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#2048118 - 03/14/13 10:07 AM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: RonTuner]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1060
Loc: Sicily - Italy
Originally Posted By: RonTuner
Here on Pianoworld, we've read about at least three systems that claim to define that "perfect" piano tuning/stretch. There's a long thread on the C.H.A.S tuning, Dirk's software, and the OnlyPure approach...

What I have noticed while using multiple software platforms, and communicating with techs trying out different paths, is that our perception for what constitutes "the perfect stretch" is influenced by the particular approach we're currently using... It's almost as if our ears get trained to listen for the results that our approach place on a piano. This also applies to aural tuning that uses the same checks over and over on every piano. Something along the lines of "yup, my checks all work out fine, the piano is as good as it can get"

Where most of the approaches fail is dealing with the more difficult scales to tune - those smaller instruments that just are tough to make musical... Maybe I'll take a look at Dirk's to see how it deals with these!



Hi Ron,

Thank you for mentioning the model I'm sharing, as you say my tunings are the result of my approach to practical "intonation" and theoretical/numerical issues.

You also mention "checks" and throughout my own research (as an aural tuner) I have considered maximum beat-coherence and whole "in tune" resonance as my right and fair targets.

I understand what you mean, when you mention "...those smaller instruments that just are tough to make musical...", and I happen to have stated that I have never had particular problems with that.

Since I believe you to be sincere, I think it is fair on my part submitting also a sample of my own tuning on a small piano, in fact the smallest Yamaha model. That was one single (my first) tuning on that worn and modest piano which had not been tuned for many years, during my stay in Paris (2010) when I first met Isaac. The site is the customer's (Sebastien Buchholz), he asked me to make a video...

"Almost" Chas, dissonances that we can still perceive clearly as dissonant, crispy as in my experience it can be (expecting more hysteresis), together with... what ever else you may notice in there.

Hmmm... I did not want myself to appear but... never mind, I apologise for that and for my casual improvisation.

http://s814.beta.photobucket.com/user/papafard/media/491_1437.mp4.html?sort=3&o=10

Regards, a.c.
.
_________________________
alfredo

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#2048232 - 03/14/13 02:21 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: RonTuner]
Tunewerk Offline
Full Member

Registered: 03/26/11
Posts: 405
Loc: Boston, MA
Originally Posted By: RonTuner
Where most of the approaches fail is dealing with the more difficult scales to tune - those smaller instruments that just are tough to make musical...


I want to add to what Ron said. It's not only the poorly scaled instruments - there is technically no ideal stretch for any two pianos! It is academically rewarding to discuss ideal frequency alignment on the modern piano, but as someone once said..

'The difference between theory and practice is, in theory, there is no difference between theory and practice, but in practice there is.'

We are dealing with imperfect bridges, imperfect strings and imperfect scales. This requires different checks and priorities every single time.

Also, Mwm, it doesn't matter whether you are tuning an equal temperament or a well temperament, the same principles apply for the best possible tuning. Different temperaments create different partial alignment points, so it changes what is desirable, but there is a best possible point for both. Within a given set of rules, there is always a best point.
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Unity of tone through applied research.

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#2048245 - 03/14/13 02:51 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Tunewerk]
Mwm Offline
500 Post Club Member

Registered: 02/20/13
Posts: 752
Originally Posted By: Tunewerk
Originally Posted By: RonTuner
Where most of the approaches fail is dealing with the more difficult scales to tune - those smaller instruments that just are tough to make musical...


I want to add to what Ron said. It's not only the poorly scaled instruments - there is technically no ideal stretch for any two pianos! It is academically rewarding to discuss ideal frequency alignment on the modern piano, but as someone once said..

'The difference between theory and practice is, in theory, there is no difference between theory and practice, but in practice there is.'

We are dealing with imperfect bridges, imperfect strings and imperfect scales. This requires different checks and priorities every single time.

Also, Mwm, it doesn't matter whether you are tuning an equal temperament or a well temperament, the same principles apply for the best possible tuning. Different temperaments create different partial alignment points, so it changes what is desirable, but there is a best possible point for both. Within a given set of rules, there is always a best point.


I agree and that is partially my point. I'm not suggesting there is an ideal mathematically derived stretch that can be used for every S&S D ever made. I'm suggesting that the best tuning for a unique piano varies from moment to moment and asking if that is your experience, and it would seem so.

