Kent, Bill, all Colleagues,

Tooner kindly writes: “I do not think there is any practical difference between Chas and mindless octaves.”

If only we could have said this six months ago! Actually Bill, reading about your tuning’s effects, the pipe organ, the crystal clear, made me think that our “sweet spot” must have been very close indeed. Will it be so?

If really Tooner were right, I could state:

So far you/we have been looking at equal beating 12ths and 15ths only as a technique, now you/we may acknowledge that it can also be the expression of the 12th root of two ET model’s improvement.

We may share the reason for discarding two unjustified theoretical assumptions - that the range of the scale module must be 12 semitones, and that the octave must be theoretically pure - and appreciate the practical outcome of a theoretical superior compromise.

All together, we may now justify a revisory effort and evaluate iH’s effects in their true light.

In fact, Chas model stretches the octave and all intervals not only because of iH, but for gaining a precise sound whole, and corrects the theoretical semitone’s value so that it can be a function of our two practicable ET constants.

This makes me convinced that Chas model’s “compromise” may one day represent the temperament reference for other (western traditional) orchestral instruments, what may finally take to a superior harmonicity degree.

I also think that ET teachings may improve in terms of clarity and exactitude, and maybe this would make our aural tuning experience shareable even more.

Regards, a.c.

First recording (.rar) of CHAS tuning on a baby Steinway S (5’ 1”, 155 cm) at MediaFire:

http://www.mediafire.com/?sharekey=20194ca8898fecef1bee9a6e9edd9c76e04e75f6e8ebb871

CHAS Tuning MP3 (Granpianoman)
http://www.box.net/shared/od0d7506cv

All Colleagues and Tooner,

You wrote (10/30/09):...“I do not know of any intrinsic value that the ancestry of a ratio could have. What is important is what the ratio will accomplish on its own.”...

My reply (11/02/09): I’d say that the intrinsic value of a ratio is its ancestry or, a ratio can have an intrinsic value depending on its ancestry. Chas ratio returns the qualities of two algebraic magnitudes, 19 root of three and 24 root of four.

You also wrote (11/20/09):...“But it is not clear why this compromise is necessary at all, let alone why a superior compromise results with this sort of equal beating.”...

More recently you wrote (11/23/09):...“So, you see the problem of equal beating octaves and 5ths as one of ascetics, that it would not sound good. But the advantage of equal beating 12ths and 15ths is that it makes a wonderful mathematical model! They both make a wonderful mathematical model, and they both can be ascetically pleasing.”...

Then you said you were talking about aesthetics.

I reply so that some unfortunate statements will not result in being misleading.

You have already acknowledged that using a Chas-type equation with two partials values makes a “wonderful mathematical model”. Now I may better explain what the “intrinsic value of a ratio” can be, and why Chas ET 12ths and 15ths equal beating is a “superior compromise”, not only compared to any pure-ratio model, but also compared to equal beating octaves and 5ths.

Let’s see. The ratio for 12ths is 3:1, the ratio for 15ths is 4:1. So, Chas EB-ET equation combines the values 3 and 4.

5ths and octaves involve ratios 3/2:1 and 2:1.

The two means/average-values tables below is worth for comparing and simply noticing what happens.





The values 3 and 4, together, can average couples (dyads) of ratios and include from 1 to 9 and up to 16.





The values 3/2 and 2 can average couples (dyads) of ratios and include only from 1 to 5.

Can we now compare 2:1, 3/2:1, 3:1 only “pure ratio” models?

Can we share a good reason for a combined "two ratios" ET model?

Can we say that ET 12ths and 15ths equal beating represents a superior compromise?

Could we ever say that it is only a question of aesthetics?

Regards, a.c.

First recording (.rar) of CHAS tuning on a baby Steinway S (5’ 1”, 155 cm) at MediaFire:

http://www.mediafire.com/?sharekey=20194ca8898fecef1bee9a6e9edd9c76e04e75f6e8ebb871

CHAS Tuning MP3 (Granpianoman)
http://www.box.net/shared/od0d7506cv

I must apologize, there must have been a problem with the server and the first means/average-values table disappeard. Here it is again, I hope it'll last.






Regards, a.c.

All Colleagues,

Before starting with Chas ET-EB system, I needed to be sure it was not a subjective preference, so I kept all my tunings (and my customers) under observation for more than 20 years.

So doing, I have also been able to confirm that, in our practice, iH is not a problem at all. Grand pianos or small spinets, ‘800 cabinets, clavichords or harpsicords, on all of them it was and it is possible to define the ET-EB form I am talking about, no matter the usual iH’s degrees. Thus I decided that there may have been a problem with the overall approach, and so I started to check our 12th root of two’s theoretical premises.

I noticed that all temperaments have one assumption in common: all theoretical models try to gain the scale by working on the scale’s mere numerical values. In other words, the beats order was/is thought as having to depend on the tones size, but in fact it (the beats order) depends on partials matchings and therefore on proportional differencies.

So, if anything, it should be the other way around: beats, i.e. differencies, should determine the scale frequencies values, and this is how I matured Chas approach and started looking for a difference-constant.

Once I experienced that octaves and fifths are the two stretchers, i.e. that the compromise had to be found between these two intervals, I got ready to notate a double difference-constant. In fact, all partials had to contribute to the optimum compromise, all intervals had to give up a small part of their “pure” value, and the correct way would have involved both stretchers, fifths and octaves.

