fly under the radar' yet result in tunings that generate comments that they just like my tunings better for some reason... For a C-C octave the M3rd progression from slowest to fastest looks to be C, D, D#, C#, F, F#, E, G#, A, G, B, A#.

I hardly tune ET anymore, so others will have to compare/contrast, but I found the alteration of Tim's SymmET to give a more bold feeling compared to the mild well temperament I use. I've set this on multiple grands at the U and one M&H 50 upright. I've asked one faculty member to let me know if he notices anything different about the tuning on one B in a teaching studio.

I'll start trying this on smaller instruments this weeek.

Ron Koval

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

Ron, 

Thanks for giving it a try, I'm looking forward to hearing what people think-- if they notice anything. Also, I haven't tried it on a smaller piano, just my "dummy" Yamaha U3. I still tune a lot of spinets and consoles, and I really think some of the mild to moderate unequal temperaments have a lot of potential in this arena. On spinets, playing with many sharps/flats is nearly impossible, since it sets the thumb on black keys, pushing fingers 2, 3, and 4 near the fallboard and way too close to the fulcrum (balance rail), making the black keys almost impossible to press down. Practically speaking, these keys are just not played that much on these pianos, so if some of the temperament "error" can be placed in its historic position, the potential to settle the poor scaling is real. Additionally, if we can improve resonance, it should effectively make the instrument sound bigger.  I've tried David Pinnegar's tuning on small pianos, and it really does improve clarity and resonance.  Unfortunately, the greater clarity accentuates the poor sound quality, not to mention the more tempered fifths start to sound really bad, especially if the voicing (or neglect of voicing) is bright. I want to find a middle ground. Spinets and consoles normally get either EBVT III or Wendall Natural Synchronous Well which tames the little beasts a little.

Peter,

I just charted EBVT I, very interesting. Thanks, Ron, for sending the offsets! I think I would personally like this more than EBVT III, but I don't think these four pure fifths with that placement (E-B, F#-C#, C#-G#, F-C) will consistently affect resonance across the entire piano. I do like the placement of the pure fifths very much in those keys, though. I might give this a try on some smaller instruments at some point.

Tim, thanks for sharing this.

As many know, I've been using very mild well temperaments as equal substitutes for many years. I've always come from the "focus on the thirds" design of temperaments, so this focus on the fifths as well as the symmetry of design resuting in a two-tier width of thirds is interesting. Even the EBVT variants are too strong for my ear. I've had a chance to tune a yet milder version due to the above mentioned G-B M3rd - I simply changed all of positive and negative offsets to .8 or -.8 which results in the same number of  "apparently pure" 5ths (Less than 0.2 beats/second) with a very slightly less jarring G-B. I appreciate subtle differences so really enjoy working with the milder changes that 'fly under the radar' yet result in tunings that generate comments that they just like my tunings better for some reason... For a C-C octave the M3rd progression from slowest to fastest looks to be C, D, D#, C#, F, F#, E, G#, A, G, B, A#.

I hardly tune ET anymore, so others will have to compare/contrast, but I found the alteration of Tim's SymmET to give a more bold feeling compared to the mild well temperament I use. I've set this on multiple grands at the U and one M&H 50 upright. I've asked one faculty member to let me know if he notices anything different about the tuning on one B in a teaching studio.

I'll start trying this on smaller instruments this weeek.

Ron Koval

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

Ron, 

Thanks for giving it a try, I'm looking forward to hearing what people think-- if they notice anything. Also, I haven't tried it on a smaller piano, just my "dummy" Yamaha U3. I still tune a lot of spinets and consoles, and I really think some of the mild to moderate unequal temperaments have a lot of potential in this arena. On spinets, playing with many sharps/flats is nearly impossible, since it sets the thumb on black keys, pushing fingers 2, 3, and 4 near the fallboard and way too close to the fulcrum (balance rail), making the black keys almost impossible to press down. Practically speaking, these keys are just not played that much on these pianos, so if some of the temperament "error" can be placed in its historic position, the potential to settle the poor scaling is real. Additionally, if we can improve resonance, it should effectively make the instrument sound bigger.  I've tried David Pinnegar's tuning on small pianos, and it really does improve clarity and resonance.  Unfortunately, the greater clarity accentuates the poor sound quality, not to mention the more tempered fifths start to sound really bad, especially if the voicing (or neglect of voicing) is bright. I want to find a middle ground. Spinets and consoles normally get either EBVT III or Wendall Natural Synchronous Well which tames the little beasts a little.