But, to go back to temperament, one can tune a organ in quarter comma meantone and not worry about stretch. But, one of the nice things about ET on a piano is that the stretch causes the fifths to beat at fairly consistant speed throughout the compass, instead of doubling per octave with no stretch. How would you tune a piano in quarter comma meantone ( also, why would you want to ) and make it sound "good" ?

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#2048264 - 03/14/13 03:23 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]
Tunewerk Offline
Full Member

Registered: 03/26/11
Posts: 405
Loc: Boston, MA
Yes, I agree with what you said here.

Tuning a piano in quarter comma meantone is something that is really not done anymore. Seventh comma is the closest thing to meantone that I know of that is used on modern pianos today.

This goes back to something else I posted months back, that inharmonicity dictates ideal tunings for a given instrument. Inharmonicity is responsible for pure thirds not sounding as rewarding and pleasing as on an organ. For this reason, there just isn't the desire to tune something that prioritizes thirds on the modern piano.

You could technically tune quarter comma on a piano, and then use the same octave stretching that is ideal to make the intervals align as used in ET. You couldn't use the same checks to do this however. Different partials and different priorities.
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Unity of tone through applied research.

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#2048301 - 03/14/13 04:29 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: alfredo capurso]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7425
Loc: France
Originally Posted By: alfredo capurso
Originally Posted By: RonTuner
Here on Pianoworld, we've read about at least three systems that claim to define that "perfect" piano tuning/stretch. There's a long thread on the C.H.A.S tuning, Dirk's software, and the OnlyPure approach...

What I have noticed while using multiple software platforms, and communicating with techs trying out different paths, is that our perception for what constitutes "the perfect stretch" is influenced by the particular approach we're currently using... It's almost as if our ears get trained to listen for the results that our approach place on a piano. This also applies to aural tuning that uses the same checks over and over on every piano. Something along the lines of "yup, my checks all work out fine, the piano is as good as it can get"

Where most of the approaches fail is dealing with the more difficult scales to tune - those smaller instruments that just are tough to make musical... Maybe I'll take a look at Dirk's to see how it deals with these!



Hi Ron,

Thank you for mentioning the model I'm sharing, as you say my tunings are the result of my approach to practical "intonation" and theoretical/numerical issues.

I understand what you mean, when you mention "...those smaller instruments that just are tough to make musical...", and I happen to have stated that I have never had particular problems with that.


http://s814.beta.photobucket.com/user/papafard/media/491_1437.mp4.html?sort=3&o=10

Regards, a.c.
.


Shame on you, Alfredo wink

That said, the main result with your tuning approach is that there is always something we can refer to, whatever the scale and piano quality.

indeed very agreable. I noticed that something similar happens when the "pure 5th" sheme is tune, but sometime (with high iH probably" the piano tone turn to a cheap organ quality (Bontempi tone) that seems to be added, above the piano harmony.

The advantage of CHAS is that it takes in account what the piano proposes .While tending to or using a theoretical scheme, you are not addicted to a particular 10th beat rate, for instance.. the scheme itself inclued enough intervals to find its place (more or less correctly against theory) naturally.

But the temp sequence have to be respected (as the method, probably)

Greetings



Edited by Olek (03/14/13 04:31 PM)
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#2048351 - 03/14/13 06:08 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1060
Loc: Sicily - Italy

Hi Mwm,

As regard to theory and practice, I would never confuse a quip that tries to be clever with something serious, ideal-academical studies do have value, when they enable us to better describe our "world".

An ideal stretch does exist, throughout the compass, in theory as far theory can go, having to combine prime numbers in a scale, and in practice, every time we aim at harmoniousness and re-find our favorite theoretical references, on every single piano.

It does matter whether you consider ET's or a well temperament, in that the "tuning principles" are very different: 12 root of two rules the octave exponentially, Cordier's ET rules a fifth, Stopper's rules a 19th, the Chas model rules the whole 88 compass.

When you ask about any WT-expansion you touch one nerve centre of tuning, carefull because... it might be... panic, and you seem to understand that any WT ends up being a quasi-ET, the more you expand it, the closer to a modern ET. So, for any WT, the "best possible" seems to be when you can confuse the WT's theory with ET practice; the same does not apply to the set of rules I refer to.

