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Bernhard, if you see that we are going in circle, please try to make an effort, wording your question in a different way.

The Chas algorithm (as you have certainly noticed) uses two partials of the harmonic series. As a consequence, the resulting scale ratio does not lead to one integer partial somewhere across the scale. That is why I wrote "I would not know how to address a comparison of that kind between one "pure" ratio and the Chas ratio, as the latter is not "pure", and it is derived from a double exponentiation."

Edit: I have seen that you had posted more. Here below is your latest post:



Help me understand, Bernhard, were you checking my expertise?
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Wise decision. I'm following suit.

Kees
PS Just to correct some disinformation A posted after copying my posts here to yet another thread. He states 4 people "defamed" him (including me of course) over the last 8 years.

However if you check A's profile and browse his posts and see who "defamed" this chas "theory" you'll get a laundry list of pretty much all the competent piano technicians that have been active on this forum over the last 8 years.

Kees,

Please post your comments here:

http://forum.pianoworld.com/ubbthreads.php/topics/1916609/1/c-ha-s-model-climates-and-comments.html
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G.R.I.M. - Università di Palermo (2009)
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

PRISTEM - Università Bocconi (2010)
Italiano - http://matematica.unibocconi.it/articoli/relazioni-armoniche-un-pianoforte
English version - http://www.pdf-archive.com/2013/04/10/chas-prof-chiriano-english/

Università di Cagliari - Tesi di Laurea (2011)
http://www.luciocadeddu.com/tesi/Cannas_triennale.pdf

Haye Hinrichsen - University of Wurzburg - Revising the musical equal temperament (2015):
http://www.scielo.br/pdf/rbef/v38n1/1806-9126-rbef-38-01-S1806-11173812105.pdf
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You say (here and in your Chas paper) that pure scale ratios, octave after octave, CONVERGE on ratio 2:1


my questions was/is:

[/quote]

your latest response was:


I was not asking if Chas ratio does LEAD to one integer partial somewhere across the scale, but

Does Chas, octave after octave, CONVERGE on ratio 2:1 or not? (Like you said that pure scale ratios, octave after octave, CONVERGE on ratio 2:1)

Bernhard,

My reply is the one above. If you have a point (and I hope you do) just make it.

Hi Kees,

Perhaps you thought I would let you get away with that nth deceitful post of yours, but I can't. This is how “true” I can be, being a piano tuner.

You report "...a laundry list of pretty much all the competent piano technicians that have been active on this forum over the last 8 years...", and you state that they would have acted like a slanderer, meaning like you.

I remember only a few others that didn't seem to approve: Bill and BDB - at some point - thought my sharing was a meaningless effort, two others didn't like my verbiage or my opinion on pure 12ths. Actually, right at the beginning one poster (Roy123) helped me solve an issue, though complaining that the paper was difficult to read and it could have been "much shorter, crisper, and more lucid.". I am still grateful for that help.

In any case, all posters were fairly respectful and never carried out a systematic defamatory action as you did. Other posters were grateful, but this is another story.

Having said that, it is no problem with my sharing, but I believe you owe an apology before you leave, no, no to me, to the researcher you insulted when you wrote “…Given the emphasis they place on making a connection with actual tuning practice, I cannot help thinking they looked for exactly those parameters that would allow them to derive the desired conclusion.”.

In a later post you explained: “The plain-language summary I posted of that paper by Haye was intended for readers who lack the technical background to figure out what it was really about.”

Now, you call that “plain-language”, but it insinuates unequivocally a case of "scientific misconduct". Haye's paper was not "..really about.." that.

The sooner you apologise, the better, then go.
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Hi Bernhard,

It took me a while to understand your last question, perhaps due to our lexicon.

You were asking: …”Does Chas, octave after octave, CONVERGE on ratio 2:1 or not? (Like you said that pure scale ratios, octave after octave, CONVERGE on ratio 2:1).”…

In my paper I had compared “pure-interval” ratios describing their trend correctly, and you asked me about the Chas incremental ratio, so that (I guess) I would say that also the latter converges on 2.

I could not understand your question because, actually, one could well grasp the answer from Table 6, or from the Conclusion: …“This system sheds light on a harmonic sequence, the series of n/n+1 values (section 4.5) which the harmonic partial values 3 and 5 also (edit: read also) converge towards in their respective logarithmic scales.”…

As a consequence, I do not really understand the point you wanted to make (let me know), and I get the idea that you may not have understood my point yet (let me know).

It is relevant that all ratios ≠ 2^(1/12) converge on 2, they will produce some “differences” close to the n/n+1 sequence shown in Table 6.