Peter,

I just charted EBVT I, very interesting. Thanks, Ron, for sending the offsets! I think I would personally like this more than EBVT III, but I don't think these four pure fifths with that placement (E-B, F#-C#, C#-G#, F-C) will consistently affect resonance across the entire piano. I do like the placement of the pure fifths very much in those keys, though. I might give this a try on some smaller instruments at some point.

Tim, thanks for sharing this.

As many know, I've been using very mild well temperaments as equal substitutes for many years. I've always come from the "focus on the thirds" design of temperaments, so this focus on the fifths as well as the symmetry of design resuting in a two-tier width of thirds is interesting. Even the EBVT variants are too strong for my ear. I've had a chance to tune a yet milder version due to the above mentioned G-B M3rd - I simply changed all of positive and negative offsets to .8 or -.8 which results in the same number of  "apparently pure" 5ths (Less than 0.2 beats/second) with a very slightly less jarring G-B. I appreciate subtle differences so really enjoy working with the milder changes that 'fly under the radar' yet result in tunings that generate comments that they just like my tunings better for some reason... For a C-C octave the M3rd progression from slowest to fastest looks to be C, D, D#, C#, F, F#, E, G#, A, G, B, A#.

I hardly tune ET anymore, so others will have to compare/contrast, but I found the alteration of Tim's SymmET to give a more bold feeling compared to the mild well temperament I use. I've set this on multiple grands at the U and one M&H 50 upright. I've asked one faculty member to let me know if he notices anything different about the tuning on one B in a teaching studio.

I'll start trying this on smaller instruments this weeek.

Ron Koval

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

Ron, 

Thanks for giving it a try, I'm looking forward to hearing what people think-- if they notice anything. Also, I haven't tried it on a smaller piano, just my "dummy" Yamaha U3. I still tune a lot of spinets and consoles, and I really think some of the mild to moderate unequal temperaments have a lot of potential in this arena. On spinets, playing with many sharps/flats is nearly impossible, since it sets the thumb on black keys, pushing fingers 2, 3, and 4 near the fallboard and way too close to the fulcrum (balance rail), making the black keys almost impossible to press down. Practically speaking, these keys are just not played that much on these pianos, so if some of the temperament "error" can be placed in its historic position, the potential to settle the poor scaling is real. Additionally, if we can improve resonance, it should effectively make the instrument sound bigger.  I've tried David Pinnegar's tuning on small pianos, and it really does improve clarity and resonance.  Unfortunately, the greater clarity accentuates the poor sound quality, not to mention the more tempered fifths start to sound really bad, especially if the voicing (or neglect of voicing) is bright. I want to find a middle ground. Spinets and consoles normally get either EBVT III or Wendall Natural Synchronous Well which tames the little beasts a little.

Peter,

I just charted EBVT I, very interesting. Thanks, Ron, for sending the offsets! I think I would personally like this more than EBVT III, but I don't think these four pure fifths with that placement (E-B, F#-C#, C#-G#, F-C) will consistently affect resonance across the entire piano. I do like the placement of the pure fifths very much in those keys, though. I might give this a try on some smaller instruments at some point.

Tim, thanks for sharing this.

As many know, I've been using very mild well temperaments as equal substitutes for many years. I've always come from the "focus on the thirds" design of temperaments, so this focus on the fifths as well as the symmetry of design resuting in a two-tier width of thirds is interesting. Even the EBVT variants are too strong for my ear. I've had a chance to tune a yet milder version due to the above mentioned G-B M3rd - I simply changed all of positive and negative offsets to .8 or -.8 which results in the same number of  "apparently pure" 5ths (Less than 0.2 beats/second) with a very slightly less jarring G-B. I appreciate subtle differences so really enjoy working with the milder changes that 'fly under the radar' yet result in tunings that generate comments that they just like my tunings better for some reason... For a C-C octave the M3rd progression from slowest to fastest looks to be C, D, D#, C#, F, F#, E, G#, A, G, B, A#.

