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Aural temperament sequences are like noses. Everyone has one and they all smell.

Likewise, there are many definitions of what it means to have an equal temperament on an actual piano with inharmonicity. We can't just go by frequencies, we have to look at beatrates.

Few would argue with a definition of ET on an inharmonic piano being when the beatrate of the M3s and the m3s (or M6s) are progressive. From previous Topics where posters shared their best efforts in setting a temperament, not only is it very rare for a temperament to meet this standard, but few or perhaps none of us consistently perceive when the RBIs are actually progressive.

I have studied many aural temperament sequences and noticed that they all require assumptions of the beat speed of the 4ths, and/or 5ths, which are proved to be correct or incorrect until no sooner than the 8th "named note" is tuned. By "named note" I mean that if tuning a ladder of CM3s: F3 - A3 - C#4 - F4 - A4 it counts as only 3 named notes F - A - C#. In other words there are only 12 "named notes", octaves don't count. At some point an RBI is tuned that either is, or is not, progressive with other RBIs. Btw, the M6-M3 outside/inside check just doesn't work in this instance but you can try to prove me wrong.

I have every reason to believe that the difficulty lies in getting the beat speed of both the 4ths and the 5ths correct. But there may be ways of looking at the aural temperament sequences that have not occurred to me. That is the real purpose of this Topic, to find different ways of looking at aural temperament sequences, not to just prove or disprove my own beliefs.

So here is my challenge: Show me an aural tuning sequence where the assumed beat speeds of the SBIs are proved correct before the 8th (when spanning a 5th) or the 9th (when spanning an octave) "named note". Or even, if you can, that an aural tuning sequence does not require the SBIs to be correct and still have the M3s and m3s (or M6s) progressive. And to be grounded in reality, the temperament must be able to be expanded and continue to have progressive RBIs. For example, an octave temperament where the M3s are nearly all the same beat speed, but still progressive, cannot be expanded and continue to have the RBIs progressive.

Oh, and Merry Christmas!


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I’m not sure I fully understand what you’re asking, but I’ll reply with the sequence I was taught (though I rarely use it exactly as described) and you can draw your own conclusions smile

A3->D3 (SBI)
A3->F3
D3->F#3
F#->A#3
D3->D4
A#3/Bb3->Eb3 (SBI)
Eb3->G3
G3->B3
Eb3->Eb4 (9th note...?)
B3->E3 (SBI)
E3->G#3
G#3->B#3/C4
E3->E4
C4->F3 (SBI, already set)
F3->A3 (already set)
A3->C#4
F3->F4

There are various checks which can be made during the sequence, such as comparing 3rds to aim for progressive beat speeds, or at the beginning comparing the M3/m3 for the A->D 5th check, etc.

Years ago I devised what I consider to be a sensible temperament sequence that I felt was better than the above at minimising errors, but I’ve never used it smile I can add it to the mix here if you’re interested.

Merry Christmas to you!

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Have not done aural tuning since I semi retired and took on one concert venu. With help we did master tunings like a PTG CTE would do and recorded them on ETD’s so whoever tuned would tune the same - it made for great stability but degraded my aural sequence ability.
Typically I used a two octave temperament as I like to include the lo tenor where lo tension and high inharmonicity happens.
I like to let the octave define the temperament.
So set A4 tune A3 slightly wide and use F3 for 3rd 10th test. I memorized 7 bps for F3 A3.
Next tune F3 to F4 much the same way and when ready, make C#4 fit in order to create cm3’s F3, A3, C#4, F4 and A4. If it don’t work simply readjust the A3 A4 octave until it does. I can describe the sequence after that but it usually works out so that everything fits and if compromises need to happen I let the 4ths and 5ths drift out a bit.

Merry Christmas 🎄


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Jeff,

I have used the following pattern (when I tune ET) for well over 20 years. Providing that you get the F3-A3 3RD exactly right (for that piano) the rest works out flawlessly with 4ths at about 1bps~. It should go w/o saying that 3RDS must progress "evenly".