“Differences” is what I have focused on, and “differences” is what the Chas model is about.

About one recent post of yours:



Well, as you have seen, you were wrong. Do not worry, I am not asking for your apologies.

I am sorry that eight years have gone since my first sharing, and during all this time you may have been misled by your own wrong interpretation of the figures contained in the Chas paper. It is evident why, as a result, you concluded that there were errors in that paper, and that I had been misled by those errors when interpreting my tuning practice.

So, I may have to clarify that – first - I approached practice, only afterwards theory. Not too many, but good 27 years of practice for achieving what I wanted to hear, and some three years of theory and numbers for sharing it.

If possible, I would appreciate if you could confirm that you have understood why the Chas algorithm addresses not one but two “pure” partials and "differences", instead of one "pure" interval.

I would also appreciate if you could rectify your statement about Chas being a wrong theory, or a wrong model, or a wrong ratio, possibly avoiding – in the future – more insinuations and/or statements that you cannot prove true.

I hope a new season will come, with further experimentation and more... respectful sharing.

Regards, a.c.
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Hi Kent,

In order to double-check what I am reporting, I would suggest to execute the same procedure that took me to those observations (this is for anyone who would like experimenting).

I would suggest to tune with an ETD any stretched ET curve "steeper" than Chas, it may be "pure" 5ths, or pure 12ths, or pure 19ths, or pure 26ths, even using the styles you have created for VT.

Mute from around A2 up to around E6;

tune centre strings according to your ETD, starting from A4-A3-F3, like if it was your aural sequence, then up to E6, and then from A3 down to A2;

then tune all the unisons from A2 up to E6.

Then check again the A4-E6 range and see if your ETD notices any pitch drop, and compare with the lower range. This might be a way to double-check what I am saying about pitch sagging, even on pianos that are very close to pitch.


Hi Bernhard,

In a different thread you wrote: ..."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."...

Please, bear in mind that pure 12ths is one possibility. When tuning center strings, we may choose to tune even pure fifths, or a milder stretch like pure 26th, that depends on the condition of the piano and on the range we are tuning, and it may vary depending on how we expand the temperament.

I was hoping to get a reply from you, after the storm you created.

Regards, a.c.
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Your procedure would demonstrate only a tuning that is not yet complete, nothing more.

I tune unisons as I go, and go back to refine and correct errors as needed.

Hi Kent,

I am trying to address one issue at a time.

The first issue is this one: depending on a certain procedure, we may observe a pitch drop while we are tuning.

The above does not address the end result or the number of corrections we would have to make, nor the number of passes we are ready to do.

The one I submitted is one procedure I may use, and it is only meant to reproduce a scenary that may explain why I use steeper stretch curves.

If, looking at that procedure, you can already "hear" the pitch drop I talk about - even on pianos that are "close to pitch" - we may skeep the experimentation and address a second issue. (Edit: Let me know)

On the other hand, that could be a starting point for those wanting to experiment and experience pitch drop at different orders of magnitude.

Regards, a.c.

Naa, this is not the right time, I guess, for trying to sort this out...

I am asked to believe that the theoretical ET "pure" 12ths scheme - in practice - it means only "clean" 12ths.

Bernhard Stopper explains that "clean" is because (*) "...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,...". (*)

And we have learnt that (*) "...If speaking of aurally pure 12ths, meaning that the overall beating (sum of beats) among the involved partials caused by non-linearity ( iH, damping, etc) is reduced preferably to the minimum, certainly yes." (*)

That means that the theoretical "pure" 12ths ET will give us - in practice - a "...minimum overall beating..", and we still have to understand whether it will be an aurally narrow or a wide beating.

Perhaps it is to early now... In order to really understand what all that is about we may have to wait another couple of years

Kent, you say that you tune unisons as you go, and I would have a sincere/plain question for you, and for any other colleague that tunes the "pure"12ths scheme with an ETA, and for colleagues who tune aurally and may want to join in:

Have you ever heard a 12th that really is "absolutely" beat-less on center strings, meaning pure as... "Pure"?

Thanks in advance.

(*) From this thread: http://forum.pianoworld.com/ubbthreads.php/topics/2670882/1.html
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Why do you ask? Since I tune unisons as I go, I would rarely if ever listen to center string 12ths.

And...

Why do you ask? Since we expect inharmonicity to make it impossible to tune 3:1 and 6:2 and 9:3, etc. to be pure simultaneously, we would not expect absolutely pure unisons. That is, even if they sounded pure, careful measurements might show some offset in the coincident partials.