I hardly tune ET anymore, so others will have to compare/contrast, but I found the alteration of Tim's SymmET to give a more bold feeling compared to the mild well temperament I use. I've set this on multiple grands at the U and one M&H 50 upright. I've asked one faculty member to let me know if he notices anything different about the tuning on one B in a teaching studio.

I'll start trying this on smaller instruments this weeek.

Ron Koval

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

Dear David,

While I understand your concern and admit that your method of tuning Kellner and Kirnberger III are my personal favorite tunings (and ones that I tune almost exclusively for my own clients with quality pianos), I also know that not everyone is going to jump on this tuning method for a couple reasons. 1) It is so different that it takes most technicians off guard (I very much include myself in this when I look back at my first time tuning it-- I thought your instructions were a little crazy), and 2) the exact method is not something that you want to freely publish and promote, for reasons I understand. In reality, Kellner and Kirnberger III-- as calculated by ETDs-- cannot do what your tuning method can do, so I am hesitant to tell other tuners that they should use these stronger temperaments when in reality they will likely be displeased with the results and believe that these stronger temperaments are just not for them.

My interest in sharing the temperament in the OP is not because I personally will use it that much, but because I think there are a number of people who would be willing to try it since it is so close to what they and their clients are used to. I almost exclusively play on pianos tuned to fairly strong unequal temperaments, and whenever I have to play in ET now, I find the piano boring, not only because of beat rate of the thirds, but the resonance that we both know is possible. An "almost ET" temperament such as in the OP has a good deal more resonance than regular ET, which itself makes the piano more exciting. One of my interests is promoting any tuning that enhances this resonance, as it will give an edge over electric keyboards, this alone hopefully being a reason for people to keep buying and tuning acoustic pianos.

Lastly, I hope that unequal tuning becomes more or less the norm in the future. For myself, it was EBVT III that gave me the courage to try something stronger. Perhaps people trying the temperament in the OP will understand something about the resonance that we both love so much and want to try something more. Perhaps they will not. Either way, I think the acoustic piano will be more enticing.

Ron, 

Thanks for giving it a try, I'm looking forward to hearing what people think-- if they notice anything. Also, I haven't tried it on a smaller piano, just my "dummy" Yamaha U3. I still tune a lot of spinets and consoles, and I really think some of the mild to moderate unequal temperaments have a lot of potential in this arena. On spinets, playing with many sharps/flats is nearly impossible, since it sets the thumb on black keys, pushing fingers 2, 3, and 4 near the fallboard and way too close to the fulcrum (balance rail), making the black keys almost impossible to press down. Practically speaking, these keys are just not played that much on these pianos, so if some of the temperament "error" can be placed in its historic position, the potential to settle the poor scaling is real. Additionally, if we can improve resonance, it should effectively make the instrument sound bigger.  I've tried David Pinnegar's tuning on small pianos, and it really does improve clarity and resonance.  Unfortunately, the greater clarity accentuates the poor sound quality, not to mention the more tempered fifths start to sound really bad, especially if the voicing (or neglect of voicing) is bright. I want to find a middle ground. Spinets and consoles normally get either EBVT III or Wendall Natural Synchronous Well which tames the little beasts a little.

Peter,

I just charted EBVT I, very interesting. Thanks, Ron, for sending the offsets! I think I would personally like this more than EBVT III, but I don't think these four pure fifths with that placement (E-B, F#-C#, C#-G#, F-C) will consistently affect resonance across the entire piano. I do like the placement of the pure fifths very much in those keys, though. I might give this a try on some smaller instruments at some point.

Tim, thanks for sharing this.