A4-A3 OCTV
A3-F3 3RD
F3-A#3 4TH
A#3-F#3 3RD
F#3-B3 4TH
B3-G3 3RD
G3-C4 4TH
C4-G#3 3RD
G#3-C#4 4TH
A#3-D4 3RD
B3-D#4 3RD
C4-E4 3RD
C#4-F4 3RD/OCTV


No checks until C#4. But that is no problem since the sequence up to that point rarely takes more than 2 minutes. When arriving at C#4, if it does not come out right on the money, 30 seconds of deduction to determine whether the problem is in the 4THS or the 3RDS or possibly a combination. Correct, and tune the last 4 3RDS and move on.

IF you want simulate a P12TH temperament, speed up both 4THS and 3RDS a tad. This will result in the OCTV a little wider, and 5THS close to pure.

I do not use 5THS as a "tuning" interval...only a quick check interval. If the 3RDS and 4THS are correct, the 5THS have no choice other than to be correct (for that piano). Everything is tailored to what the piano "tells" me. Yes...they talk back.

There is a process for determining the "correct" speed of the F3-A3 3RD (Jack Stebbins published this in a PTJ article a number if years ago). This process is brilliant, however by the time I go through it to make the determination, I could have tuned the temperament twice through already. Therefore I generally choose to guess (based on the relative size, quality, and observable scaling of the instrument) and go. If I need to go back, I don't care as I can usually fix it quickly.

That's my story and I'm stickin' with it.

Peter Grey Piano Doctor


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Jeff,

I have used the following pattern (when I tune ET) for well over 20 years. Providing that you get the F3-A3 3RD exactly right (for that piano) the rest works out flawlessly with 4ths at about 1bps~. It should go w/o saying that 3RDS must progress "evenly".

A4-A3 OCTV
A3-F3 3RD
F3-A#3 4TH
A#3-F#3 3RD
F#3-B3 4TH
B3-G3 3RD
G3-C4 4TH
C4-G#3 3RD
G#3-C#4 4TH
A#3-D4 3RD
B3-D#4 3RD
C4-E4 3RD
C#4-F4 3RD/OCTV


No checks until C#4. But that is no problem since the sequence up to that point rarely takes more than 2 minutes. When arriving at C#4, if it does not come out right on the money, 30 seconds of deduction to determine whether the problem is in the 4THS or the 3RDS or possibly a combination. Correct, and tune the last 4 3RDS and move on.

IF you want simulate a P12TH temperament, speed up both 4THS and 3RDS a tad. This will result in the OCTV a little wider, and 5THS close to pure.

I do not use 5THS as a "tuning" interval...only a quick check interval. If the 3RDS and 4THS are correct, the 5THS have no choice other than to be correct (for that piano). Everything is tailored to what the piano "tells" me. Yes...they talk back.

There is a process for determining the "correct" speed of the F3-A3 3RD (Jack Stebbins published this in a PTJ article a number if years ago). This process is brilliant, however by the time I go through it to make the determination, I could have tuned the temperament twice through already. Therefore I generally choose to guess (based on the relative size, quality, and observable scaling of the instrument) and go. If I need to go back, I don't care as I can usually fix it quickly.

That's my story and I'm stickin' with it.

Peter Grey Piano Doctor


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Oops...sorry for the double post. Did not intend that to happen.

Peter Grey Piano Doctor


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Greetings,
When tuning aurally, I use a C fork.

From C I tune down a 5th to the F with the m3/M3 test, leaving a fifth that I know to be tempered narrow. Then I tune a tempered 4th up from C, using the M3/M6 test. Then I listen to what kind of octave the piano will deliver. If it show itself to be "good", I tune the Bb between my F's. Once I have the octave containing these two fifth and two fourths, it is rather easy to make decisions on how much stretching is needed.