Therefore we could say that, with 12th root of two, fifths, thirds with the other intervals are stretched in favor of only theoretical 2:1 octaves, but in fact 12ths and 15ths can stretch all intervals, in theory and in practice, in favor of a beating whole. All intervals can actually be thought as equal rank stretchers, all together sharing in the most intrinsic correlation amongst scale frequencies and beats.

Chas ET-EB 12ths and 15ths can express a synchronic beat order. This means that tones do not produce out of time beats, nor unconvenient contrasts and so beats and partials together can gain the greatest overtones outcome, in synergistic terms. In other words, proportional beats can turn into energy and enhance the sound-whole with more sounds. This is what I hear, this is what I experience every time I tune.

Chas system translates my aural tuning experience and it is meant to share an assumption-free, correct and reliable temperament model, together with its two practicable EB constants. It numerically proves the ultimate proportion between all partials differencies and the scale foundamental frequencies, it proves the symmetries within four octaves and the whole’s stability deriving from ET-EB 12ths (narrow) and 15ths (wide).

In terms of means, Chas model uses our own (aural tuners) “key”: beats, i.e. differencies. This explains the delta and s difference-factors inside the Chas formula.

Chas algorithm is so powerful as to enable any frequencies logarithmic progression, even pure-ratio-based scales like 2:1 or 3:1 ETs, so in a way it may be considered “dogma-free”, but it features finally a reachable target for all tuners, the precise equal-difference that will open to a perfectly resonant beating whole.

CHAS article - G.R.I.M. (Department of Mathematics, University of Palermo, Italy):

http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

CHAS Tuning MP3 (Granpianoman) on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

Regards, a.c.

Alfredo,

your theory does not answer why not taking instead for example a model like: (This is not the model i personally prefer, just an alternative to the CHAS model)

(6 − ∆*s1)^ (1/31) = (4 + ∆*s)^ (1/ 24)

with a solution of ∆ = 0.00230684644393...
and an slightly smaller incremental ratio than CHAS of: 1.059488545...
(which would result with better thirds for example...)

Analog to section 3.4 of the CHAS paper, we would have 63 steps (compared to only 49 in CHAS, i guess the CHAS model wants to appear superior because it provides 49 steps compared to only 13 in the standard ET model),
with a scale ratio of:

(6 + ∆ )^2

We also have a perfectly balanced system around step 31:

0*(4+∆)→24 → 31 → 38*(4+∆)→62
0→7 *(4+∆) → 31 *(4+∆)→55→62
0*(6-∆) → 31 *(6-∆)→ 62

ETC.

As i already mentioned, Guerino Mazzola has provided a general formula which can take every form of ET and non ET for the harmonic tones, CHAS does not provide something new here.

An "s" term alike element, which enables the CHAS model to take every size, is generally implemented in tuning programs by additional terms to hold for stretch caused by inharmonicity for example, also nothing new here.

Finally describing the standard ET in CHAS terms, with s=0 we get:
(3 − ∆*s1)^ (1/19) = (4)^ (1/ 24)
and a solution for ∆*s1=0,0033858462466..., the standard ET incremental factor, 1.059463094359295..

We can get this equation into another form by replacing 4^(1/24) with 2^(1/12):
(3 − ∆*s1)^ (1/19) = (2)^ (1/12)

If we multiply by ^19 and ^12 we get:

(3 − ∆*s1)^12 = 2^19
now we multiply out the left term and bring the difference to the right side:

3^12=2^19+∆*s1

if we express the difference as a factor (which has several advantages, when calculating with frequencies), we can write:

3^12=2^19*∆' (note*)

and we divide by 2^7:

we get:

3^12/2^7=2^12*∆'

which is simply our well old fifths circle with ∆' for the pythagorean comma. CHAS model is simply another form of the fifths cirlce, (as is my model too) not a spectacular new academic model as it may appear.

This is my last post to this thread.

All the best,

BS

(note*) you can find this "natural" form of the fifth circle in my paper:
http://www.piano-stopper.de/dl/PTG2008_StopperTemperament.pdf

Hello, the logic escapes me and is certainly good and true, but musically it does not suit my ear. Indeed larger tunings in the medium range are appreciated for jazz harmony with lot of sevenths but the treble lack liveness, and the basses are too tight to me, with too slow beats in the low medium.

Certainly practical, but too close to me and too "straight" where is the contrast and tonality ? it need more stretch in the beginning of the treble and bass.

I don t want to be short there, I simply say what my ears tell me. could be a question of habit, but in the end we need to play and to play together with other instruments as well.

the thirds are all but lively, you may not notice because you listen to the tuning while playing.

I feel more musical to "follow the piano" more than to use a layer of theory? Thanks for the recording anyway.

I send a friend which is very good to tune the "Cordier" temperament method, to tune a small C2 Yamaha at a pianist customer of mine (leaving far from my place). They finally told me that they called another tuner to tune the piano "normally" after him.
Others appreciate his tunings, and the C2 is a small piano hence that large tuning decompress the harmonic content so it make sense. It simply did not fit the pianists ears and he noticed that soon.

Kamin, thank you for commenting. For me it will be interesting to know about your tastes and tunings, I will soon reply to you.


