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

You should engage Bill Bremmer in a discussion of Reverse Well.

Reverse well can not be classified as a deliberate progressively tuned ET and has nothing to do with iH.

I think at this point, there is no point discussing anything with Prout. He never explains anything, and makes claims about things that he cannot possibly know, like what people he has never met hear. It is time to dismiss him as a quack.

Hi Prout,

There is half a phrase in that post of yours that I like, it is "...use of any temperament that elevates the idea that all intervals should beat..".

I cannot expect you to understand why "all intervals should beat", perhaps you can understand that your passion for UT's, WT's and Just Intonation may find room somewhere else, fog or clear?



Hi Bernard,

You wrote: .."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."..

I have to say that in my calculations, the Chas octave width (for s = 0) in cents is 1200.45. Am I wrong?

..."...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."...

This is good news, do you have any material that you can share?

..."..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,..."..

Well, in theory many ratios you listed above have slow beating intervals close to perfect interval ratios, etc...but, in my experience, the question is: what do we hear at the end of our tuning? Can you hear "pure 12ths" at the end of your aural or ETD tuning?

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

That is Ok indeed, thanks for checking. When a piano is flat I always tune a steeper curve and use all intervals, including 12ths and 15hts, as a reference to keep control on what I am doing. And I do tune also pure 12ths - on center strings - every time I feel that that is enough on that particular piano, in order to anticipate pitch-sagging. This is explained here:
http://forum.pianoworld.com/ubbthreads.php/topics/1326050/1.html

More tomorrow, as I had a long day.

Regards, a.c.

All:

There is a slight difference between BB's Mindless Octaves and C.H.A.S.

Mindless octaves has the common note on top, which makes sense when expanding the temperament upward. It also means that the beatspeed of inferred 4th dictates the beat speed of the 12th and 15th even when the tones are inharmonic.

C.H.A.S. has the common note on bottom and the beatspeed of the inferred 4th does not determine the beatspeed of the 12th and 15th. Alfredo chose the common note to be on the bottom because you cannot build a house from the roof down, but only from the bottom up. I wonder how he would dig a well.

Anyhoo, the width of an octave is slightly different between these two stretch schemes. Not that either could be tuned that accurately, let alone anyone telling the difference.

The slight difference of mindless octaves and Chas has already been discussed some years ago here. But i was saying "equivalent" not the same, meaning a difference of 0,09 cents (0,02 Hz at A4) over an octave, or 0,0075 cents between a halftone step (0,002 Hz at A4) should be valid to qualify as equivalent (maybe similar is a better term) in real world tuning practice, as piano frequencies fluctuate around at a much higher difference. As i mentioned, the ET - list is extensable by any combination of 12ths and 8ths, so it is possible to approximate Chas (which Alfredo approximates numerically) also with a pure interval. I should add, all without iH (not only iH but other nonlinear factors like damping), which must be considered separately and add or remove some amount of stretch on their own into the equation.

If speaking of aurally pure 12ths, meaning that the overall beating (sum of beats) among the involved partials caused by nonlinearity ( iH, damping, etc) is reduced preferrably to the minimum, certainly yes.

@ Stretch scheme - I understand that a refresh may be needed.

The method that Bill calls “mindless octave”, as he himself describes it, is meant to be a “mindless” way to tune "tempered" octaves up the scale, and Bill saw that method demonstrated by Steve Fairchild.

It is therefore a method that addresses the easy-mindless tuning of octaves up the scale. The upper octaves are tuned balancing 12ths and 15ths, so the newly tuned “mindless” octave will somehow "mirror" the fourth below that is actually used as a reference. This could be good practice.

One by one, all the fourths below will determine the expansion of the temperament in a way that those new higher octaves, yes, will be tempered, but - unless fourths are tempered truly progressive, and within a truly progressive contest - octaves, together with 12ths and 15ths and all the other intervals involved may get assorted, narrow or wide, as Bill himself observed and stated long ago.

Not even the pure 26ths ET “stretch scheme” can be compared to that method, as ET implies progressive intervals. Again, one should have progressive fourths in the temperament as a reference, and please note (now talking about methods), progressive contiguous thirds by themselves do not grant that.

Eight years have gone, one wouldn't say.

Bernhard, you wrote: ..."The slight difference of mindless octaves and Chas has already been discussed some years ago here. But i was saying "equivalent" not the same, meaning a difference of 0,09 cents (0,02 Hz at A4) over an octave, or 0,0075 cents between a halftone step (0,002 Hz at A4) should be valid to qualify as equivalent (maybe similar is a better term) in real world tuning practice, as piano frequencies fluctuate around at a much higher difference."...

Well, here is what you were saying: "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."...