After that I tune, beginning on C, G3,D4,A3,E4,B3,F#3,C#4,Ab3,Eb4,

There are checks along the way, gradually increasing in number as I progress. When the E4 is tuned, I expect to hear 7-8-9-10 bps, respectively, from the F-A,F-D,G-E,C-E. following that is comparing the G-B M3 to the F-D 6th. when the F# is tuned, I can see if the F#-Bb third is evenly between it adjacent thirds. When the C# is tuned as a fifth to the F#, I can compare the A-C# to the G-E 6th. Temper the G# from the C# and I can tell if it lies between its adjacent thirds, the G#
-F 6th should be 1/2 bps faster than the G-E.

This temperament will stop the lights on my SAT's norma FAC, which is pretty close to as evenly tempered as most pianos will allow. By deciding on the relationship of fifth to octave at the very beginning, i have established the limits I need to observe in all the fifths.
Regards,

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Originally Posted by jsilva
I’m not sure I fully understand what you’re asking, but I’ll reply with the sequence I was taught (though I rarely use it exactly as described) and you can draw your own conclusions smile

A3->D3 (SBI)
A3->F3
D3->F#3
F#->A#3
D3->D4
A#3/Bb3->Eb3 (SBI)
Eb3->G3
G3->B3
Eb3->Eb4 (9th note...?)
B3->E3 (SBI)
E3->G#3
G#3->B#3/C4
E3->E4
C4->F3 (SBI, already set)
F3->A3 (already set)
A3->C#4
F3->F4

There are various checks which can be made during the sequence, such as comparing 3rds to aim for progressive beat speeds, or at the beginning comparing the M3/m3 for the A->D 5th check, etc.

Years ago I devised what I consider to be a sensible temperament sequence that I felt was better than the above at minimising errors, but I’ve never used it smile I can add it to the mix here if you’re interested.

Merry Christmas to you!

Thanks! Basically up a 3rd, up 3rd, down a 5th with octaves added in to span from D3 to F4. Seems odd it doesn't go to F#4. But E3 I think is the ninth note. Let's see: A, D, F, F#, A#, D#, G, B, E, G#, C, C#. OK, now if the 5ths are tuned too pure where would it show up? Not sure as F and A are tuned early, but C# is last. I'll have to think a bit...

But YEAH, please let us know your "sensible" temperament sequence and most importantly why.


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Originally Posted by Gene Nelson
Have not done aural tuning since I semi retired and took on one concert venu. With help we did master tunings like a PTG CTE would do and recorded them on ETD’s so whoever tuned would tune the same - it made for great stability but degraded my aural sequence ability.
Typically I used a two octave temperament as I like to include the lo tenor where lo tension and high inharmonicity happens.
I like to let the octave define the temperament.
So set A4 tune A3 slightly wide and use F3 for 3rd 10th test. I memorized 7 bps for F3 A3.
Next tune F3 to F4 much the same way and when ready, make C#4 fit in order to create cm3’s F3, A3, C#4, F4 and A4. If it don’t work simply readjust the A3 A4 octave until it does. I can describe the sequence after that but it usually works out so that everything fits and if compromises need to happen I let the 4ths and 5ths drift out a bit.

Merry Christmas 🎄


Thanks, Gene. Looks like another up a third up a third, down a 5th but starting with a CM3 ladder spanning a 10th, as many modern temperaments do. Then "... if compromises need to happen I let the 4ths and 5ths drift out a bit." Alrighty then!


Jeff Deutschle
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Originally Posted by P W Grey
Jeff,

I have used the following pattern (when I tune ET) for well over 20 years. Providing that you get the F3-A3 3RD exactly right (for that piano) the rest works out flawlessly with 4ths at about 1bps~. It should go w/o saying that 3RDS must progress "evenly".