Originally posted by me:

The article describes the theoretical and mathematical foundations that can enumerate ETs, including 19th root of three, and the basic 12ths and 15ths opposite equal beating ET. This is why I say: now, 12ths and 15ths opposite equal beating ET model has got a precise name.
As simple as that.

Bernhard Stopper, you wrote:

..."Exactly for this, we have Mazzolas formula/model already. And his model can not only enumerate any ET model but also any possible non-ET model, thus beeing superior over CHAS, which is limited to ET. As you are very talented in twisting the meaning of critical reviews about your CHAS model into the opposite and constantly ignoring existing, predating, valuable and even superior models to CHAS, i will stop the conversation here again.”...

Professor Mazzola’s formula does not isolate with figures, nor evidenciate 12ths and 15ths opposite equal beating ET. Probably, not being a piano tuner, he could not have that kind of clue, nor that standard urge.

This is probably why he himself, wrote back to me (months ago) and warmly suggested to go for a pubblication in the JMM.

Chas limited to ET? You are wrong, the algorithm can define the precise ratio also for single tones.

Bernhard Stopper, you started your "conversation" with your “cello scrotum” rotten insinuation (05/07/2009).

Now, about ignoring other predated models, go and read. None of them is Chas EB-ET. And I could never have immagined your way through false and defamatory statements.



a.c.



.

As i mentioned already in my post from May, 20 2009, the cello scrotum publication is a brilliant article proving deficits of peer review processes of scientific journal articles. I was just guessing if your Chas paper could have been of this category after the missing references to existing state of the art developed in the recent years to overcome the limits of stand ET in piano tuning and the offensive language you was using. This isn´t a rotten insinuation at all.

Instead, you should welcome to get critical reviews, which could help you to eventually refine your paper if you plan for a publication in a scientific journal, which i would recommend you warmthly too, like Prof. Mazzola did.

Again the link to the cello scrotum article for those who are interested:
http://www.timesonline.co.uk/tol/life_and_style/health/article5601050.ece



Of course, if the s variable is not only a scalar variable, but a vector variable with different values/coefficients for every note. In that case, any figurative aspects of the Chas model are lost and one can use the simplest form of describing tones, namely by a general vector variable containing the frequencies of every single tone´s partial(s).


Mazzola´s model allows for visualization of tunings in the three dimensional Euler space for example.


The evidence of 12ths and 15ths opposite equal beating is not yet proved to be necessary, and rather an arbitrary and subjective selection as i figured out in my recent posts.


Bremmers mindless octaves ET model is exactly Chas EB-ET.


12ths and 15ths opposite equal beating tuning method and ET model (Bill Bremmer described his method in words, it has become a model then, it must not necessary be described by mathematical formalism) has got a precise name already, called "mindless octaves".

Stopper,

In my opinion you are offending also PW colleagues and readers.

..."The evidence of 12ths and 15ths opposite equal beating is not yet proved to be necessary, and rather an arbitrary and subjective selection as i figured out in my recent posts."...

This is written in Chas research report, section 2.0.

..."Bremmers mindless octaves ET model is exactly Chas EB-ET."...

What is Chas EB-ET model is explained in the research report. What is Bill's, is very well written in PW.

CHAS article - G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

In my opinion, you and Tooner are now mystfying the truth, and I find this sickening. Fortunately, Bill and I have long written to each other about his mindless octaves technique, EBVT and Chas model. Bill would never dare to pretend what it can not be.

Originally Posted By: alfredo capurso

This is why I say: now, 12ths and 15ths opposite equal beating ET model has got a precise name.
As simple as that.

Stopper, you write:..."12ths and 15ths opposite equal beating tuning method and ET model (Bill Bremmer described his method in words, it has become a model then, it must not necessary be described by mathematical formalism) has got a precise name already, called "mindless octaves".

Ok Stopper, look at methods, words and models the way you prefere.

In practice, this is one example of how Bill Bremmer tunes 12ths and 15ths (Chas Topic - 06/02/09): “I routinely see them invert themselves: the 12th becomes wider than the double octave”.

This is the tuning Bill may like the best, call it words, method or technique, but it is not Chas EB-ET theoretical model nor Chas practical equal beating tuning form (12ths and 15ths equal beating along the whole keyboard). And Bill in his honesty would never dare to state lies.

Chas is a new temperament theory derived from my practice.

http://en.wikipedia.org/wiki/Theory

Since all this is quite common knowledge, I can only think of yours as a deceitful intention. Your dwelling then is sick, therefore I have nothing more to tell you.

Bill, all this may be only market strategy, I'm sorry too.
I apologize with all readers, I never meant to share this odious burden.

Posted here on 5/11/2009: About theory and tuning - you may ignore theory and tune aurally in a casual or personal way, or use an ETD without careing what’s behind it. Maybe a simple question of knowledge and consciousness that is up to you.

a.c.

.

Dear Colleagues,

I’m trying to turn the recent falsifications in a sort of challenge, in a chance to grow in terms of consciousness.

Only now I understand how my detractors have tried, for seven months, to mystify and reduce the value of the Chas research report, with out-of-theme subjects, insinuations, with insults and absurd arguments. The idea of having taken part in a devilish project makes me shiver.

Eventually, these posters could not hide anymore the value of Chas theory but they have attempted to mix things up again. All their lies and all their ambiguities are written though, they have been well traced too, and paradoxically they themselves are confirming now the relevance of what I am trying to share.