The above information is simply wrong. When dealing with numbers, I have to ask you to be rigorous, at least when you mention Chas. Also, I cannot share your "real world tuning practice" notion, in my idea there is more than one "world", therefore piano frequencies may also fluctuate around very low differences.

..."..it is possible to approximate Chas (which Alfredo approximates numerically) also with a pure interval."..

I am not sure I get what you mean in brackets.

..."I should add, all without iH (not only iH but other nonlinear factors like damping), which must be considered separately and add or remove some amount of stretch on their own into the equation."...

s-sure.

More tomorrow.

Regards, a.c.
.

Accepted.



From my calculations, Chas octave (s=0) turns out to be 1200.46. Would you consider a tolerance of 0.01 cts over an octave as acceptable then?

No, Bernhard, no tolerance admitted intentionally, that was a typo. You stand correct, my apologies.

Hi Bernhard,

If I understand correctly, with aurally-check 12ths you are saying that there is an "..overall beating (sum of beats) among the involved partials caused by nonlinearity..." that can be "reduced preferably to the minimum".

I wonder, could the same "minimum_overall beating" (for the same reasons) apply to some other theoretical intervals typical of the pure 12ths "stretch scheme"?

If I didn't hear perfectly still 12ths, perhaps I would say... certainly not pure, but could we guess whether that minimum overall beating sounds like a narrow or a wide 12th?

Regards, a.c.
.

A slight nitpick if I may, since the discussion is getting precise.
iH is not non-linear, it is a consequence of the (linear) equation for the vibrations of a stiff string. Similarly for damping.

If I understand correctly an aurally pure 12th will be close to a pure 3:1 in the treble, but will be wide of that (3:1) if 6:2 and higher partials become audible in the lower ranges, and those beats (3:1, 6:2, ...) are balanced to create an aurally pure sound. (This answers Alfredo's question also hopefully.)

Kees

Think of whole tone octave purity before tuners were aware (about > 50 years ago) of single partial beatings.

Thank you, Kees.

So, if I understand correctly, in the treble a pure 3:1 may sound close (how close? a bit narrow?) to a pure 12th, and that could then be represented with the pure 12th theoretical ratio 3^(1/19), whilst in the mid-range we need to represent what happens with a greater theoretical ratio, a scale ratio that - in practice - can balance 3:1 and 6:2, otherwise the 6:2 will make the 12ths sound aurally narrow. Correct?

Thank you, Bernhard.

In my other post, I was saying... "I wonder, could the same "minimum_overall beating" (for the same reasons) apply to some other theoretical intervals typical of the pure 12ths "stretch scheme"?

I was asking that because I would like to understand to what extent the beat-phenomenons that derive from a certain theoretical pure ratio make sense, once we are dealing with pianos.

And I was saying: .."If I didn't hear perfectly still 12ths, perhaps I would say... certainly not pure, but could we guess whether that minimum overall beating sounds like a narrow or a wide 12th?

That's not correct.

The notation "3:1" means the 3d partial of the bottom note equals the first partial of the top note.

Due to inharmonicity the 3d partial of the bottom note has frequency more than 3 times that of the first partial of the bottom note, so it follows that the frequency ratio of the first partials is larger than 3 and if for some reason you want to divide that uniformly it would result in semitones larger than 3^(1/19) by an amount depending on the inharmonicity of the piano under consideration.

Kees

Think of whole tone octave purity before tuners were aware (about > 50 years ago) of single partial beatings.
[/quote]

This sounds like a deliberate falsehood from a sales pitch.

Tuners have been painfully aware of single partial beating, to my knowledge for almost a hundred years probably since the introduction of smaller pianos. Tuners wrote of touching strings at node points in order to isolate single partials for comparative tuning purposes. (Pianomaker magazine from 1920's). Then, of course, this was made visual by the strobotuner some 80 years ago.

I experimented with a strobe tuner some years ago. I actually found myself wishing I had one with me last week when I had to tune an "impossible" set of bass strings on a small but otherwise fine and reputable instrument. None of the discussion here would have been helpful, in fact, the major problem was an apparent previous attempt to tune to the twelfths coming from the recalcitrant bass strings resulting in a grossly overstretched tenor region. (I was the third tuner in as many days to be called in). I may have been the only one that had the complainant to hand but I tuned through the noise from upper partials and made some judicious alterations to the temperament in order to accommodate some fifths and thirds that were a bit fast at the top range of the covered strings and everyone was happy . And yes, occasionally using a thin wedge at a node point just like those poor ignorant tuners of old. (Oh, this piano was more than fifty years old). The piano had previously been tuned successfully up to the point of the renewed search for a tuner by an older gentleman who had retired.

I notice the return of the strobe pattern in some modern ETD's currently being advertised. It seems that when far enough out on a limb, the wise thing is to scramble back down and start to climb the tree again.