A4-A3 OCTV
A3-F3 3RD
F3-A#3 4TH
A#3-F#3 3RD
F#3-B3 4TH
B3-G3 3RD
G3-C4 4TH
C4-G#3 3RD
G#3-C#4 4TH
A#3-D4 3RD
B3-D#4 3RD
C4-E4 3RD
C#4-F4 3RD/OCTV


No checks until C#4. But that is no problem since the sequence up to that point rarely takes more than 2 minutes. When arriving at C#4, if it does not come out right on the money, 30 seconds of deduction to determine whether the problem is in the 4THS or the 3RDS or possibly a combination. Correct, and tune the last 4 3RDS and move on.

IF you want simulate a P12TH temperament, speed up both 4THS and 3RDS a tad. This will result in the OCTV a little wider, and 5THS close to pure.

I do not use 5THS as a "tuning" interval...only a quick check interval. If the 3RDS and 4THS are correct, the 5THS have no choice other than to be correct (for that piano). Everything is tailored to what the piano "tells" me. Yes...they talk back.

There is a process for determining the "correct" speed of the F3-A3 3RD (Jack Stebbins published this in a PTJ article a number if years ago). This process is brilliant, however by the time I go through it to make the determination, I could have tuned the temperament twice through already. Therefore I generally choose to guess (based on the relative size, quality, and observable scaling of the instrument) and go. If I need to go back, I don't care as I can usually fix it quickly.

That's my story and I'm stickin' with it.

Peter Grey Piano Doctor

Wow, cool. I think the accuracy would rely on beatrate memory and progression memory. You say no checks until the 9th note, which is probably predictable. "If the 3RDS and 4THS are correct, the 5THS have no choice other than to be correct (for that piano)." Well, maybe and maybe only for that sequence, and maybe only for you. Another thing for me to consider, which is EXACTLY why I started this Topic. Thanks!


Jeff Deutschle
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Originally Posted by Ed Foote
Greetings,
When tuning aurally, I use a C fork.

From C I tune down a 5th to the F with the m3/M3 test, leaving a fifth that I know to be tempered narrow. Then I tune a tempered 4th up from C, using the M3/M6 test. Then I listen to what kind of octave the piano will deliver. If it show itself to be "good", I tune the Bb between my F's. Once I have the octave containing these two fifth and two fourths, it is rather easy to make decisions on how much stretching is needed.

After that I tune, beginning on C, G3,D4,A3,E4,B3,F#3,C#4,Ab3,Eb4,

There are checks along the way, gradually increasing in number as I progress. When the E4 is tuned, I expect to hear 7-8-9-10 bps, respectively, from the F-A,F-D,G-E,C-E. following that is comparing the G-B M3 to the F-D 6th. when the F# is tuned, I can see if the F#-Bb third is evenly between it adjacent thirds. When the C# is tuned as a fifth to the F#, I can compare the A-C# to the G-E 6th. Temper the G# from the C# and I can tell if it lies between its adjacent thirds, the G#
-F 6th should be 1/2 bps faster than the G-E.

This temperament will stop the lights on my SAT's norma FAC, which is pretty close to as evenly tempered as most pianos will allow. By deciding on the relationship of fifth to octave at the very beginning, i have established the limits I need to observe in all the fifths.
Regards,

Thanks Mr. Foote:

A 4th and 5th sequence! And determining how they should sound and the size of the octave at the beginning. Not every tuner appreciates the richness of the SBIs, especially the 5ths. It was pointed out to me once that with the M6 outside, M3 inside test, the M3 beats a bit slower and that when considering inharmonicity and any additional stretch it might be better to use the M3 that is a semitone higher, or at least allow the M3 be a bit slower than the M6. Have you noticed that at all?

OK F#3 is the ninth note. This is the first instance of tuning the lower note of an M3 and as you note it fits chromatically between two other M3s. If the SBIs are tempered too much, F#-A# will beat too fast; if tempered too little it will beat too slow. Before that, a tuner might not know if their tempering of the SBIs is correct.