With their devious deeds, by rereading their posts and/or noticing their silence, we may keep on training our insight power and our comparing skill, what is useful (in my opinion) for tuning too.

On your part, you may now open more to a new approach to the temperament and, maybe in a while, try the gaining of Chas beating whole.

Now you may appreciate the difference between having to refer to 12th root of two ET ratio, and having a correct ET theory’s ratio as a solid reference, as well as a tool for gaining any ET ratio.

We may be able to share also Chas Preparatory Tuning, the SBI's (slow beating intervals) control and progression, how they can make “that little difference” and how they could help me gain Chas pure tuning form.

Quite recently, an American colleague wrote to me kindly asking to know more about me. Today, since my professional route may not be understood as an incentive nor as ostentation, I can post my reply.

Regards, a.c.


CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):

http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

CHAS Tuning MP3 (Granpianoman) on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv


.

Alfredo:

You could counter the posts of the detractors of your theories (including me) by referencing posts of the supporters (I do not remember any).

Dear Colleagues,

I’m trying to turn the recent falsifications in a sort of challenge, in a chance to grow in terms of consciousness.

Only now I understand how my detractors have tried, for seven months, to mystify and reduce the value of the Chas research report, with out-of-theme subjects, insinuations, with insults and absurd arguments. The idea of having taken part in a devilish project makes me shiver.

Eventually, these posters could not hide anymore the value of Chas theory but they have attempted to mix things up again. All their lies and all their ambiguities are written though, they have been well traced too, and paradoxically they themselves are confirming now the relevance of what I am trying to share.

With their devious deeds, by rereading their posts and/or noticing their silence, we may keep on training our insight power and our comparing skill, what is useful (in my opinion) for tuning too.

On your part, you may now open more to a new approach to the temperament and, maybe in a while, try the gaining of Chas beating whole.

Now you may appreciate the difference between having to refer to 12th root of two ET ratio, and having a correct ET theory’s ratio as a solid reference, as well as a tool for gaining any ET ratio.

We may be able to share also Chas Preparatory Tuning, the SBI's (slow beating intervals) control and progression, how they can make “that little difference” and how they could help me gain Chas pure tuning form.

Quite recently, an American colleague wrote to me kindly asking to know more about me. Today, since my professional route may not be understood as an incentive nor as ostentation, I can post my reply.

Regards, a.c.


CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):

http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

CHAS Tuning MP3 (Granpianoman) on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

.

Bill, thank you.

I do think that your tuning are different from Chas EB-ET, and I'm looking forward to appreciating them on a real piano.

Actually, I think that the recent vicious attempts to squeeze Chas temperament into your technique have damaged your image too, regarding both your favorite ET routine tuning and your EBVT model.

These have been some of my consequent readings:

http://en.wikipedia.org/wiki/Moral_turpitude

http://en.wikipedia.org/wiki/United_States_defamation_law#Defamation_per_se

http://en.wikipedia.org/wiki/Intent



Regards, a.c.


Kent,

You ask:..."Why do you feel the need to use flowery analogy in speaking with experienced professional tuners?"...

Because the use of an analogy may help, be him/her a pro tuner or an apprentice.

Quote: So, I never go directly for the Chas form.

..."Specifically, why not?
Are you claiming that your temperament and/or stretch level of your tuning requires some special technique that must be followed in order for a professional tuner to execute your tuning with stable results?"...

Why not, it is explained in the same post, because the piano, like a bow, will adjust on an overall "at rest" condition. About my technique, I do not think it is special, and I'm actually trying to make it more common.

If that execution is required? Yes, and it gets stable results. Could you please answer me about the possible date of our meeting?

Thanks and regards, a.c.

.

And here is something I was reading:

http://en.wikipedia.org/wiki/Martyr_complex

Kamin,

yes, tuning mid-strings I go for an accentuated raise of pitches and for faster beat rate progressions, so that the piano can then settle on Chas form.

By readind this thread you may find out that many issues have already been discussed. I sincerely apologize, but I do not have the time to write about the same issues again and again. I'd rather suggest a more attentive reading, if there is a real interest.

For istance, about my need for a preparatory tuning I wrote in May 23, 2009 and August 01, 2009:

"When in the treble you can check octaves, 10ths, 12ths, 15ths, 17ths and 19ths you do not need to check 5ths anymore. Check for progressive octaves (check with middle string only), tune middle string a bit higher, i.e. make your check-intervals a bit wider, so that when you join left and right strings you can get stable and constant 12ths and 15ths equal beating."

Chas ET Temperament Theory has two mathematical constants: 12ths and 15ths opposite equal beating all along the keyboard. This strictly requires progressive octaves and progressive SBI.

About what's happening and about the latest lies, you may get your own opinion. Please mind, I'm not pushing you towards any of this reading.

Bill Bremmer (June 21, 2009):..."I also learned from Kent that it doesn't matter how wide or narrow the octave is. Since he had explained it to me, I heard it from other sources as well.

Regarding whether 5ths and 12ths become wide or not, they do, I am convinced of that. I learned that very long ago from Steve Fairchild who demonstrated it at a PTG convention. Now, I take what Kent said about my post to heart but the figures as I posted them still suggest as much.

Now, if you continue this technique upwards, you will inevitable find a point where both the double octave and the 12th will both stop the pattern and to the ear, both will sound perfectly in tune. When you continue upwards, you will find the exact opposite of what you found at F5. When the 12th stops the pattern, the double octave will be wide, when the double octave stops the pattern, the 12th will be narrow, still each by a very small amount.