As many know, I've been using very mild well temperaments as equal substitutes for many years. I've always come from the "focus on the thirds" design of temperaments, so this focus on the fifths as well as the symmetry of design resuting in a two-tier width of thirds is interesting. Even the EBVT variants are too strong for my ear. I've had a chance to tune a yet milder version due to the above mentioned G-B M3rd - I simply changed all of positive and negative offsets to .8 or -.8 which results in the same number of  "apparently pure" 5ths (Less than 0.2 beats/second) with a very slightly less jarring G-B. I appreciate subtle differences so really enjoy working with the milder changes that 'fly under the radar' yet result in tunings that generate comments that they just like my tunings better for some reason... For a C-C octave the M3rd progression from slowest to fastest looks to be C, D, D#, C#, F, F#, E, G#, A, G, B, A#.

I hardly tune ET anymore, so others will have to compare/contrast, but I found the alteration of Tim's SymmET to give a more bold feeling compared to the mild well temperament I use. I've set this on multiple grands at the U and one M&H 50 upright. I've asked one faculty member to let me know if he notices anything different about the tuning on one B in a teaching studio.

I'll start trying this on smaller instruments this weeek.

Ron Koval

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

Dear David,

While I understand your concern and admit that your method of tuning Kellner and Kirnberger III are my personal favorite tunings (and ones that I tune almost exclusively for my own clients with quality pianos), I also know that not everyone is going to jump on this tuning method for a couple reasons. 1) It is so different that it takes most technicians off guard (I very much include myself in this when I look back at my first time tuning it-- I thought your instructions were a little crazy), and 2) the exact method is not something that you want to freely publish and promote, for reasons I understand. In reality, Kellner and Kirnberger III-- as calculated by ETDs-- cannot do what your tuning method can do, so I am hesitant to tell other tuners that they should use these stronger temperaments when in reality they will likely be displeased with the results and believe that these stronger temperaments are just not for them.

My interest in sharing the temperament in the OP is not because I personally will use it that much, but because I think there are a number of people who would be willing to try it since it is so close to what they and their clients are used to. I almost exclusively play on pianos tuned to fairly strong unequal temperaments, and whenever I have to play in ET now, I find the piano boring, not only because of beat rate of the thirds, but the resonance that we both know is possible. An "almost ET" temperament such as in the OP has a good deal more resonance than regular ET, which itself makes the piano more exciting. One of my interests is promoting any tuning that enhances this resonance, as it will give an edge over electric keyboards, this alone hopefully being a reason for people to keep buying and tuning acoustic pianos.

Lastly, I hope that unequal tuning becomes more or less the norm in the future. For myself, it was EBVT III that gave me the courage to try something stronger. Perhaps people trying the temperament in the OP will understand something about the resonance that we both love so much and want to try something more. Perhaps they will not. Either way, I think the acoustic piano will be more enticing.

Ron, 

Thanks for giving it a try, I'm looking forward to hearing what people think-- if they notice anything. Also, I haven't tried it on a smaller piano, just my "dummy" Yamaha U3. I still tune a lot of spinets and consoles, and I really think some of the mild to moderate unequal temperaments have a lot of potential in this arena. On spinets, playing with many sharps/flats is nearly impossible, since it sets the thumb on black keys, pushing fingers 2, 3, and 4 near the fallboard and way too close to the fulcrum (balance rail), making the black keys almost impossible to press down. Practically speaking, these keys are just not played that much on these pianos, so if some of the temperament "error" can be placed in its historic position, the potential to settle the poor scaling is real. Additionally, if we can improve resonance, it should effectively make the instrument sound bigger.  I've tried David Pinnegar's tuning on small pianos, and it really does improve clarity and resonance.  Unfortunately, the greater clarity accentuates the poor sound quality, not to mention the more tempered fifths start to sound really bad, especially if the voicing (or neglect of voicing) is bright. I want to find a middle ground. Spinets and consoles normally get either EBVT III or Wendall Natural Synchronous Well which tames the little beasts a little.