Isaac,

Thank you for your comment, I share what you say.

But... you know me too well.. believe me.. I'm still ashamed!! blush

Regards, a.c.
.
_________________________
alfredo

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#2048401 - 03/14/13 08:13 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]
Phil D Offline
500 Post Club Member

Registered: 01/15/10
Posts: 551
Loc: London, England
When an aural tuner achieves the most pleasing compromise amongst all the pitches of the piano, he has made some value judgements along the way, according to what pleases him the most. Others would make different judgements, as they have different tastes.

Your analogy with a 'perfect ET' is false - there is no such thing as one single perfect ET. There is the theoretical ET, based upon A=440 and the 12th root of two ratio between semitones, but this is purely theoretical. There are, however, many actual ETs that can be tuned on a (well-scaled) piano, and this is what the aformentioned aural tuner will have tuned on the piano. An actual ET is one where there is an equal ratio between each semitone, and there is a nigh-infinite array of these that can be applied to a piano and it be pleasing.


Edited by Phil D (03/14/13 08:13 PM)
_________________________
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The Cycling Piano Tuner

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#2048677 - 03/15/13 11:12 AM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Phil D]
Mwm Offline
500 Post Club Member

Registered: 02/20/13
Posts: 752
Originally Posted By: Phil D
When an aural tuner achieves the most pleasing compromise amongst all the pitches of the piano, he has made some value judgements along the way, according to what pleases him the most. Others would make different judgements, as they have different tastes.

Your analogy with a 'perfect ET' is false - there is no such thing as one single perfect ET. There is the theoretical ET, based upon A=440 and the 12th root of two ratio between semitones, but this is purely theoretical. There are, however, many actual ETs that can be tuned on a (well-scaled) piano, and this is what the aformentioned aural tuner will have tuned on the piano. An actual ET is one where there is an equal ratio between each semitone, and there is a nigh-infinite array of these that can be applied to a piano and it be pleasing.


I have re-read the entire thread, and I am unable to find a reference to 'perfect ET'. There was one mention of 'perfect tuning/stretch'. To discuss ET in any meaningful fashion, one must clearly define the ab initio condition. In this case, your definition of the theoretical ET is correct for this discussion. However, your statement regarding 'actual ET' is analagous to stating that a women can be 'partially pregnant'. In my 'observed reality', either a women is pregnant, or a women is not pregnant. I am not aware of a 'nigh-infinite array' of states of being pregnant.

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#2048693 - 03/15/13 11:59 AM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]
Mwm Offline
500 Post Club Member

Registered: 02/20/13
Posts: 752
Originally Posted By: Mwm
Originally Posted By: Phil D
When an aural tuner achieves the most pleasing compromise amongst all the pitches of the piano, he has made some value judgements along the way, according to what pleases him the most. Others would make different judgements, as they have different tastes.

Your analogy with a 'perfect ET' is false - there is no such thing as one single perfect ET. There is the theoretical ET, based upon A=440 and the 12th root of two ratio between semitones, but this is purely theoretical. There are, however, many actual ETs that can be tuned on a (well-scaled) piano, and this is what the aformentioned aural tuner will have tuned on the piano. An actual ET is one where there is an equal ratio between each semitone, and there is a nigh-infinite array of these that can be applied to a piano and it be pleasing.



I have re-read the entire thread, and I am unable to find a reference to 'perfect ET'. There was one mention of 'perfect tuning/stretch'. To discuss ET in any meaningful fashion, one must clearly define the ab initio condition. In this case, your definition of the theoretical ET is correct for this discussion. However, your statement regarding 'actual ET' is analagous to stating that a women can be 'partially pregnant'. In my 'observed reality', either a women is pregnant, or a women is not pregnant. I am not aware of a 'nigh-infinite array' of states of being pregnant.


I should add that Schrodinger (please excuse the lack of the umlaut) posits that a women can be both pregnant and not pregnant at the same time -at least until you observe her condition.

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#2048705 - 03/15/13 12:45 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]
Mwm Offline
500 Post Club Member

Registered: 02/20/13
Posts: 752
I stand corrected regarding the use of "perfect ET". I, myself, used the term. I apologize for impugning Phil D's integrity.