This means (at least by my reasoning), that the 12th has become wide and therefore the 5th as well. However, at this point, the coincident partials for the 5th may well be out of hearing range and therefore, however wide they may be won't matter because they cannot be heard. In any case, a slightly wide 5th is not unpleasant to the ear, especially that high up where the sustain is so short."...

My detractors could well understand and remember thas Chas EB-ET Theory is then original.

Regards, a.c.

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):

http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

CHAS Tuning MP3 (Granpianoman) on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

I find Capurso´s statement (last line) not to be evident:


Bill is describing in the posts you are quoting here a "tweaked" METHOD of his initial idea (The MODEL) of opposite equal beating duodecimes and double octaves. And the MODEL he described, is equivalent to the CHAS ET-EB MODEL form.

Quote from Bill Bremmers own words: (http://www.ptg.org/pipermail/pianotech/2002-January/101241.html)

"Essentially, it is an *Equal Beating* compromise between the Double Octave and the Octave and Fifth."


Also, i don´t find this statement to be evident:

My statements about all harmonic ET models is, that all (including Chas model, Chas EB-ET form and mindless octaves, Cordiers pure fifth temperament, my own etc.) are mathematically valid.

What i am saying is, that there is no evidence of "Chas EB-ET 12ths and 15ths opposite equal beating" form over other forms of equal temperament, by the arguments from section 4 given in the Chas research report. (Falsification to follow)

not enough brain time to dive into the understanding now (bu I will try) but large fifths are eventually ugly in the high treble as in the medium range (I mean no precise limit but probably above the minor third major sixth equivalence)

Is the reasoning true to remember that partials only modify the global tone pitch perception), I truly try to avoid listening to partials particularly when tuning fifths.

And I can promise you that I have seen thirds progression that wher giving the impression of a nice progressiveness, while the partials where not at all following the same speed progression if I listen to them used to test more precisely. So what ... ?

For me, only piano tuning models that address iH are mathematically valid. This is not the case in models that produce a single semitone or incremental ratio, such as the models you mentioned. As an aural tuning model, they are valid. But not as a mathematical model. There is no application for the resulting ratio in inharmonic theory.

I agree that this statement needs correction for the piano models. I will correct my statement into "...all harmonic ET models..."

Bernard:

Good enough, although I was hoping to see the math that applies iH. Perhaps the way your program does... (Just Fishing)

This is for sharing a part of my experiences, matured through my professional route. Nobody is forced into this reading. Also, I apologize for my style and please, acknowledge most part of the content as representing only very personal opinions.

I was living in Padua when I stopped my law studies to go to Milan at the age of 21. There I started my technical apprenticeship and, two years later, I started collaborating with the Italian dealer of Yamaha pianos. I could then improve my skills in Paris and Hamburg, with the teachings of the most motivated German and Japanese technicians, so that I could hold for 15 years the position of Yamaha chief technician for all of Italy. Ten years ago, my companion, our two children and I moved back to where I was born, close to the sea and to a very generous nature.

What I happen to have found is a solid theoretical reason for stretching the octaves together with 3ds, 5ths and all intervals, this reason being having to interrelate all partials effects in a practicable ET scale. Today it is Chas Theory's mathematical rule.

All started when I asked myself: why should octaves be theoretically pure? Actually, why should any interval be theorized as beatless? Can zero-beating be reasonable? Yes, I could understand why the ancients could strive for “purity”, how that concept could represent the ultimate inspiration for human being, how it could well express perfection, so much so that we could not resist the application of this concept to numbers and models, as well as to waters, stones, metals, down to purebred animals and human race.

Also the most recent ET models promote a “pure” concept, pure 5ths or pure 12ths, this is fair enough. I’m actually describing what I simply call a pure beating-whole.

Tuning may be looked at as a dilemma, i.e. a circumstance in which a choice must be made between two or more alternatives that seem equally undesirable. In my opinion also, having to choose between pure 3ds, pure 5ths, pure octaves or pure intervals can only end up in a dilemma, but if we think in terms of “pure whole" we may appreciate Chas Theory's approach.

Octaves and 12ths are the real scale’s stretchers, i.e. partial 2 and 3 and they, together with all the other intervals, are able to hold the semitone scale. Now we may well consider a set that is pure, in that all partials and all intervals, in theory as in practice, can contribute to the tonicity and the stability of a beating-whole.

Maybe this concept itself is the most delicate issue, what makes this transition difficult, going from a pure-interval set to a purely beating-whole.

12 root of two ET model did not resolve the conflict known as the comma simply because, keeping up the tradition, it fixed a pure octave. Chas ET Theory resolves this conflict at its roots, and this can be said metaphorically as well as mathematically: I needed to renounce any “pure interval” root, and I needed to use a Delta Difference for partials 3 and 4 roots. This is why in Chas equation you now find 19 root of 3 and 24 root of 4, two roots instead of one single root, so to intermodulate one octave with the next one.

I think that in the comma conflict iH may as well result neutral. What we know for sure is that iH is responsible for the increase of the actual frequencies values. This does not mean that, due to iH, we must stretch octaves, nor that we should have beatless octaves, but only that a beatless octave will not be an actual 2:1 frequency ratio. In other words, we could tune beatless octaves, in which case we would not get the so called ET progression, and iH would still be there, neutral.