And...

Why do you ask? Assuming you are considering the problem of tuning pure 12th equal temperament, the 12th is only one interval. In a real world situation, the aim is to tune a best-fit compromise, so in a real sense, one cannot tune any one interval until one knows how the other intervals are faring in the sea of inharmonic inconsistency.

Thank you, Kent, for your reply.

…“Why do you ask? Since I tune unisons as I go, I would rarely if ever listen to center string 12ths.”…

You are right, I could have deduced that, but I preferred to double-check. Our practice/procedure is pretty different, though I could not exclude that you knew already about different results, and I ask because I wonder if you have an idea of how “pure”, meaning perfectly beat-less a 12th can be, on center strings, and how they sound, quality-wise.

This conversation we are having, in my idea, may explain our early divergent comments on the pure 12ths scheme, remember some years ago? Well, I am tempted to conclude that we were and we are talking about two different tunings, and that might be why our opinions were (and are) different.

Remember how we could believe that our tunings are a “variant” of 12th-root-of-two, due to iH and all the rest? Hmm… To offer you an anticipation, with pure 12ths we could be facing a similar case… At the end it might be the other “variant”, due to iH and all the rest

Anyway, let us take one thing at a time.

..."..Why do you ask? Since we expect inharmonicity to make it impossible to tune 3:1 and 6:2 and 9:3, etc. to be pure simultaneously, we would not expect absolutely pure unisons.”…

I’d better clarify, I am not asking how “pure” a unison can sound, I wonder if you know how “pure” a 12th can sound, on center strings, and what that particular stretch sounds like, musically speaking, in a span of four octaves.

In general, I do consider what you wrote above, adding that it is “..impossible to tune 3:1 and 6:2 and 9:3, etc. to be pure simultaneously..”, I do not see any meaning in a theoretical ET scheme that suggests one pure interval.

…“That is, even if they sounded pure, careful measurements might show some offset in the coincident partials.”…

As I am not sure what you mean with “..if they..”, I do not know any more if you are talking about 12ths or unisons. I am sorry. Would you clarify that for me?

..."..Why do you ask? Assuming you are considering the problem of tuning pure 12th equal temperament, the 12th is only one interval.”…

I agree, in this present case “pure 12th” is meant to be “the one” interval that should denote that particular “equal temperament” stretch scheme.

In my idea (and daily experience), “pure” means pure, i.e. beat-less, perfectly still; now I hear you saying “clean”, recently I have read about “minimum overall beating”, and I feel like I may have lost (and we may lose) the common theoretical reference as well as the practical, objective (and easy) check.

Take the 12th-root-of-two stretch scheme - for example - would you describe that as an octave with “minimum overall beating”? Take “pure 5ths”, would that be fifths with a “minimum overall beating”? And pure 19ths or 26ths?

Where is the gap, I wonder, is it between theory and practice, as Lawrence P. 'Yogi' Berra would suggest, or between what we actually hear (plus our human bias, as a PW friend would suggest) and what we try to describe/represent (name, call, denominate, how to say?)?

...“..In a real world situation, the aim is to tune a best-fit compromise, so in a real sense, one cannot tune any one interval until one knows how the other intervals are faring in the sea of inharmonic inconsistency.”

Hmm… Maybe this is where our reports may differ, based on our individual experience, and I am sincerely happy to know about your “real world”.

In my real world, my target is not a “best-fit compromise”, every single time I aim at a very precise ET “form”, like a network. Sure, inharmonicity and other things (read weird scaling, pitch sagging etc.) can somehow modify the form, but not the specific intervals that denote my favourite scheme, that would be unfortunate, I would consider that to be my fault.

Back to my point, in my experience, on center strings, we can well achieve an ET-curve with aurally (perfectly) beat-less 12ths in a range of four octaves or so, then we could judge that theoretical scheme (aurally/musically) regardless of unisons or else, and then we could decide whether we like that stretch or what. That is why I was proposing my procedure a few posts ago.

What do you think, could that be a valid double-check?

Regards, a.c.
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Typo. Sorry. Should have said:

Since we expect inharmonicity to make it impossible to tune 3:1 and 6:2 and 9:3, etc. to be pure simultaneously, we would not expect absolutely pure 12ths.

"but not the specific intervals that denote my favourite scheme."

So, which is more important, the overall progression of the temperament, or tuning the specific intervals that denote [your] favorite scheme?

I say the progression is more important as denoted by the relative beat speeds of the various tuning intervals. To make individual intervals more important would surely introduce errors elsewhere in other intervals.