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Hey Folks, this Topic is about how others tune, not how I do. But by coincidence I was asked for my sequence in the IC Tuner Topic. You can see it there and make comments there if you wish. But let's try not to slosh back and forth between the two. The other Topic is really to help Bill. Seems he is willing to alter his app to specifically meet our needs.


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Originally Posted by UnrightTooner
Originally Posted by Gene Nelson
Have not done aural tuning since I semi retired and took on one concert venu. With help we did master tunings like a PTG CTE would do and recorded them on ETD’s so whoever tuned would tune the same - it made for great stability but degraded my aural sequence ability.
Typically I used a two octave temperament as I like to include the lo tenor where lo tension and high inharmonicity happens.
I like to let the octave define the temperament.
So set A4 tune A3 slightly wide and use F3 for 3rd 10th test. I memorized 7 bps for F3 A3.
Next tune F3 to F4 much the same way and when ready, make C#4 fit in order to create cm3’s F3, A3, C#4, F4 and A4. If it don’t work simply readjust the A3 A4 octave until it does. I can describe the sequence after that but it usually works out so that everything fits and if compromises need to happen I let the 4ths and 5ths drift out a bit.

Merry Christmas 🎄


Thanks, Gene. Looks like another up a third up a third, down a 5th but starting with a CM3 ladder spanning a 10th, as many modern temperaments do. Then "... if compromises need to happen I let the 4ths and 5ths drift out a bit." Alrighty then!
Originally Posted by UnrightTooner
Originally Posted by Gene Nelson
Have not done aural tuning since I semi retired and took on one concert venu. With help we did master tunings like a PTG CTE would do and recorded them on ETD’s so whoever tuned would tune the same - it made for great stability but degraded my aural sequence ability.
Typically I used a two octave temperament as I like to include the lo tenor where lo tension and high inharmonicity happens.
I like to let the octave define the temperament.
So set A4 tune A3 slightly wide and use F3 for 3rd 10th test. I memorized 7 bps for F3 A3.
Next tune F3 to F4 much the same way and when ready, make C#4 fit in order to create cm3’s F3, A3, C#4, F4 and A4. If it don’t work simply readjust the A3 A4 octave until it does. I can describe the sequence after that but it usually works out so that everything fits and if compromises need to happen I let the 4ths and 5ths drift out a bit.

Merry Christmas 🎄


Thanks, Gene. Looks like another up a third up a third, down a 5th but starting with a CM3 ladder spanning a 10th, as many modern temperaments do. Then "... if compromises need to happen I let the 4ths and 5ths drift out a bit." Alrighty then!

An example of checks after getting CM3’s close as possible is to tune A#3 to F3 as a P4 and D4 to A3 as a P 4 then listen to beat rates F3-A3= 7, F3-D4(6th) =8 and A#3-D4=9 then already tuned C#4-A3 should be a hair slower than A#3-D4. If there are any problems this is where they show up and it’s usually the C#4. From here it’s easy to start extending down toward A-2 with octaves or 4ths/5ths and RBI checks.


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I'll be away from the internet for a number of days (Ahhh...), so don't think I am ignoring this Topic. I'll make replies when I return from the "real" world.


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Hi Jeff. Hope you had a good few days away.

The topic of aural temperament setting is always close to me as well since I do it at least once almost every day and on all types of pianos. A satisfacory equal temperament as practical as possible in the first five or six minutes is the aim, but there times when I chose to, or am required to, tune an unequal temperament.

I am always keen to try and experiment with new temperament sequences and I usually find myself casually switching methods in subtle ways every few weeks or so just for the variety.

The approach that I first learnt some 50 years ago now, and that seems generally to result in the best outcome, is the the traditional and time honoured 4th and 5th sequence from A4 with careful evaluation of M3rds and M6ths and their progression as they appear. A common element to my method also is that of balancing 4ths and 5ths for a note from an already established M2nd. Establishing a contiguous M3rd ladder is also often a great help in providing semi-immutable anchor points, but not necessary.