Chas Theory describes and supports all this with logic and faultless mathematical evidences. The traditional concept of a pure interval, be it the octave or what ever interval, has litterally kept all this secret, it has obscured the possibility to conceive the 88 sounds set purely as a beating-whole, it has forced us into thinking that there was no way to resolve the partials conflict, that there was no way to simply relate all partials effects in a sound scale, that tuning can only be a compromise.

Some say they manage to use iH for stretching octaves correctly and this may confirm that iH is not a problem, that if anything iH can be of aid. So iH may not be thought as a foe. The “against each other” factors were the partials, since they all can produce the commas, so all together they call for the fairest interrelation.

This is where SBI and RBI took me with their smoothest beat-rate progressions. This is when I finally trusted my musical ear. For many years, while tuning mid-strings, I had used my sense of rhythm for checking beats and my taste, but after unisons and some playing my musical ear was not satisfied.

Then I decided to go for a preparatory tuning and a wider stretch-curve untill, after unisons, my ear could discover a wonderful effect, like if a chorus of hundreds of people was there, all singing an astonishing amount of overtones, and the clearest sound, what in my experience only the clearest water can recall.

A great opportunity was given to me for years, when I had to follow some piano competions, and for up to 15 days I could see the day by day effect of time and heavy playing on my tunings. I had to work at night but that silence was gold. Then I could well evaluate the piano settling down tendency and adjust my preparatory tuning. Then I started thinking in dynamic terms and I accepted the necessity for a wider stretched preparatory tuning, despite what my musical ear would suggest.

Since then, when tuning mid-strings, I may have to go even beyond an aural pure 5th (on mid-string), so that after unisons I can gain Chas tuning form. Some questioning would be fully justified: Which Theory results in an "optimum"? Where is the "sweet spot"?.

In my opinion, the answer has to be given at two different levels, one being relative to us, the other being theoretical. At a relative level, subjective preferences may play an important role. This is why, musically, all temperaments can be valid. At a theoretical level, Chas is the ET Temperament Theory that mathematically relates all partials effects, so putting an end to the commas conflict, the temperament’s age-old problem.

a.c.

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Hello, Alfredo,
I think I begin to get it.

To say it short, what I understand is that you let the justness of the piano be driven by the partials series, which gives a lot of air to the tuning (decompression of the spectra as I call it !).

The defect is that this will depart from justness by a variable point depending of the piano (while indeed giving a guarantee that the partial mix is well evened along the scale, with the same relation reproducing itself.

some scales have moderate ih others no, and one some instruments the progression is not that perfect

I have to hear again that piano, to be honest I have left after the second time because I was not convinced by the harmonic behavior (as said possible twisted hearing because of so called "perfect pitch")

I wish I could follow the maths but aint the case.

Did you try other approaches ?

As you said iH is an advantage, it allow to open the tuning.

I dont get your point with the central string, I guess you tune one doublet, then the other, indeed a guarantee against the usual drift, as it is done when tuning aurally, but the final pitch I am after is the one of the center string.

There are funny things in tuning , one of my colleagues produced much appreciated tunings when he was tuning with the right pedal engaged (as I trained a tad to do). I recall that one day that I had do that way, the piano was really very lively and singing as have been noticed by the engineer and pianist, who asked me what did I do to the piano.

But not a beats method there, out of thirds 4th and 5ths evened in the octave (same kind of thing as you, without the maths behind)

indeed a more sexy theory than any straight approach, but then, what music is it for ? when one need a close harmony dark piano for chamber music how is the harmony ? etc etc.

Your welcome if you come by, to show the way you lay that temperament/tuning, must be fun !

If you mostly worked on Yamahas I understand your need for more lively tunings !! (joking)

I don't know really if piano tuners worry about that comma (due to the piano iH)

But the basic Yamaha tuning also rely on theoretical basic frequencies,(or beats speed) if you do that too much you can have a bad sounding instrument without noticing as the ear accommodates with time.
I always wondered if the Yamaha approach was an intention to add some deepness to the instrument, by emphasis on close harmony and straight forward lining of 4:2 2:1.
Air quality in Yamaha tone it what misses indeed (comparatively with S....) I'll make friends at Yamaha !

I like the way the low basses align to mediums, but i think I understand what disturbs me (a little, in fact).

Tonality impression is not very present.


This is totally driven by the piano, the opposite of usual tuning to beat rates standards, but also the opposite of for instance "pure fiths" method where the fifth is made "pure" in intention to help the inharmonicity to be adbsorbed (if I get the point), hence a layer of justness added to the piano's own justness.

I believe the tuner have to provide a mix between what the instrument seem to want naturally and what he, the tuner, will accept as justness, contrast, harmony.
How to get there while passing by a mathematical model is above my understanding.

I for instance don't like so much the first harmonies at the beginning of the recording, (slow tenths, sing like chinese bells I believe that this low stretch medium lives room for the highly stretched treble - ) the FD sixth that also make that gamelan tone, then it gets better, (some unisons moaning) but no definitively the high treble is not even, when was the piano tuned ? the recording was in winter ?

D6 is low D7 as well, the A's don t line in the treble (out of sequence)

I like the high and medium bass C major harmony , moderate stretch, warm, nice and very well phasing for that small piano.

