Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum C.HA.S. equal temperament

Good evening Alfredo. I greatly respect your investigations into temperaments. I reviewed the thread you posted above from 2014. In it I found the same reservations then that I have now regarding tempering the octave. I stated then that the inherent inharmonicity of the piano, at least in my case, requires, in order to create a 'harmonious' tuning, that the octave be stretched considerably beyond the mathematical value you determine for C.HA.S. That is, of course, also the case for every other possible 12 tone temperament on my piano.

I cannot form an opinion on stretching octaves on a non-inharmonic instrument, other than to say that my preference has always been for the past 50 years to tune the instruments that I did play (not the piano) to as close to 'just' as was possible for the repertiore I was playing. I tune my clavichords to a Kirnberger meantone variant. I now tune my piano to Young 1799 when my wife is not around, EVBT III sometimes when she is, and ET, as determined from the physical iH measurement of the first 32 partials of the bass and tenor strings of my piano, and as many partials as exist below 20kHz in the rest of the piano.

Essentially, I want pure, non-beating intervals, if possible. A pure, beatless Major 3rd is a thing of beauty. There is a calmness that is simply not possible in ETs. I don't mind the 'swirling' resonances of the inharmonic partials and the out-of-tune beatings of piano when tuned in some ET, but it is not calm. It is like always hearing singers producing vibrato, 'leaving the listener in doubt as to just what pitch is being aimed for', as opposed to a men and boys cathedral choir singing in just, vibrato less harmony, and using vibrato as an ornament, not the 'main course'.

Hi prout,

I would never discuss your own preferences. You say.. "..A pure, beatless Major 3rd is a thing of beauty", I may say that to me it sounds purely colorless, dull, lifeless, but that is not the point I was addressing. Here you mentioned the Chas "raw" values for octaves stretch, remember? And so, I meant to re-address you to other observations.

Cheers

That was me being a little too acerbic and you both missed my point.,a point I, and others have been attempting to make in the last few posts. Come to think of it, all three of you missed it.

"A tuning that beautiful must be close to c.a.H.s". -Alberto

Hilariously arrogant but

It is.

When you leave an octave to chance like that and it ends up .00063, that's close enough.

The addition of unison strings made it .9987.

OK. Already I feel like I've trodden in more than I can chew.
Now that Toni has penetrated the smoke screen and attempted the initial moves in establishing chas. can Alfredo give us a constructive critique of his single string temperament that he so kindly and courageously published so that we all can have a starting point in order to understand this thing in a practical way?

The way Toni seems to be understanding it would result in a quite narrow temperament octave on pretty much every piano. I have no problem with this, there's lots of precedent for heading in this direction to a certain extent. (Narrow middle octaves enabling more stretch in the outer octaves without going outside the realms of rationality where collaborating musicians are involved is not unheard of).

There must be very little that's totally new in piano tuning.

If you really have anything to say in plain language ...

......we're listening.

Hi rxd,

You are correct, in regard to tuning practice I haven't done much, I have just worked out some interval checks that interlace 4ths and 5ths, and enable me to set the premises for aiming at my favorite tuning curve, reproducing it with a satisfactory degree of exactitude.

Perhaps you have already looked at the sequence flowchart I am sharing, there I mention the first five intervals of the sequence and their beat-rate proportion. It is not much, but it gives me the possibility to place the beat rate of the other SBIs in between, and have the thirds and sixths progression ready for the expansion.

I am not sure of what you mean when you say " ..can Alfredo give us a constructive critique of his single string temperament..", perhaps you can re-word that question?

Also when you say "..it would result in a quite narrow temperament octave..", I an not sure I understand, do you hear A3-A4 narrow, there?

Regards, a.c.

Ok, I am in the process of reading the original 2009 paper on C.HA.S.

If I am correct in my interpretation of the English translation of the original Italian, C.HA.S. is entirely based on the inharmonicity of the piano. It is dynamic. That is, Alfredo has essentially created a two octave structure in which there is beat synchronicity between the 12th and 15th partials, with the 12th being narrow and the 15th being equally wide. This 'zero sum' is expanded through out the compass as the inharmonicity changes. Notice that I said 'partials', not intervals. There is no static interval width.

The formula, once understood, uses the variable iH (interpreted either aurally, or with an ETD) to produce an equal beating temperament.

I have not finished the paper yet, but so far, with careful reading, it entirely makes sense. It is an ET with minimal or no stretch beyond what the piano wants. This is potentially very cool, though I think it is only one of many ways in which a fine aural tuner hears the instrument. It does, however, have great potential for a software based algorithmic approach in which iH is measured, plugged into Alfredo's formula, and a very fine tuning produced.

I would like to apologize publicly to Alfredo for misinterpreting my first reading and discussion of his temperament. I thought it was 'classical', that is to say, a mathematical formula that existed without concern for the instrument on which it is tuned. That is clearly not the case.