Evenly progressive M3rds and at least one other progressive interval as well may define equal temperament in theory, but is not worth loosing sleep over if it is not absolutely perfect. I personally place more emphasis on even sounding tempered 4ths and 5ths and their particular tempered sound. I always finish a temperament tuning with balancing the 4ths and 5ths with the established M2nds. In fact, iterating that method more that once tends to converge the temperament closer to equal. There is also the opportunity then to more carefully set and render the strings at the same time with appropriate hammer manipulation. That is something that experience teaches despite everybody seeming to think that they are the expert.

Aural tuning temperament sequences is interesting. I have used an ETD for a while but it became sooooo boring, and the results often were not so perfect.


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One has to find out what the piano will give you when you temper it. And I mean the whole compass, not just an octave or two in the middle. Like Gene says, it all starts with octave widths. Then you figure out how to divide them as evenly as possible.

Like Peter notes, the 4ths at around 1bps in the f33-f45 octave are the most common result. So start with those rates and see what you get in the 5ths and octaves connected to the 4th.

So interval sequence does not need to be set in stone. I change mine up as I go. I just get in there and start tuning and follow my ear where it takes me.


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Originally Posted by UnrightTooner
Originally Posted by P W Grey
Jeff,

I have used the following pattern (when I tune ET) for well over 20 years. Providing that you get the F3-A3 3RD exactly right (for that piano) the rest works out flawlessly with 4ths at about 1bps~. It should go w/o saying that 3RDS must progress "evenly".

A4-A3 OCTV
A3-F3 3RD
F3-A#3 4TH
A#3-F#3 3RD
F#3-B3 4TH
B3-G3 3RD
G3-C4 4TH
C4-G#3 3RD
G#3-C#4 4TH
A#3-D4 3RD
B3-D#4 3RD
C4-E4 3RD
C#4-F4 3RD/OCTV


No checks until C#4. But that is no problem since the sequence up to that point rarely takes more than 2 minutes. When arriving at C#4, if it does not come out right on the money, 30 seconds of deduction to determine whether the problem is in the 4THS or the 3RDS or possibly a combination. Correct, and tune the last 4 3RDS and move on.

IF you want simulate a P12TH temperament, speed up both 4THS and 3RDS a tad. This will result in the OCTV a little wider, and 5THS close to pure.

I do not use 5THS as a "tuning" interval...only a quick check interval. If the 3RDS and 4THS are correct, the 5THS have no choice other than to be correct (for that piano). Everything is tailored to what the piano "tells" me. Yes...they talk back.

There is a process for determining the "correct" speed of the F3-A3 3RD (Jack Stebbins published this in a PTJ article a number if years ago). This process is brilliant, however by the time I go through it to make the determination, I could have tuned the temperament twice through already. Therefore I generally choose to guess (based on the relative size, quality, and observable scaling of the instrument) and go. If I need to go back, I don't care as I can usually fix it quickly.

That's my story and I'm stickin' with it.

Peter Grey Piano Doctor

Wow, cool. I think the accuracy would rely on beatrate memory and progression memory. You say no checks until the 9th note, which is probably predictable. "If the 3RDS and 4THS are correct, the 5THS have no choice other than to be correct (for that piano)." Well, maybe and maybe only for that sequence, and maybe only for you. Another thing for me to consider, which is EXACTLY why I started this Topic. Thanks!

Occasionally, if I feel I need a check early, after tuning the F3-A#3 4th, I will jump to A#3-D4 3RD and listen to the speed of the A3-D4 4th. If it seems out of line I can go back and re-evaluate.

Solid memory of beat rates (almost a feel actually) is definitely a must for this method. Works great though.

Peter Grey Piano Doctor


Peter W. Grey, RPT
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Originally Posted by Chris Leslie
Hi Jeff. Hope you had a good few days away.