The harmonic progression generally speaking lack liveliness, (may be coherence) and that I cant get why. may be old hammers/strings and unisson attack quality impede the clarity so the tone is more nasal than you wish.

A professional tuning in anycase, thats not the question.

Indeed some "air" despite a fair use of the sustain pedal.

I am just trying to state what I hear/feel , sorry to forget convolutions, I for that try to avoid any personal attack that is far from my mind please believe that.


As a tuner I believe you get as much servicing the piano that you let the instrument dictate its own justness 100%. That is a very respectable approach, but is it practicable ?


Best regards.

Makes me think that the result may not be far from what I had with the tuning made with right pedal engaged (hence immediate stability, and tuning in the natural resonance of the instrument more)

When notes are played together, the partials literally seem to "jump of the box" and the piano sing as if the pedal was engaged. That is the effect I hear in your recording unless you use the pedal more than I think.

Explain also why FBI can be progressive while not responding to usual tests correctly.

The fact that my colleague (now retired, the one that tuned often with pedal engaged ) used a descending octave with a fourth within to place its bass justness (while comparing at each note with major/minor triad in the medium) seem to confirm the use of the double octave an the 12th partials to drive the justness.

btw he tuned his ascending octaves playing an octave containing the upper major third, this guarantee you that you have lively thirds all along the scale.

That said, I recall (on Steinway D) his high basses region was more active with faster tenths than I and others where using (then the low basses where tighter except the last 4-5 notes).

Best regards

Kamin, thank you very much for your comments and your deep analysis.

...“you let the justness of the piano be driven by the partials series, which gives a lot of air to the tuning (decompression of the spectra as I call it !).”...

Yes.

...”The defect is that this will depart from justness by a variable point depending of the piano (while indeed giving a guarantee that the partial mix is well evened along the scale, with the same relation reproducing itself."..."some scales have moderate ih others no, and one some instruments the progression is not that perfect”...

I agree, piano scaling can be improved. To improve it, we/they need the most correct and reliable references.

...“I wish I could follow the maths but aint the case.”...

Do not let maths embarrass you. Chas maths is quite straight, maybe a symbol free analogy wiil do (posted June 4, 2009).

...“Did you try other approaches ?”...

I guess you are referring to “justness” which I understand as “euphonicity”. I could compare mine with many other approaches, listening to other colleagues tunings with them there, I had no reason for departing from mine and those Colleagues happened to agree.

..."tuning with the right pedal engaged"...

Interesting, never seen, hope to know more. I do not engage that pedal for tuning, yes for checking the whole resonance effect.

...“I dont get your point with the central string… but the final pitch I am after is the one of the center string.”...

I mute from mid-bass strings-crossing to C6 and tune central strings, then unisons, then C#6’s central, C6’s right, C#6’s left, next central, previous right, next left and so on, up to B7.

...“But not a beats method there, out of thirds 4th and 5ths evened in the octave (same kind of thing as you, without the maths behind)”...

About SBI, in my tuning SBI are progressive and I invert the 5ths beat rate progression in my first sequence steps, so that A3-E4 beats narrower than D4-A4.

...“indeed a more sexy theory than any straight approach, but then, what music is it for ? when one need a close harmony dark piano for chamber music how is the harmony ? etc etc.”...

What a compliment! Let’s hope it will not compete with viagra...they’d kill me! About "a close harmony dark piano for chamber music" could you explain more? You know, as I write, I believe Chas Temperament Theory can represent the correct reference, in terms of partials interrelations, for eventually improve the tempering of other "fixed tempered" instruments.

...“Your welcome if you come by, to show the way you lay that temperament/tuning, must be fun !”...

I hope so, I look forward.

..."If you mostly worked on Yamahas I understand your need for more lively tunings !! (joking)"...

Well, actually you are quite right, some of them are a bit dull but you well know, standards variate from a single piano to another one, also for other makes. Generally speacking, I like St..depth, Bec…silvery, Bos…majesty, but then a Petrof exib. model happened to have much of these qualities...you never know.

...“I don't know really if piano tuners worry about that comma (due to the piano iH)”...

I wish they did not. In any case, in my opinion the approach to theory can be more correct.

..."But the basic Yamaha tuning also rely on theoretical basic frequencies,(or beats speed) if you do that too much you can have a bad sounding instrument without noticing as the ear accommodates with time.”...

If “ear accommodates with time” this may regard also our musical ear, mhhh...when, how, why does ear accomodation take place? Say we do not leave any "place", any reason, can that take place? I do not have the answer, but working with beats for me is like playing with rhythm, that does not tire me.

...“I always wondered if the Yamaha approach was an intention to add some deepness to the instrument, by emphasis on close harmony and straight forward lining of 4:2 2:1.”...

I do not really know but, say you are right, deepness is to any piano's advantage, do you agree?

Regards, a.c.

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):

http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

CHAS Tuning MP3 (Granpianoman) on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

Kamin,

about the Chas recording you kindly write:...“Makes me think that the result may not be far from what I had with the tuning made with right pedal engaged (hence immediate stability, and tuning in the natural resonance of the instrument more)”...

I’m really curious about this technique, could you say more about it.

...“When notes are played together, the partials literally seem to "jump of the box" and the piano sing as if the pedal was engaged. That is the effect I hear in your recording unless you use the pedal more than I think.”...