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#2048772 - 03/15/13 03:50 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]
Tunewerk Offline
Full Member

Registered: 03/26/11
Posts: 405
Loc: Boston, MA
Phil is absolutely correct in saying 'nigh-infinite' pleasing states of ET. Equal temperament, along with any other temperament is a fixed scale compromise where not all partials will be satisfied.

This is where a lot of people end up in endless arguments of misunderstanding, different levels of education, etc.

I feel there is an optimal state of ET for a given piano, but one could get really particular and say, for a given repertoire of music, there might be a better fit here or there.

It is the art of finding a perfect solution at the moment for a given piano, from an imperfect, mathematically irresolvable set of variables.
_________________________
www.tunewerk.com

Unity of tone through applied research.

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#2048781 - 03/15/13 04:03 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Tunewerk]
Mwm Offline
500 Post Club Member

Registered: 02/20/13
Posts: 752
Originally Posted By: Tunewerk
Phil is absolutely correct in saying 'nigh-infinite' pleasing states of ET. Equal temperament, along with any other temperament is a fixed scale compromise where not all partials will be satisfied.

This is where a lot of people end up in endless arguments of misunderstanding, different levels of education, etc.

I feel there is an optimal state of ET for a given piano, but one could get really particular and say, for a given repertoire of music, there might be a better fit here or there.

It is the art of finding a perfect solution at the moment for a given piano, from an imperfect, mathematically irresolvable set of variables.


Again, I must disagree, though it is a matter of semantics, rather than a lack of common ground. I agree with Phil and with you regarding pleasing states of - perhaps the best term is - Well Temperament. My semantic argument is simply that 12 tone ET is a mathematically derived system for tuning a western standard keyboard. ANY tuning on an acoustic piano can never achieve ET and be pleasing, so why don' t we all use the term Well Temperament, which is actually what everyone is talking about.

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#2048839 - 03/15/13 07:10 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7425
Loc: France
Ha ! Msw demasqued, in the end (LOL) 00:00 in the night and still papering, while listening Cuban and Senegalese music from beforethen.

Good night all ....
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


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#2048916 - 03/15/13 11:06 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1701
Loc: Vancouver, Canada
Originally Posted By: Mwm
Originally Posted By: Tunewerk
Phil is absolutely correct in saying 'nigh-infinite' pleasing states of ET. Equal temperament, along with any other temperament is a fixed scale compromise where not all partials will be satisfied.

This is where a lot of people end up in endless arguments of misunderstanding, different levels of education, etc.

I feel there is an optimal state of ET for a given piano, but one could get really particular and say, for a given repertoire of music, there might be a better fit here or there.

It is the art of finding a perfect solution at the moment for a given piano, from an imperfect, mathematically irresolvable set of variables.


Again, I must disagree, though it is a matter of semantics, rather than a lack of common ground. I agree with Phil and with you regarding pleasing states of - perhaps the best term is - Well Temperament. My semantic argument is simply that 12 tone ET is a mathematically derived system for tuning a western standard keyboard. ANY tuning on an acoustic piano can never achieve ET and be pleasing, so why don' t we all use the term Well Temperament, which is actually what everyone is talking about.

The term "Well Temperament" is already taken to denote unequal temperaments without a wolf.

Kees

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#2048922 - 03/15/13 11:26 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]
Tunewerk Offline
Full Member

Registered: 03/26/11
Posts: 405
Loc: Boston, MA
Originally Posted By: Mwm
I agree with Phil and with you regarding pleasing states of - perhaps the best term is - Well Temperament. My semantic argument is simply that 12 tone ET is a mathematically derived system for tuning a western standard keyboard. ANY tuning on an acoustic piano can never achieve ET and be pleasing, so why don' t we all use the term Well Temperament, which is actually what everyone is talking about.


No, absolutely not. Both Phil and I are talking about the many variations of equal temperament possible on the piano: Not simply derived from the 12th root of 2, but from the 19th root of 3, and the 7th root of 1.5.. or any variation in between.

Equal temperament on the piano is the practice of equally dividing the semitones within a fixed ratio. In practice, stretch is added as well, in equal amounts, ideally.

Well temperament is a broad term for historical sets of unequal temperament.. meaning the steps are designed unequally to satisfy one set of interval partials over another. There are nigh-infinite variations of this too.