The topic of aural temperament setting is always close to me as well since I do it at least once almost every day and on all types of pianos. A satisfacory equal temperament as practical as possible in the first five or six minutes is the aim, but there times when I chose to, or am required to, tune an unequal temperament.

I am always keen to try and experiment with new temperament sequences and I usually find myself casually switching methods in subtle ways every few weeks or so just for the variety.

The approach that I first learnt some 50 years ago now, and that seems generally to result in the best outcome, is the the traditional and time honoured 4th and 5th sequence from A4 with careful evaluation of M3rds and M6ths and their progression as they appear. A common element to my method also is that of balancing 4ths and 5ths for a note from an already established M2nd. Establishing a contiguous M3rd ladder is also often a great help in providing semi-immutable anchor points, but not necessary.

Evenly progressive M3rds and at least one other progressive interval as well may define equal temperament in theory, but is not worth loosing sleep over if it is not absolutely perfect. I personally place more emphasis on even sounding tempered 4ths and 5ths and their particular tempered sound. I always finish a temperament tuning with balancing the 4ths and 5ths with the established M2nds. In fact, iterating that method more that once tends to converge the temperament closer to equal. There is also the opportunity then to more carefully set and render the strings at the same time with appropriate hammer manipulation. That is something that experience teaches despite everybody seeming to think that they are the expert.

Aural tuning temperament sequences is interesting. I have used an ETD for a while but it became sooooo boring, and the results often were not so perfect.

Sorry, I had to kinda chuckle when I read this. Have you thought about going into politics? laugh laugh laugh

"Establishing a contiguous M3rd ladder is also often a great help in providing semi-immutable anchor points, but not necessary."

Actually I agree completely. wink

Having all RBIs beat progressive is a worthwhile goal, because it is rarely achieved. As Robert Browning wrote, "Ah, but a man's reach should exceed his grasp, Or what's a heaven for?"

There can be a number of limiting factors, I believe, such as scaling, pinblock condition, string rendering friction points, hammer technique, the chosen temperament sequence, and the ability to judge beatrates, not to mention out-of-tune dog howls!

The required accuracy for progressive RBIs is pretty daunting. If each note is tuned to an ideal pitch, they all must be within about 2/10 of a cent to guarantee progressive RBIs. Of course, this in not how an aural temperament is set but rather by listening to the beatrates of intervals. This gives some more wiggle room, but if there is more than one or two notes 1/2 cent off from the ideal pitches, it is doubtful that progressive RBIs will be the result.

But this Topic is about the limiting factor that we can do something objective about - the temperament sequence. I find little true analysis of them, but a lot of self-serving anecdotes. Take the ladder of CM3s you mention. How many have stopped to consider how far off they could be and still be progressive? Or ever try to tune the four of them independently (starting with F, F#, G, and G#) and see, without checking the beatspeed of the M3s in any other ladder while tuning, if you end up with 12 chromatic, progressively beating M3s? All other intervals can be disregarded in this experiment.

Other parts of tuning sequences can and should also be analyzed. For instance, given one of your M2s, assuming it is 200 cents wide, how much error will there be if a note is tuned as a 4th to one of the notes of the M2 and a 5th to the other, resulting in these two intervals having the same beatspeed?
about 1/2 cent


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Originally Posted by Ed McMorrow, RPT
One has to find out what the piano will give you when you temper it. And I mean the whole compass, not just an octave or two in the middle. Like Gene says, it all starts with octave widths. Then you figure out how to divide them as evenly as possible.

Like Peter notes, the 4ths at around 1bps in the f33-f45 octave are the most common result. So start with those rates and see what you get in the 5ths and octaves connected to the 4th.

So interval sequence does not need to be set in stone. I change mine up as I go. I just get in there and start tuning and follow my ear where it takes me.

Hmmm, kinda like the line from the "King and I" when the Prince asks how he will know what to do when he is King - when you are King, you will know how to be King.