It was not me playing that piano, I asked my colleague Alessandro Petrolati to play it, so that he could have a direct feel of Chas tuning. About the partials, that “jumping of” effect is what I hear too, and I relate it to the resonant power of the tuned frequencies. In other words, by ordering all the partials interrelations, it is like setting “entry frequencies”, so that any string is ready to resonate and give out the relative partials in a sort of coherent share.

...“Explain also why FBI can be progressive while not responding to usual tests correctly.”...

I’m not sure I’m getting your point, anyway...we needed to get the ET ratio for the scale’s 4ths, simply because 4ths with their wideness can proportionate the progressions of all intervals. You may have read the symbol-free analogy (06/04/09) I addressed you to. You notice that we can get all ratios of any kind simply by adjusting the arbitrary “s” variable, what determines the wideness of 4ths.

...“The fact that my colleague (now retired, the one that tuned often with pedal engaged ) used a descending octave with a fourth within to place its bass justness (while comparing at each note with major/minor triad in the medium) seem to confirm the use of the double octave an the 12th partials to drive the justness.”...

Yes, the use of the double octave an the 12th works for “justness” and, if you were to adopt Chas Theory’s rule, i.e. equal beating all along the keyboard, up to the 88th tone, it would work as a precise, solid and reliable reference for tuning an ever coherent and univocal SBI and FBI progression. This can now be called ET, in that it is what we mean when we say ET, what we needed for approving ET, both in terms of justness and practicableness.

You know Kammin, in my pro experience I have met so many tuners and very often felt their embarrassement and frustation, wondering about an abstract idea of ET and yet having to somehow argue and justify their quasi-ET tunings. Out of interest, about writing styles, octaves, ET definition and more, have a look in this thread, from 06/21/09, you only find confirmations of what I’m saying. Lots of confusion and approximation that turns in frustration and vivid wits. Little tuning, but lots of acrobatics.

About the recorded Steinway s, strings, pins and hammers (still to be voiced) had been changed three weeks earlier…when I knew that...I thought I was going to waste my time...and yet it did not go bad at all. My colleague was astonished for what he called “light”, brightness. Yet, on those small instruments, iH is still the argument for “relative”, quasi-ET tuning.


Best regards, a.c.

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):

http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

CHAS Tuning MP3 (Granpianoman) on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

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Tooner, you may understand why I do not feel that relaxed, why I do not manage to behave as I could and reply to you.

Leave your representation of Chas Theory aside, your personal understanding about theoretical models and tuning unsolved problems, how you and our cello expert have tried to banalize the Chas discovery and the research report, leave all this aside, I feel embarrassed mostly because I can not trust your intentions.

Nothing drammatic, but you may know the way it goes, when something you could never expect actually happens and it takes you beyond your immagination.

I would like to tell you how I’m grateful to you for giving me many (very many) opportunities to describe Chas, for helping me with my English, for offering me a chance to deepen many relevant tuning issues but, only considering my own limits, it happens that you (and Stopper) have gone over the top (my top).

Actually, if I were to reply to you I would have good reasons for asking myself: do I suffer from martyr complex? Am I looking for more insults? Is this me being a masochist?

Fortunally I feel quite balanced, with my family, my job, my friends and my hobbies. Also I deeply know that I’m trying to share Chas only because I sincerely believe in what this temperament may represent, how it resolves the partials order and how and why it accurately gains what other researchers and I have long been looking for, not an easy method but the scale partials interrelations. I have got no words to tell you how I feel about it.

I tend to believe that in the U.S. you may have different standards, when discussing with people you do not personally know. Maybe you can tell each other orrible things - look at the other thread - and go, the next day, for an aperitif, but it is not so where I live, nor in my environment. In my family we respect people’s intelligence, no matter the origins, and behave in the effort to be sincere, to result univocal, reliable and trusty.

I respect you (and Stopper) at a human level, only I do not manage to rely on my sporting spirit, to be casual when it comes to coherence and truth. Said that, I apologize for my limits and I sincerely wish you a Merry Xmas.

a.c.

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Alfredo:

Sincere wishes for a Merry Christmas to you also.

My Post with the link about the Martyr Complex was in response to your post with links on Moral Turpitude, Defamation and Intent. What is sauce for the goose is sauce for the gander.

You can blame my actions on my former 24 year career of going to sea if you like. There were many times when we would want to kill each other one moment and then desperately need each other the next. (I have some interesting scars...)

You can also take criticism as constructional whether it is meant to be or not. If it is false criticism it can be ignored. If there is merit to a criticism, regardless of the intent or origin, it can be used in a positive way. But Pride must first be dealt with, which is much easier said than done for all of us.

..."You can also take criticism as constructional whether it is meant to be or not."...

I'm not referring to accidental constructural criticism, but to deliberate destructive actions.

..."If it is false criticism it can be ignored."...

I can not ignor a defamer, maybe you can and that is good for you.

..."If there is merit to a criticism, regardless of the intent or origin, it can be used in a positive way."...

Yes, to a certain extent though (in my case), then it turns into moral and intellectual damage and it can not go "regardless" anymore, the intent becomes foundamental.

About having to deal with Pride, by reading Chas Topic you may understand how I do not mind some training. As I tell you, I do not know anymore if you do not understand or if you pretend not to understand. But now that is only my dilemma.

..."What is sauce for the goose is sauce for the gander."...

Perhaps is that sauce I'm simply not interested in.

a.c.

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