Go to www.rollingball.com to see Jason Kanter's representations and the difference.
_________________________
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Unity of tone through applied research.

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#2049073 - 03/16/13 10:17 AM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]
Mwm Offline
500 Post Club Member

Registered: 02/20/13
Posts: 752
Kees - regarding WT - Exactly.

Phil and Tunewerk - I have visited Rollingball many times. There is only one ET. There is an arbitrarily large number of equal temperaments. My confusion was with the use of capital letters.

In the end however, I would suggest that, unlike the organ, where you can impose an arbitrary equal temperament on the entire instrument without worrying about inharmonicity, you all tune aurally for a pleasing result without too much concern over the underlying mathematics of the final (or, if you actually tried to use a mathematically derived impure octave et ) of the final temperament.

If I am wrong, please provide me with the actual algorithms used in tuning a piano, with accompanying evidence that the starting algorithm and the final resulting algorithm once you have finished tuning, are the same.

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#2049125 - 03/16/13 12:07 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1936
Loc: Suffolk, England
Originally Posted By: Mwm
I have found that, once I tuned the piano, then re-recorded all the notes to check the stretch again, it recalculated the stretch closer to the theoretical Railsback curve, though the section breaks are still clearly evident in the curve.

Mwm, this could be due to the effects of your tuning but it might also be due to variations in the dynamics of playing the notes before and after.

There are more harmonics in louder sounds and less in softer ones. Dirk's tuner would be working with a different set of data in each case.

PS
One of the effects of your tuning I had in mind was unisons. Olek alludes to this in his post below:

Originally Posted By: Olek
ABout tuning with ETD, I believe that waht "saves" the tuners using them is that the unisons are build by ear, so the basis proposed is just a skeleton, and the "real tuning" is done while tuning unison (if the tuner is capable of doing so)

The problem in the end is that when one want to have a slightly different stretch at unison time that mean he have to compute the tuning again, and generally the tuner does not

The level of tweaking possible at unison time is not so low


Edited by Withindale (03/16/13 04:22 PM)
Edit Reason: PS
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Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#2049139 - 03/16/13 12:47 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7425
Loc: France
sorry, wrong thread...

Apparently the best ETD are the ones that use a set of rules , with or without limits ?

list priority given to the different intervals (weight)

Upper and lower limit, and rules regarding progression

Then the result computed is the "less bad" solution

I believe that what makes the difference with other ETD in Drk's tuner is the selection for the partial used for the display. It is done on a note by note basis (so the same string should be used to sample and to tune)

Dirk seem to state that there is too much inconsistency in partials,(false beats) to use systematically the same, or to use multiple partials without quality evaluation

I just can witness that it works fine (the computation is also an iterative process)

Editing the set of rules, as in Verituner, would be a must

ABout tuning with ETD, I believe that waht "saves" the tuners using them is that the unisons are build by ear, so the basis proposed is just a skeleton, and the "real tuning" is done while tuning unison (if the tuner is capable of doing so)

The problem in the end is that when one want to have a slightly different stretch at unison time that mean he have to compute the tuning again, and generally the tuner does not

The level of tweaking possible at unison time is not so low

But I question the accuracy of the first string tuned, it should lower a little when the last strings are tuned
Also once the unison is tuned, is not the pitch of the first string modified also ? Not only because of bridge motion and tension, but just because the other strings couple, then it could be experimented , measuring a string not coupled (other are muted)
And the same once the unison is tuned (other strings muted as well)

I would believe that the pitch will be different


Edited by Olek (03/16/13 03:08 PM)
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


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#2049390 - 03/16/13 10:39 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: DoelKees]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 592
Loc: Canberra, ACT, Australia
Originally Posted By: DoelKees
Originally Posted By: Mwm
Originally Posted By: Tunewerk
Phil is absolutely correct in saying 'nigh-infinite' pleasing states of ET. Equal temperament, along with any other temperament is a fixed scale compromise where not all partials will be satisfied.

This is where a lot of people end up in endless arguments of misunderstanding, different levels of education, etc.

I feel there is an optimal state of ET for a given piano, but one could get really particular and say, for a given repertoire of music, there might be a better fit here or there.