Equal beating 12ths and 15ths have been advocated by Bill Bremmer for a long time.

Kees

Hi Prout,

Thank you for your comment.

Let me clarify one thing, you wrote "..with the 12th being narrow and the 15th being equally wide..", and perhaps that terminology is confusing.

Perhaps it is more correct .."..with the 12ths and the 15ths that diverge equally from their pure ratio..". In fact, "beating" might be a slightly different thing.

More later.

Regards, a.c.

Yes. I mentioned in my post that C.HA.S, aurally tuned, is much like most fine tunings, in that the iH of the piano must be considered at the root of any possible tuning. I could see C.HA.S. as an overlay on the basic iH.

prout

Hi Prout,

I need to say that this morning, reading that you could go through the Chas paper and appreciate the content made me very happy. That paper becomes incomprehensible for some expert readers, thank you, as you are helping me with that.

This model needed to be "dynamic" and needed to represent different "s" tuning curves, even beyond the basic inharmonicity.

With s = 1 the stretch is minimal, as you say.

Yes, every aural tuner will hear the "instrument" differently, and perhaps the instrument behaves differently, depending on the tuner

As for the "equal beating 12ths and 15ths", I myself have been a source of confusion, that is probably why Kees pops up. And perhaps I need to say again that the Chas ET model is not a "method" for expanding a tuning, as described by Bill Bremmer eight years ago:

Re: CIRCULAR HARMONIC SYSTEM - CHAS - #1198042 - May 12, 2009 08:38 PM

"The idea which I called "mindless octaves" is a very simple one indeed. At one PTG Convention, I observed Steve Fairchild RPT demonstrate it but I really didn't understand what he was doing at the time. Only later did I realize that the concept I had hit on purely by trial and error was what Steve had been doing.
//Snip//
The "mindless octaves" idea is nothing more than making an exact compromise between the double octave and the octave and 5th (12th). I use the sostenuto pedal to do it. When I used the idea, I heard clarity and beauty that I had never heard before and the feedback from customers kept me at it. To me, it was such a simple technique that it became habitual, within my muscle memory to perform, I didn't really have to concentrate when doing it, I could be thinking about something else, it was just mindless yet the technique yielded such consistent and perfected results each and every time. I later discovered that the aural technique could be as accurate and consistent as any ETD would provide. I use it today when I set up a custom ETD program and when I conduct a PTG Exam Master Tuning."

You wrote: ..."I thought it was 'classical', that is to say, a mathematical formula that existed without concern for the instrument on which it is tuned. That is clearly not the case."

Thanks for reading that paper carefully.

Regards, a.c.
.

For those new to the topic this thread will be interesting:
http://forum.pianoworld.com/ubbthreads.php/topics/2659720/1.html

Kees

Not sure how your reply is a reply to my post, but it is of course obvious that the iH of the piano must be considered for not just most, but all tunings, and not just "fine" ones, but even rough ones.

Stopper advocates pure 12ths across the board (not sure which 12ths in the bass, not 3:1 for sure) and Alfredo advocates equal beating 12ths and 15ths across the board (not sure which 12ths and 15ths in the bass, not 3:1 and 4:1 probably)

There, now I've explained C.HA.S.^(R) and Stopper's stretch schemes for ET in one sentence.

Kees

Thank you, Kees, in my previous post I had forgotten to copy the relative link:

http://forum.pianoworld.com/ubbthreads.php/topics/1213402/2.html.

As I mentioned, Chas represents 12ths and 15ths that deviate numerically from their pure value of the same amount.

Regards, a.c.
.

[/quote]
As I mentioned, Chas represents 12ths and 15ths that deviate numerically from their pure value of the same amount.

Regards, a.c.
[/quote]
.

Just to complete the list (ET size expressed in size of octaves, as this gives more feel for the "stretch" than the halftone step factor or the pure interval base):

Pure 26ths ET (aka Bremmers mindless octaves (publication date?), equivalent to CHAS) represents 12ths and 15ths (two 8ths) that deviate numerically from their pure value of the same amount, resulting in an octave width of 1200.54 cents without iH.

Pure 19ths ET represents 12ths and 8ths that deviate numerically from their pure value of the same amount, resulting in an octave width of 1200.76 cents without iH.

Pure 12ths ET (Stopper 1988) represents 8ths and 5ths that deviate numerically from their pure value of the same amount, resulting in an octave width of 1201.23 cents without iH.
http://www.piano-stopper.de/dl/EUROPIANO_3_88_STOP.pdf

Pure 16ths ET represents 12ths and 5ths that deviate numerically from their pure value of the same amount, resulting in an octave width of 1201.80 cents without iH.