Peter,

I just charted EBVT I, very interesting. Thanks, Ron, for sending the offsets! I think I would personally like this more than EBVT III, but I don't think these four pure fifths with that placement (E-B, F#-C#, C#-G#, F-C) will consistently affect resonance across the entire piano. I do like the placement of the pure fifths very much in those keys, though. I might give this a try on some smaller instruments at some point.

Tim, thanks for sharing this.

As many know, I've been using very mild well temperaments as equal substitutes for many years. I've always come from the "focus on the thirds" design of temperaments, so this focus on the fifths as well as the symmetry of design resuting in a two-tier width of thirds is interesting. Even the EBVT variants are too strong for my ear. I've had a chance to tune a yet milder version due to the above mentioned G-B M3rd - I simply changed all of positive and negative offsets to .8 or -.8 which results in the same number of  "apparently pure" 5ths (Less than 0.2 beats/second) with a very slightly less jarring G-B. I appreciate subtle differences so really enjoy working with the milder changes that 'fly under the radar' yet result in tunings that generate comments that they just like my tunings better for some reason... For a C-C octave the M3rd progression from slowest to fastest looks to be C, D, D#, C#, F, F#, E, G#, A, G, B, A#.

I hardly tune ET anymore, so others will have to compare/contrast, but I found the alteration of Tim's SymmET to give a more bold feeling compared to the mild well temperament I use. I've set this on multiple grands at the U and one M&H 50 upright. I've asked one faculty member to let me know if he notices anything different about the tuning on one B in a teaching studio.

I'll start trying this on smaller instruments this weeek.

Ron Koval

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

Dear David,

While I understand your concern and admit that your method of tuning Kellner and Kirnberger III are my personal favorite tunings (and ones that I tune almost exclusively for my own clients with quality pianos), I also know that not everyone is going to jump on this tuning method for a couple reasons. 1) It is so different that it takes most technicians off guard (I very much include myself in this when I look back at my first time tuning it-- I thought your instructions were a little crazy), and 2) the exact method is not something that you want to freely publish and promote, for reasons I understand. In reality, Kellner and Kirnberger III-- as calculated by ETDs-- cannot do what your tuning method can do, so I am hesitant to tell other tuners that they should use these stronger temperaments when in reality they will likely be displeased with the results and believe that these stronger temperaments are just not for them.

My interest in sharing the temperament in the OP is not because I personally will use it that much, but because I think there are a number of people who would be willing to try it since it is so close to what they and their clients are used to. I almost exclusively play on pianos tuned to fairly strong unequal temperaments, and whenever I have to play in ET now, I find the piano boring, not only because of beat rate of the thirds, but the resonance that we both know is possible. An "almost ET" temperament such as in the OP has a good deal more resonance than regular ET, which itself makes the piano more exciting. One of my interests is promoting any tuning that enhances this resonance, as it will give an edge over electric keyboards, this alone hopefully being a reason for people to keep buying and tuning acoustic pianos.

Lastly, I hope that unequal tuning becomes more or less the norm in the future. For myself, it was EBVT III that gave me the courage to try something stronger. Perhaps people trying the temperament in the OP will understand something about the resonance that we both love so much and want to try something more. Perhaps they will not. Either way, I think the acoustic piano will be more enticing.

Ron, 

Thanks for giving it a try, I'm looking forward to hearing what people think-- if they notice anything. Also, I haven't tried it on a smaller piano, just my "dummy" Yamaha U3. I still tune a lot of spinets and consoles, and I really think some of the mild to moderate unequal temperaments have a lot of potential in this arena. On spinets, playing with many sharps/flats is nearly impossible, since it sets the thumb on black keys, pushing fingers 2, 3, and 4 near the fallboard and way too close to the fulcrum (balance rail), making the black keys almost impossible to press down. Practically speaking, these keys are just not played that much on these pianos, so if some of the temperament "error" can be placed in its historic position, the potential to settle the poor scaling is real. Additionally, if we can improve resonance, it should effectively make the instrument sound bigger.  I've tried David Pinnegar's tuning on small pianos, and it really does improve clarity and resonance.  Unfortunately, the greater clarity accentuates the poor sound quality, not to mention the more tempered fifths start to sound really bad, especially if the voicing (or neglect of voicing) is bright. I want to find a middle ground. Spinets and consoles normally get either EBVT III or Wendall Natural Synchronous Well which tames the little beasts a little.