I am also amazed to read about "guessing" the size of a twelfth in a quasi intellectual thread such as this when a comprehensive range of internal and external test intervals are readily available on the piano being tuned.

Those tuners of > 50 years ago may have been onto something.

Removing the piano entirely from the equations is far too clever.

I had thought when this stuff first started that it was harmless crackpot stuff and yes, we are all painfully familiar with the problems inherent in small pianos but when a client cannot get their piano tuned competently from a recognised piano establishment any more, and the subterfuges necessary for small pianos finding their way into the tuning of larger pianos, is this stuff, presented with risible arrogance being taken too seriously to the point that it is actually damaging to the future of the profession?

My thanks to those who patiently point out the errors in the mathematics and logic.

How's sales?, by the way.

You know what the sign ">" means?


apparent...so you don´t know...


A grossly overstretched tenor region because of "recalcitrant bass strings" can not happen when tuning aurally, as the tenor section is tuned first. One ETD comes to my mind, where this may happen by design, but this would affect any ET size.


Fifths are faster in a pure octave ET as they are in a pure twelfths ET.


I don´t see that this may damage the future of the profession. It rather supports the future of the profession.

Kees,

There must be a misunderstanding somewhere. I am not addressing basic notions, whole tone octave purity, or iH as it is understood. I was trying to reason on beat perception in order to understand whether Bernhard, while mentioning pure 12ths, is actually achieving close to pure 12ths.

This interest of mine comes from a recent conversation I had with Kent where, mentioning pure 12ths, he would suggest to call them "clean" 12ths.

And because Bernhard has mentioned "minimum_overall beating", I wonder how that beating sounds to him, if wide or narrow.

Perhaps some differences in our practice become significant, for instance tuning mid-strings first on a wide range, which allows the tuning of perfectly still/beat-less 12ths (as demonstrated recently at a convention in Canada) or unisons as you go, but beyond that, I wonder what is left there of an original (edit: theoretical) pure-interval strech scheme.

Apologies for some background noise.
.

Dear Alfredo,

this is the goal with pure twelfths.

Minimal overall beating means clean to me. I use that description (minimum overall beating) to make clear that if speaking of a pure or clear interval on a piano, there are generally all but at LEAST one partial pair that have not the same frequency, but are tuned to a target, where they sound perfectly clean, still, beat-less, same as you possibly demonstrated successfully in Canada.



I see a serious gap between what you do in practice (essentially a pure twelfths temperament) and what you have theoretically build around about that as Chas theory:

You tune pure twelfths on the middle string over a vast part of the piano (pure twelfths equal temperament).

On a second step you tune unisons and claim by pitch sagging or coupling of the tree strings the pitch drops exactly for the specific amount that after tuning the unisons, the resulting twelfths are exactly of Chas twelfths size.

This contradicts my understanding of the physical relativity principle.

- Think about the lower note when tuning the unison, it drops too, right? If the dropping is the same, is the resulting twelfth logically not of the same size as before? Are you aware that pitch dropping from coupling does not occur on every note? How can you expect then that the resulting twelfth will land exactly on the Chas size twelfth, with your own claimed precision of 0.01 cts over an octave, that is required to be classified as a Chas interval?

- Let´s assume ideally that exactly the required pitch drop occurs from whatever effect, when starting with unison tuning : What will happen when tuning the unisons downward from the temperament region where the unisons are already tuned (and thus do not drop anymore): must not the lower note stay exactly where it was to obtain a Chas size twelfth? Or let´s assume the upper note dropped only half the amount required to obtain a Chas size twelfth: Must not climb the lower note toward the upper note then?

- Let´s proceed with finishing unisons upwards from the temperament region in the treble on the first twelfth above the temperament twelfth (i.e. D3-A4), AFTER completing the unisons over the temperament twelfth. If the pitch dropped over all notes by unison tuning in the temperament twelfth, all twelfths of the middle string in the second twelfth section above the temperament are wider of pure of an amount of the pitch drop of the notes of the temperament twelfth. Must not the notes drop then two times the pitch drop of the temperament twelfth to obtain a Chas size twelfth? And must not the notes in the twelfth above the second twelfth above the temperament twelfth drop three times the amount of the drop in the middle region?

Frankly, to me your concept of obtaining a Chas tuning by tuning unisons from pure twelfths temperament on the middle string is wishful thinking. What you get after tuning unisons after a pure twelfth temperament on the middle strings instead is more or less a pure twelfths temperament (which as a result sound wise is not wrong at all .

If you want a Chas tuning, you may preferrably do something Bill Bremmer does with mindless octaves, what would probably represent more a Chas tuning than your actual approach.

Not bad, thanks.