Pure 20ths ET represents 12ths and two 5ths that deviate numerically from their pure value of the same amount, resulting in an octave width of 1202.13 cents without iH.

(....this list can be extended by any number of combinations of twelfths, octaves or fifths and fourths which are just fractions of twelfths and octaves)

Pure 5ths ET, (Kolinski 1959), resulting in an octave width of 1203.35 cents without iH.

Any real number value (Geometrie der Töne, G. Mazzola 1990), resulting in an octave width of any real number value cents without iH.

Not to forget Haye Hinrichsen who came up with his own octave size for lowest entropy he calculated for a group of 88 notes with a harmonic power spectrum (no iH) to be 1200.6 cents. link:
http://www.scielo.br/scielo.php?scr...11172016000100410&lng=en&tlng=en

My calculations for lowest entropy tend to pure 12ths ET, when not throwing only 88 harmonic spectrum tones into the equation, but including inharmonic spectrum tones also.

Anyway, the generally observed pure effect of pure 12th ET is mainly caused by an at the same time synchronous effect of a large number of slow beating intervals having quasi perfect interval ratios, coupled with an asynchronous effect influencing fast and slow beating intervals by the slight offsets in the octaves, reducing the perception of those beats (even of the major thirds, which are slightly faster than in standard ET) significantly. Another important effect is the melodic correction for the high treble and low bass: Standard ET usually hangs in the treble and creates basses that are too high. In pure 12th ET, the two notes of an octave sound "the same" when played successively.

(No thread hijacking intended, but pure 12ths ET is practiced by Alfredo in his preparatory tuning process, so this should be ok)

Bernhard Stopper

Both of my comments above were, in part, the result of a wine induced fog. Sorry.

I am not sure why I comment on ET tunings. Perhaps because, while I abhor ET, I am forced to employ it in my work. There is something always disturbing when playing Chopin, Debussy, Ravel, whomever, and landing on a interval that is meant to be the tension resolution of a phase, only to find it beating like some superannuated soprano. It is my opinion, obviously not shared by others, that these composers did not intend this to be the case, though they may have suffered under the same disability.

I would not be sure that you are in good society with these composers, Chopin for example preferred Montal as tuner, who deliberately tuned ET and not one of the well temperament or meantone/meantone derivative temperament tuners who were en vogue in academic circles at this time (most of them promoting their own holy grail of temperament).

Bernhard Stopper

I am not suggesting that any composer I mentioned preferred a WT over a ET. Chopin's preferred tuner, like all tuners, could not produce an ET on any piano, since the physics of the instrument prevents the tuner from so doing. It is quite possible that Montal's 'ET' used the iH of Chopin's instruments in a way that made Chopin's use of 'remote' keys very calm, or, that because they were calm, Chopin chose to write in those 'remote' keys. We can never know.

But I do know that the underlay of constant beating inherent in an inharmonic instrument adds a veil of haze to the purity of the potential sound that is then made worse by the use of any temperament that elevates the idea that all intervals should beat, whether or not that beating has musical value, as opposed to just being accepted as a necessary compromise in tuning.

I am forced by my work to play in all keys. For me, an on-the-fly just intonation would be fun to use. There was (is?) a company based in Vancouver in the early 1990s called Justonic Tuning Inc. that provided software to do this on digital keyboards.

First you say that you do not like equal temperament on pianos, and then you say that equal temperament cannot be tuned on pianos. So since you have never heard equal temperament on pianos, how do you know you do not like it?

The tuners of today and the past (including Montal) could indeed tune ET on any piano. ET on pianos (ih involved) is defined as progressively (as progressive as iH allows) increasing interval beatings along the scale, in most cases keeping a base interval aurally as pure as possible (even in CHAS were Alfredo claims no interval is pure, the 26ths are pure (exactly pure in case of no iH and aurally pure as possible with iH)). As long as everything is in a tolerable tolerance, pro tuners classify such progressive intervals as ET.



No this is not possible. I am pretty sure from what i read from your posts so far you are informed enough about iH that it is by definition impossible to calm remote keys by iH with progressively tuned intervals. Maybe another wine fog?

Bernhard Stopper

You're funny! Thanks for that.

What I do know is that I really do not like ET on an organ, which is possible, frequent, and I spent too many decades fighting.

No one has ever heard ET on a piano, including you as a member of the set. What I do not like is the attempt at approximating ET on a piano. It is ever so much easier to tune a UT and know that intentionally, some intervals will sound harsh and some will sound sublime. When the harsh and sublime intervals are crafted into a beautiful piece of music, the result is a musical experience beyond a level that is obtainable when every interval is, more or less, sort of, hopefully, evenly harsh, or, dare I say it, out-of-tune.

I know my opinion is not main stream, and I am happy to bow out and let the ET proponents bask in harsh glare of their temperament.

I remain,

PRO UT