Peter,

I just charted EBVT I, very interesting. Thanks, Ron, for sending the offsets! I think I would personally like this more than EBVT III, but I don't think these four pure fifths with that placement (E-B, F#-C#, C#-G#, F-C) will consistently affect resonance across the entire piano. I do like the placement of the pure fifths very much in those keys, though. I might give this a try on some smaller instruments at some point.

Tim, thanks for sharing this.

As many know, I've been using very mild well temperaments as equal substitutes for many years. I've always come from the "focus on the thirds" design of temperaments, so this focus on the fifths as well as the symmetry of design resuting in a two-tier width of thirds is interesting. Even the EBVT variants are too strong for my ear. I've had a chance to tune a yet milder version due to the above mentioned G-B M3rd - I simply changed all of positive and negative offsets to .8 or -.8 which results in the same number of  "apparently pure" 5ths (Less than 0.2 beats/second) with a very slightly less jarring G-B. I appreciate subtle differences so really enjoy working with the milder changes that 'fly under the radar' yet result in tunings that generate comments that they just like my tunings better for some reason... For a C-C octave the M3rd progression from slowest to fastest looks to be C, D, D#, C#, F, F#, E, G#, A, G, B, A#.

I hardly tune ET anymore, so others will have to compare/contrast, but I found the alteration of Tim's SymmET to give a more bold feeling compared to the mild well temperament I use. I've set this on multiple grands at the U and one M&H 50 upright. I've asked one faculty member to let me know if he notices anything different about the tuning on one B in a teaching studio.

I'll start trying this on smaller instruments this weeek.

Ron Koval

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

Dear David,

While I understand your concern and admit that your method of tuning Kellner and Kirnberger III are my personal favorite tunings (and ones that I tune almost exclusively for my own clients with quality pianos), I also know that not everyone is going to jump on this tuning method for a couple reasons. 1) It is so different that it takes most technicians off guard (I very much include myself in this when I look back at my first time tuning it-- I thought your instructions were a little crazy), and 2) the exact method is not something that you want to freely publish and promote, for reasons I understand. In reality, Kellner and Kirnberger III-- as calculated by ETDs-- cannot do what your tuning method can do, so I am hesitant to tell other tuners that they should use these stronger temperaments when in reality they will likely be displeased with the results and believe that these stronger temperaments are just not for them.

My interest in sharing the temperament in the OP is not because I personally will use it that much, but because I think there are a number of people who would be willing to try it since it is so close to what they and their clients are used to. I almost exclusively play on pianos tuned to fairly strong unequal temperaments, and whenever I have to play in ET now, I find the piano boring, not only because of beat rate of the thirds, but the resonance that we both know is possible. An "almost ET" temperament such as in the OP has a good deal more resonance than regular ET, which itself makes the piano more exciting. One of my interests is promoting any tuning that enhances this resonance, as it will give an edge over electric keyboards, this alone hopefully being a reason for people to keep buying and tuning acoustic pianos.

Lastly, I hope that unequal tuning becomes more or less the norm in the future. For myself, it was EBVT III that gave me the courage to try something stronger. Perhaps people trying the temperament in the OP will understand something about the resonance that we both love so much and want to try something more. Perhaps they will not. Either way, I think the acoustic piano will be more enticing.

