(--------------- * MERRY XMAS *

Alfredo:

"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."

I patiently tried to show you some things but decided to stop when I got too aggravated. It is only normal for such frustrations to be felt personally - for both of us.

Yes, Merry Christmas and remember that this is a Season of Promise that one day All will be made Right.

Right.

a.c.

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Alfredo:

Found a Proverb you can consider: "Faithful are the wounds of a friend; but the kisses of an enemy are deceitful." Proverbs 27:6.

I am not your enemy.

"Faithful are the wounds of a friend; but the kisses of an enemy are deceitful."

Thanks Jeff, I share the meaning of those words. What is there, in between a friend and a not-enemy?

a.c.

An acquaintance. I would prefer colleague, but it just did not happen.

I'll post the link in the Chas thread...

http://dl.free.fr/bbsIDOhsS (it is a wav file may be long to download, I will try to make a MP3 for the unisons tuning)

here is what I get , the basses I only used fourths, the treble only large fifths, the temperament I used a 2bps fourth and a low stretch octave, then I tried to stick to that interval size.

In the end some double octaves beats too much, the triples sounds Ok, it may be long from the Alfredo tuning but I forget the instructions at home !

Back to the champaign !

Kamin, I can not listen to your recording due to a problem in the audio device on my PC.

Thanks so much for your trial, finally you are putting so many words into practice. I would not be happy with a short reply, so please wait...just a few bottles...

a.c.

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Alfredo, it was not a real trial, I did not have the precise instructions so it stay where my understanding was, thats it, not much !

I have something I dont get with your method : the ih curve is raising in the low medium with the plain wire shortening, then the high basses have low ih that progressively goes up when we go down the scale.

is your beat "inversion" on the low slow beating intervals taking that in account, or is it a model based on theory ?


In the low medium area, I see no way to reconciliate intervals while sticking to a model unless you dont care with some of them. if you stick with an even progression of FBIO you get an eveness that is near theory.

If you stay within some partial reference, the progressivness change speed, more or less brutally depending of the way the tuner compromise to hide those scaling defects.

Kamin,

you kindly ask: ..."is your beat "inversion" on the low slow beating intervals taking that in account, or is it a model based on theory ?"...

About practice: the 5ths beat rate inversion (on centre strings), in between A3 and A4, is technically needed to gain Chas. From A0-E1 (were I avoid 5th’s beat) upward, 5ths get narrower and narrower, 4ths and octaves less and less wide. C3-F3 and C3-G3 (on centre strings) have the same beat rate, then 4ths get wider and wider, 5ths keep on getting narrower and narrower ‘till they invert (on centre strings). To invert 5ths, do so that G#3-D#4 and A#3-F4 have the same beat rate.

About theory: first I had to consolidate my tuning evidencies, then I kept those evidencies under observation for two decades, them being the result of a precise approach, on which basis I could elaborate Chas Theory. Finally I extracted the model's constants and gained the mathematical evidencies. Hardly ever iH has been a problem, never on concert pianos.

..."In the low medium area, I see no way to reconciliate intervals while sticking to a model unless you dont care with some of them. if you stick with an even progression of FBIO you get an eveness that is near theory. If you stay within some partial reference, the progressivness change speed, more or less brutally depending of the way the tuner compromise to hide those scaling defects...

In the low medium area, on badly scaled pianos you may need to favor some intervals, in that case I go for RBI’s smootheness and coherence. More often I go down the bass with 4ths, 5ths, octaves, 10ths, 17ths, 24ths (triple octave + 3rd) all together. If I’m forced to sacrifice one interval, it will not be a fifth. Mind you, I’m talking of very fine iH troubles and in those cases I prefere a wider octave to a narrow fifth.

I’m still waiting for an answer from Bill, in general about the existence of ET (and what all people is then talking about). Chas ET does exist, I can tune it on any size piano (what makes it shareable) and the resulting sound whole is so right, so resonant and musical that usually dissonant chords open to overtones in a way you could never predict (my judgement, but not only mine). Kamin, for me it is a true sound festival, it’s like a real overtones bath.