It is the art of finding a perfect solution at the moment for a given piano, from an imperfect, mathematically irresolvable set of variables.


Again, I must disagree, though it is a matter of semantics, rather than a lack of common ground. I agree with Phil and with you regarding pleasing states of - perhaps the best term is - Well Temperament. My semantic argument is simply that 12 tone ET is a mathematically derived system for tuning a western standard keyboard. ANY tuning on an acoustic piano can never achieve ET and be pleasing, so why don' t we all use the term Well Temperament, which is actually what everyone is talking about.

The term "Well Temperament" is already taken to denote unequal temperaments without a wolf.

Kees

Yes, but with a couple of poodles, a few Irish terriers, a dalmatian and a couple of Rottweiler puppies.
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

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#2049394 - 03/16/13 10:43 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]
BDB Offline
Yikes! 10000 Post Club Member

Registered: 06/07/03
Posts: 21396
Loc: Oakland
I think the generalized term is "singing dogs!"
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Semipro Tech

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#2049722 - 03/17/13 02:19 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]
Tunewerk Offline
Full Member

Registered: 03/26/11
Posts: 405
Loc: Boston, MA
Originally Posted By: Mwm
Phil and Tunewerk - I have visited Rollingball many times. There is only one ET. There is an arbitrarily large number of equal temperaments. My confusion was with the use of capital letters.

In the end however, I would suggest that, unlike the organ, where you can impose an arbitrary equal temperament on the entire instrument without worrying about inharmonicity, you all tune aurally for a pleasing result without too much concern over the underlying mathematics of the final (or, if you actually tried to use a mathematically derived impure octave et ) of the final temperament.

If I am wrong, please provide me with the actual algorithms used in tuning a piano, with accompanying evidence that the starting algorithm and the final resulting algorithm once you have finished tuning, are the same.


This is a very confusing post to me. You say there is only one ET, but an arbitrarily large number of equal temperaments. You identify ET and equal temperament as different concepts?

I'm not sure how the mathematics applying/not applying to the final temperament on a real piano has become part of this argument. It seems a real non-sequitur.

The entire reason why aural tuning is good is because it is sensitive to anomalies. Anomalies are not a part of a simple algorithm.

I can say that general ruling algorithms are a process to good aural tuning, but not overall scale-wide algorithms. This is the problem with machines that aural tuning seeks to improve upon.
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#2049754 - 03/17/13 03:53 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Tunewerk]
Mwm Offline
500 Post Club Member

Registered: 02/20/13
Posts: 752
Originally Posted By: Tunewerk
Originally Posted By: Mwm
Phil and Tunewerk - I have visited Rollingball many times. There is only one ET. There is an arbitrarily large number of equal temperaments. My confusion was with the use of capital letters.

In the end however, I would suggest that, unlike the organ, where you can impose an arbitrary equal temperament on the entire instrument without worrying about inharmonicity, you all tune aurally for a pleasing result without too much concern over the underlying mathematics of the final (or, if you actually tried to use a mathematically derived impure octave et ) of the final temperament.

If I am wrong, please provide me with the actual algorithms used in tuning a piano, with accompanying evidence that the starting algorithm and the final resulting algorithm once you have finished tuning, are the same.


This is a very confusing post to me. You say there is only one ET, but an arbitrarily large number of equal temperaments. You identify ET and equal temperament as different concepts?

I'm not sure how the mathematics applying/not applying to the final temperament on a real piano has become part of this argument. It seems a real non-sequitur.

The entire reason why aural tuning is good is because it is sensitive to anomalies. Anomalies are not a part of a simple algorithm.

I can say that general ruling algorithms are a process to good aural tuning, but not overall scale-wide algorithms. This is the problem with machines that aural tuning seeks to improve upon.


Equal Temperament is defined as 12 equally tempered semitones within an octave that is a precise 2 to 1 ratio. The use of the concept "equal temperament" refers to 12 equally tempered semitones where the octave size is unrestricted.

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#2049764 - 03/17/13 04:06 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]
Mwm Offline
500 Post Club Member

Registered: 02/20/13
Posts: 752
I think we are all getting a bit confused here, myself included. I have a long history with non piano instruments where it is possible, since these instruments do not exhibit inharmonicity, to precisely tune octaves. In this case, the possibility of using UTs and also, the theoretically perfect 12th semitone ET, actually exists. But the piano is different, hence this discussion.