Ron, 

Thanks for giving it a try, I'm looking forward to hearing what people think-- if they notice anything. Also, I haven't tried it on a smaller piano, just my "dummy" Yamaha U3. I still tune a lot of spinets and consoles, and I really think some of the mild to moderate unequal temperaments have a lot of potential in this arena. On spinets, playing with many sharps/flats is nearly impossible, since it sets the thumb on black keys, pushing fingers 2, 3, and 4 near the fallboard and way too close to the fulcrum (balance rail), making the black keys almost impossible to press down. Practically speaking, these keys are just not played that much on these pianos, so if some of the temperament "error" can be placed in its historic position, the potential to settle the poor scaling is real. Additionally, if we can improve resonance, it should effectively make the instrument sound bigger.  I've tried David Pinnegar's tuning on small pianos, and it really does improve clarity and resonance.  Unfortunately, the greater clarity accentuates the poor sound quality, not to mention the more tempered fifths start to sound really bad, especially if the voicing (or neglect of voicing) is bright. I want to find a middle ground. Spinets and consoles normally get either EBVT III or Wendall Natural Synchronous Well which tames the little beasts a little.

Peter,

I just charted EBVT I, very interesting. Thanks, Ron, for sending the offsets! I think I would personally like this more than EBVT III, but I don't think these four pure fifths with that placement (E-B, F#-C#, C#-G#, F-C) will consistently affect resonance across the entire piano. I do like the placement of the pure fifths very much in those keys, though. I might give this a try on some smaller instruments at some point.

Tim, thanks for sharing this.

As many know, I've been using very mild well temperaments as equal substitutes for many years. I've always come from the "focus on the thirds" design of temperaments, so this focus on the fifths as well as the symmetry of design resuting in a two-tier width of thirds is interesting. Even the EBVT variants are too strong for my ear. I've had a chance to tune a yet milder version due to the above mentioned G-B M3rd - I simply changed all of positive and negative offsets to .8 or -.8 which results in the same number of  "apparently pure" 5ths (Less than 0.2 beats/second) with a very slightly less jarring G-B. I appreciate subtle differences so really enjoy working with the milder changes that 'fly under the radar' yet result in tunings that generate comments that they just like my tunings better for some reason... For a C-C octave the M3rd progression from slowest to fastest looks to be C, D, D#, C#, F, F#, E, G#, A, G, B, A#.

I hardly tune ET anymore, so others will have to compare/contrast, but I found the alteration of Tim's SymmET to give a more bold feeling compared to the mild well temperament I use. I've set this on multiple grands at the U and one M&H 50 upright. I've asked one faculty member to let me know if he notices anything different about the tuning on one B in a teaching studio.

I'll start trying this on smaller instruments this weeek.

Ron Koval

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99

Hello, I would love some feedback on a temperament I created. It should pass for equal temperament in how it sounds and functions, though in reality it is unequal (but not in any historical sense).

I tune my own grand pianos to a modified Kirnberger III and love it, mostly using David Pinnegar's formula. One thing I've noticed is that unequal temperaments in general, and especially certain ones, make the piano considerably more resonant. I did a technical at my chapter on the subject late last year, having a Steinway O tuned to Kirnberger III and a Steinway L tuned to ET.  Without question to the group, the O was far more resonant, which could be proven through ghosting intervals on each piano separately, listening to the volume and sustain. For me, this translates a more exciting performance with the added benefits of greater clarity and sustain.

My observation is that unequal temperaments that have larger numbers of pure 5ths become noticeably more resonant, especially when every chord has at least one note that is "linked" to a pure fifth, at least this is my hypothesis. To test, I created a temperament I'm calling "symmetrical unequal," which symmetrically places four pure fifths spaced in minor 3rds (C#-G#, E-B, G-D, Bb-F). This allows every major and minor chord to have 1-3 notes "linked" to pure fifths. To make this possible, the eight other tempered fifths are slightly increased to nearly 3 cents narrow. Major 3rds surrounded by the pure fifths are slightly more tempered (a little over 15 cents wide) and major 3rds between tempered fifths are slightly better than ET, of course. Minor 3rds retain the same beat rates as ET.

I've included the offsets below. Again, I would love your feedback! To my ear, the piano feels more resonant and clear, but plays like ET. It's also possible that after trying so many temperaments, my brain is playing tricks on me. 😂

Symmetrical Unequal Temperament 

C 0
C# -0.97
D 0.99
D# 0
E -0.97
F 0.99
F# 0
G -0.97
G# 0.99
A 0
A# -0.97
B 0.99