Jeff Deutschle
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Originally Posted by P W Grey
Originally Posted by UnrightTooner
Originally Posted by P W Grey
Jeff,

I have used the following pattern (when I tune ET) for well over 20 years. Providing that you get the F3-A3 3RD exactly right (for that piano) the rest works out flawlessly with 4ths at about 1bps~. It should go w/o saying that 3RDS must progress "evenly".

A4-A3 OCTV
A3-F3 3RD
F3-A#3 4TH
A#3-F#3 3RD
F#3-B3 4TH
B3-G3 3RD
G3-C4 4TH
C4-G#3 3RD
G#3-C#4 4TH
A#3-D4 3RD
B3-D#4 3RD
C4-E4 3RD
C#4-F4 3RD/OCTV


No checks until C#4. But that is no problem since the sequence up to that point rarely takes more than 2 minutes. When arriving at C#4, if it does not come out right on the money, 30 seconds of deduction to determine whether the problem is in the 4THS or the 3RDS or possibly a combination. Correct, and tune the last 4 3RDS and move on.

IF you want simulate a P12TH temperament, speed up both 4THS and 3RDS a tad. This will result in the OCTV a little wider, and 5THS close to pure.

I do not use 5THS as a "tuning" interval...only a quick check interval. If the 3RDS and 4THS are correct, the 5THS have no choice other than to be correct (for that piano). Everything is tailored to what the piano "tells" me. Yes...they talk back.

There is a process for determining the "correct" speed of the F3-A3 3RD (Jack Stebbins published this in a PTJ article a number if years ago). This process is brilliant, however by the time I go through it to make the determination, I could have tuned the temperament twice through already. Therefore I generally choose to guess (based on the relative size, quality, and observable scaling of the instrument) and go. If I need to go back, I don't care as I can usually fix it quickly.

That's my story and I'm stickin' with it.

Peter Grey Piano Doctor

Wow, cool. I think the accuracy would rely on beatrate memory and progression memory. You say no checks until the 9th note, which is probably predictable. "If the 3RDS and 4THS are correct, the 5THS have no choice other than to be correct (for that piano)." Well, maybe and maybe only for that sequence, and maybe only for you. Another thing for me to consider, which is EXACTLY why I started this Topic. Thanks!

Occasionally, if I feel I need a check early, after tuning the F3-A#3 4th, I will jump to A#3-D4 3RD and listen to the speed of the A3-D4 4th. If it seems out of line I can go back and re-evaluate.

Solid memory of beat rates (almost a feel actually) is definitely a must for this method. Works great though.

Peter Grey Piano Doctor

Peter, I thought more about your sequence than all the others put together. smile Is it what you came up with or someone else?

When tuning your 8th note, G#3, you have chromatic notes spanning a 5th. If the 5th is reasonable, the 4ths are consistent and both the m3s and M3s are equally progressive, I believe this 8-note temperament can be expanded with only perhaps very minor changes.

What I don't believe (and it took some considering) is "If the 3RDS and 4THS are correct, the 5THS have no choice other than to be correct (for that piano)."

Consider if the lower M3s are tuned not quite as wide as they should and the upper M3s a bit wider than they should be with the 4ths spot on. The 5ths would sound great, too. Even the m3s would be progressive, but with the lower ones beating a bit faster than they should and the upper ones beating a bit slower, the opposite of the M3s. The F3-F4 temperament would pass every test, until you go to expand it. THEN the problems with ALL the intervals and the octaves will show up. But sure, they can be smoothed out. In a way a temperament spans 88 notes. wink

But leaving that disagreement behind, there is much to be said for your sequence. It is easy to remember. It quickly gets to where there are sufficient chromatic RBI beatrate checks (I am not a fan of CM3s...). And checking the F3-C4 fifth on the 7th note will keep you out of the weeds early in the sequence before you get lost.


Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?
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