Bill writes:...“If I were only tuning ET...I might want to get some kind of variation from what would otherwise be a completely sterile sound.”...

What does Bill mean? What is a "completely sterile sound"?

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

.

Hello Alfredo

Thanks for your answer, indeed even on concert pianos there is an iH jump, even if smaller.

please confirm your idea the term narrow fifth , and wide octave. more than 1:2 et 2:3 or is it tuner's language (faster beating than usual) ?

I dont know what Bills mean with "sterile sound" , but it remains me some pianos that lack projection, then the right pedal may be on to blend a little, and hamony is poor.

I find the too precise progressivness tiring when it is done, I believe that the tuner follow the tone the instrument is giving at the moment of tuning,he modify the stretch demending of the room and the piano acoustics. That is giving some movment in the progression, tempered with the use of RBI's, I have tuned with a VT100for years, thet EDT is very healthy and his advantage is that he will compute the tuning based on many partials of the 88 notes. In the end it makes so much compromizing that the tuning is near the perfect moderate Yamaha concert tuning, but without the liveliness so the tuner have to keep his ears open and not rely 100% on the machine if he want to keep some (and for Steinwya he have to modify the program guidelines, in the end I only used it as an examinator, and when it have been robbed to me I just did not car eto buy another one it is a tool to make money, but I disovered I could make Pitch raises in an efficient manner because my ears had catched the kind of necessary raise ..

That said one partial driven tuning is also nice from the low partials harmony point of view, but the method is heard as a forced eveness, so I am unsure it is the best choice for a piano.

You can install on a piano any kind of method, that will be more or less transparent to the listener.
The piano have its voice, I believe it dictate what he can and what he cannot do, if forced in a differnet justness as pure fifth for instance, this is not transparent to the listeneer, it bring its musical ear in another concept of harmony.

Indeed sticking to the partial series will give a jump in resonance, and it is very pleasing. In the end the classical harmony is what may be the most difficult to attain, when the piano play with another instrument as a flute, or even a vilin (then the top treble may be high enough to please the vilolonist)

WHat makes Bill with the mindless octaves makes me think of the day where the conductor told me (half an hour before the rehearsal) that the pitch had to be 440 (while most of our concert pianos where tuned to 442 Hz).

I had to lower the A4 exactly to 440 , the A3 less, all the remaining temperament fifths less and less, then make a few octaves high and low until it reconciliates with the 442 tuning (at last it could be audible)

Nobody complained, and the tuning was strange but playeable !

I wonder if the "mindless octave" equity between 15th and double octave departs from the tempermanent, and even it a little when going to the treble and bass (may be no ?)

Back to eating now !!!


I'll give a try with the instructions, but I need to understand the logic too.!


What I agree with is that all octaves are false in our usual way of tuning !!


Best

Hello.

Kamin, thank you:....“please confirm your idea the term narrow fifth , and wide octave. more than 1:2 et 2:3 or is it tuner's language (faster beating than usual) ?”...

Octaves, 4ths and 5ths can be progressive and in Chas tuning they are progressive. I will explain in detail how to deal with these intervals in Chas Preparatory Tuning. Midrange octaves do not beat, they have a propensity (or propension?) to beat, in fact they roll, i.e. they open towards a beat like for a long long wave, what you hear as a mmmmuuuuoooooo coming in a shorter and shorter time, as you move toward the extremities. Octaves progression is so smooth and gentle that it takes (about) 40 notes to get 1/bps. You ask me to compare with usual, but I do not know if a “usual” exists, for what I’ve heard and from what I read there seems to be an infinite variety of ways.

...“I dont know what Bills mean with "sterile sound" , but it remains me some pianos that lack projection, then the right pedal may be on to blend a little, and hamony is poor.”...

I do not think Bill was referring to pianos, but tunings.

...“I find the too precise progressivness tiring when it is done, I believe that the tuner follow the tone the instrument is giving at the moment of tuning,he modify the stretch demending of the room and the piano acoustics.”...