I see no benefit to evaluating the stretch with only center strings. (A drawback though would be that I thought you said you tuned center strings more steeply than your end result. So how does listening to only center strings evaluate your chosen stretch?) A piano has trichords; I check tunings with all strings tuned and sounding.

I wrote: .."...but not the specific intervals that denote my favourite scheme."

Hi Kent, you wrote: ...“So, which is more important, the overall progression of the temperament, or tuning the specific intervals that denote [your] favorite scheme?”

They are equally relevant, progression to denote ET and specific intervals in order to denote the model.

…“I say the progression is more important as denoted by the relative beat speeds of the various tuning intervals. To make individual intervals more important would surely introduce errors elsewhere in other intervals.”…

The two things are strictly interrelated when you think in terms of “form”, the progression stands for ET, some individual intervals denote the model.

...“I see no benefit to evaluating the stretch with only center strings. (A drawback though would be that I thought you said you tuned center strings more steeply than your end result. So how does listening to only center strings evaluate your chosen stretch?) A piano has trichords; I check tunings with all strings tuned and sounding.”…

Hmm… Are we missing the point? I do tune steeper curves, depending on the piano condition, brand, age, depending on how it reacts while I am tuning etc… But I was inviting you to evaluate pure 12ths on center strings, because on center strings you/we can actually tune truly “pure” 12ths, and tell how we like them. Was not that clear above?

…“..(… So how does listening to only center strings evaluate your chosen stretch?)…

That is not so difficult, with a bit of experience you can anticipate the dynamics of the piano you are tuning. And you can always double-check, before and during unisons, and correct where needed.
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You make your points and I'll make mine. Thanks.

The width of ET can only be determined by the pattern of beat rates, not by an individual interval.

If you wish to understand why some techs can be so overwhelmingly resistant to following your prescriptions for executing tunings, become adept at tuning with an ETD.

Hi Kent,

You wrote: "The width of ET can only be determined by the pattern of beat rates, not by an individual interval."...

We may need a clarification. For how fundamental beats are, I worked on a ET model based on beats, in this sense we may project the very same scenery, you call it "pattern", I call it "web", or network, or beat-whole, ET as a beat-geometry.

On the other hand, an ET model requires only a scale ratio, and the latter could be referred to only one interval, like 12th-root-of-two, or other "one-pure-interval" ratios, as we have seen. One thing you may notice is that those "pure" ratios actually brake the beat "pattern", since they favor an individual zero-beating interval.

..."..If you wish to understand why some techs can be so overwhelmingly resistant to following your prescriptions for executing tunings, become adept at tuning with an ETD."

Hmm... Perhaps we misunderstood. The procedure I posted recently was meant to address one issue: why I tune steeper ET curves. I thought you and Bernhard (and perhaps others) wanted to understand, and so I offered one procedure on which you could elaborate further, even taking measurements with your ETD's and perhaps report on pitch sagging of different magnitude.

Then I asked you: Have you ever heard a 12th that really is "absolutely" beat-less on center strings, meaning pure as... "Pure"?

Now I know that you tune unisons as you go, nevertheless I think it could be interesting if you gave yourself the chance to listen only to center strings, you might be able to check the 12ths you tune (and all the other intervals) much more precisely, hear (or measure) whether those 12ths are actually beat-less, perhaps you could play a beat-less_12ths _ET-scale - on center strings, for once - and let me know how you like it. Above I posted the reason:

You make it very difficult to answer respectfully.

I am a fully qualified aural tuner. I know what it sounds like to listen only to center strings.

I do not believe that I am the one here who needs to broaden my tuning experience.

You would do well to become familiar with visual tuning techniques, but I already suggested that.

I'm done. Bye.

Hi Kent,

I am really sorry, I do not understand what is wrong with what I wrote, I would like you to trust me when I say that I try to communicate in the most simple way, trying to be clear and straightforward, never doubting about your expertise and your knowledge.

Possibly, what you wrote or how I happen to misunderstand English could take me to a certain idea. Be sure, the last thing I would do is to show little respect.

My apologies, if I misunderstood it was not intentional.

The reply of mine you quoted above follows that question of mine: "Have you ever heard a 12th that really is "absolutely" beat-less on center strings, meaning pure as... "Pure"?", and your reply: "Why do you ask? Since I tune unisons as I go, I would rarely if ever listen to center string 12ths.".

Now you write: "..I know what it sounds like to listen only to center strings."...

Well, I wish you had told me that straightaway, my reply would have been different.

Today it was a killer, many challenging pianos and a concert prep right at the end... More later on...

Regards, a.c.
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