As I look at the options available for tuning a piano, I wonder if an et that is not based on the 2-1 octave is more appropriate, since, in the end, that seems to be what you all do anyway, just by ear, not by math. Don't get me wrong, I have the greatest respect for and envy of professional tuners who take their art as seriously as you all do here at PW. I am not among your group however, and am interested in both the art and the science of tuning as it relates to the piano and no other instrument.

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#2049773 - 03/17/13 04:31 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7425
Loc: France
The problem with the piano is that we are cheating by obligation, so your description can be correct, if one state of "acoustically just" intervals .
( at the piano the enlarged octave is still a 2:1 in the ear of the listener, test seemed even to show it sound more 2:1 than the actual theoretical 2:1 based on partial match) .

The actual theory we base our work on is in the end not well stated, that is the main problem.

Then ET can be using a range of intervals as long they are the same size.

All intervals are a left other of others, the rest is a priority question.

I dont know why the ear is satisfied with that evening of the spacing and recognize it as "in tune", but probably the piano ask for that predictability, while at the same time it allows for more use of partial matching.

I also find some "elegance" in a nicely tuned ET on a piano, white it is something about individual tone more than harmony .




Edited by Olek (03/17/13 04:57 PM)
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#2049787 - 03/17/13 04:52 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1701
Loc: Vancouver, Canada
Originally Posted By: Mwm
Equal Temperament is defined as 12 equally tempered semitones within an octave that is a precise 2 to 1 ratio. The use of the concept "equal temperament" refers to 12 equally tempered semitones where the octave size is unrestricted.

Defined by you maybe, but not by the rest of the world.

Kees

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#2049801 - 03/17/13 05:05 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: DoelKees]
Mwm Offline
500 Post Club Member

Registered: 02/20/13
Posts: 752
Originally Posted By: DoelKees
Originally Posted By: Mwm
Equal Temperament is defined as 12 equally tempered semitones within an octave that is a precise 2 to 1 ratio. The use of the concept "equal temperament" refers to 12 equally tempered semitones where the octave size is unrestricted.

Defined by you maybe, but not by the rest of the world.

Kees


I apologize for my ignorance. I am a literalist, which frequently gets me into a lot of trouble. Please, please give me definition of Equal Temperament for Dummies, which, in this case, is me. I literally don't understand how, in purely physical terms, an octave, which is precisely tuned to a two to one ratio, and then divided into 12 equal semitones, can have more than one solution. I understand that, if you change the octave size, of course you can an arbitrarily large number of solutions. Please help me here with a bit of math.

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#2049806 - 03/17/13 05:15 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]
Mwm Offline
500 Post Club Member

Registered: 02/20/13
Posts: 752
Originally Posted By: Mwm
Originally Posted By: DoelKees
Originally Posted By: Mwm
Equal Temperament is defined as 12 equally tempered semitones within an octave that is a precise 2 to 1 ratio. The use of the concept "equal temperament" refers to 12 equally tempered semitones where the octave size is unrestricted.

Defined by you maybe, but not by the rest of the world.

Kees


I apologize for my ignorance. I am a literalist, which frequently gets me into a lot of trouble. Please, please give me definition of Equal Temperament for Dummies, which, in this case, is me. I literally don't understand how, in purely physical terms, an octave, which is precisely tuned to a two to one ratio, and then divided into 12 equal semitones, can have more than one solution. I understand that, if you change the octave size, of course you can an arbitrarily large number of solutions. Please help me here with a bit of math.


I really do want to know the definition that the rest of the world uses for ET. I have looked at all my music text books, the Encyclopedi Britannica, various physics books that I have lyiing around, and, as a last resort, the internet. Every definition I have run into so far, where the the 2 to 1 octave is divided into 12 equal semitones, has only the twelth root of two function as solution.l

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#2049807 - 03/17/13 05:16 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1936
Loc: Suffolk, England
Originally Posted By: Mwm
I literally don't understand how, in purely physical terms, an octave, which is precisely tuned to a two to one ratio, and then divided into 12 equal semitones, can have more than one solution.

You are absolutely right but that solution is of little use for tuning pianos.

Originally Posted By: Mwm
I understand that, if you change the octave size, of course you can an arbitrarily large number of solutions.

This topic was originally about which of those solutions represents a good tuning for a piano.
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Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#2049847 - 03/17/13 06:32 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Withindale]
Mwm Offline
500 Post Club Member

Registered: 02/20/13
Posts: 752
Originally Posted By: Withindale
Originally Posted By: Mwm
I literally don't understand how, in purely physical terms, an octave, which is precisely tuned to a two to one ratio, and then divided into 12 equal semitones, can have more than one solution.

You are absolutely right but that solution is of little use for tuning pianos.

Originally Posted By: Mwm
I understand that, if you change the octave size, of course you can an arbitrarily large number of solutions.

This topic was originally about which of those solutions represents a good tuning for a piano.


Precisely, and that is where I had hoped this discussion would lead. It would appear from my own experience tuning aurally and also using Dirk's tuner that the ideal, not real, tuning for a piano converges on a non log two solution, and, though there are unique anomalies found in every piano, one could start from the non log two base, and refine your tuning from there. I am aware a few of the various alternatives , but am not knowledgeable regarding their desirability as a baseline.

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#2049895 - 03/17/13 07:47 PM Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]
Phil D Offline
500 Post Club Member

Registered: 01/15/10
Posts: 551
Loc: London, England
Originally Posted By: Mwm
Originally Posted By: Withindale
Originally Posted By: Mwm
I literally don't understand how, in purely physical terms, an octave, which is precisely tuned to a two to one ratio, and then divided into 12 equal semitones, can have more than one solution.

You are absolutely right but that solution is of little use for tuning pianos.

Originally Posted By: Mwm
I understand that, if you change the octave size, of course you can an arbitrarily large number of solutions.

This topic was originally about which of those solutions represents a good tuning for a piano.


Precisely, and that is where I had hoped this discussion would lead. It would appear from my own experience tuning aurally and also using Dirk's tuner that the ideal, not real, tuning for a piano converges on a non log two solution, and, though there are unique anomalies found in every piano, one could start from the non log two base, and refine your tuning from there. I am aware a few of the various alternatives , but am not knowledgeable regarding their desirability as a baseline.


Mwm,

The source of your confusion is the assumption that Equal Temperament is based on the octave ratio of 2:1. Because different instruments have different levels of inharmonicity (and few have zero - the pipe organ being the only one I can think of right now), this is rarely the case.

In reality the definition of ET has to be relaxed to allow for as much consonance as possible. The size of the octave can be varied. The only thing that needs to remain constant for a tuning to be ET is for the ratio between frequencies of subsequent notes to be the same. For 'standard' ET which you are thinking of, this ratio is equal to the twelfth root of two - "what semitone ratio, repeated twelve times, produces an octave twice the frequency?" is the reason for this. But one could equally ask, "what semitone ratio, repeated 19 times, produces an octave-plus-fifth that is 3 times the frequency?", or "What semitone ratio, repeated 7 times, produces a fifth that is 1.5 times the frequency?". These would be the 19th-root of 3 ET, which produces a pure 3:1 octave-and-fifth but an octave slightly wide of the 2:1 ratio, or the 7th root of 1.5 ET which produces a pure 5th but an octave even wider of the 2:1 ratio.

Don't think of ETs definition as prescriptive. It is descriptive - there is an aim, to produce the maximum possible consonance without bias towards any particular key. If we sit down and think about it, we can come up with the systems described above. If we sit down at a piano and attempt it, we will probably arrive at something very similar to them.

For reference:
the 12th root of 2 is 1.059463 which gives an octave ratio of 2:1
the 19th root of 3 is 1.059526 which gives an octave ratio of 2.0014:1
The 7th root of 1.5 is 1.059634 which gives an octave ratio of 2.00387:1

So as you can see, the difference is very small. I would say you will almost certainly never find a piano that any tuner would tell you is best tuned using an octave ratio as small as 2:1 because of inharmonicity. And due to the effects on the other intervals, you are also unlikely to find a piano that any tuner would tell you is best tuned using the 2.00387:1 (pure fifths) tuning, due to the extra widening of all the other intervals. The most consonant tuning is likely to be achieved using somewhere between the two, but not necessarily 2.0014:1.


Edited by Phil D (03/17/13 07:49 PM)
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