Physically tiring or musically tiring? In the first case, precise progressions are a real challenge every time, as in any sport where the highest precision is required, here would be with beats and rate/rhythm. Musically, precise progressions are as tiring as perfect “in tune” can be, for me. I enjoy a perfectly “tuned” singer, violin and so on down (or up) to pianos. I enjoy being able to give myself up to a perfectly melodious voice, it goes straight to my deepest inwardness, it makes me feel in the most right and fair “place”, it makes me forget my physicalness, it opens to a dimension in which I wonder upheld and safe.

You say “...I believe that the tuner follow the tone the instrument is giving at the moment of tuning...”, I wish it was true. I tend to be more realistic and, for what I’ve seen and heard, I’d say: the tuner follows the tone given by his/her own chemistry and skill, he/she modifys the stretch depending on his/her inner room and the piano acoustics, for how he/she manages to care about.

...“That said one partial driven tuning is also nice from the low partials harmony point of view, but the method is heard as a forced eveness, so I am unsure it is the best choice for a piano.”...

Kamin, it will depend. One may prefere to look through a glass, I love looking through crystal. One may prefere potatos for a game of bowls, I prefere spheres.

...“You can install on a piano any kind of method, that will be more or less transparent to the listener.”...

You see, I love variety in timbre and colour, but it has to be in tune.

...“The piano have its voice, I believe it dictate what he can and what he cannot do, if forced in a differnet justness as pure fifth for instance, this is not transparent to the listeneer, it bring its musical ear in another concept of harmony.”...

Chas does not describe pure fifths nor pure 12ths. Chas Preparatory Tuning does (on centre strings) and that is the way you get there.

...“Indeed sticking to the partial series will give a jump in resonance, and it is very pleasing. In the end the classical harmony is what may be the most difficult to attain, when the piano play with another instrument as a flute, or even a vilin (then the top treble may be high enough to please the vilolonist)”...

Today I can state that the “in tune” line (or level) is perfectly shareable and, by comparison, nobody would go for a lame tuning, as original or unique as it could ever be. If the musician can not compare, then he/she will more or less accept what is given.

...“WHat makes Bill with the mindless octaves makes me think of the day where the conductor told me (half an hour before the rehearsal) that the pitch had to be 440 (while most of our concert pianos where tuned to 442 Hz).”...

Bill uses 12ths and 15ths equal beating for expanding his temperament, up to some point where he has to compromise, due to his own temperament in the midrange.

Chas equal beating 12ths (narrow) and 15ths (wide) is the sound whole’s symmetry Rule you can aim at, by adopting a preparatory tuning. So, Chas Theory’s final form and practical tuning is 12ths and 15ths all along the keyboard. You will not go for that though, because Chas tuning can only and will only result from your preparatory tuning.

...“I'll give a try with the instructions, but I need to understand the logic too.!”...

Thanks a lot. Tell me where I can help.

...“What I agree with is that all octaves are false in our usual way of tuning !!”...

That “false” is only the result of lack of reliable references and approximations, octaves simply need to be truly progressive.

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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Hi ALfredo,

I'll send you links to boring tunings, some lack of stretch, some are too straight against the 12 th in the medium then change method so they have incoherence somewhere.

Yes working a tuning may be tiring, but rewarding as well, nothing new !.

In the end I have find the too much evened tunings boring, if the eveness is only due to a bunch of compromising it finally loose sense , and the ear better like a clear opinion as long as it is used on the whole instrument.

for instance the tuner is obliged to refrain to use extra large tuning in the medium range, because he will then have problems with the high treble, or he tunes very tight the medium and cant find an opening to tone higher.

Anyway, whatever way is used, if it is done in a musical way, the result will be nice (of course the piano may give the impression to be perfectly singing just)

Have a nice day !

I am impatient to read your instructions in the "preparatory" tuning, seem very esoteric to me up to now !

Kamin,

I thank you for giving me an opportunity to look at the meaning of “esoteric” in depth. I understand your issue and this may explain my pleasure to make this concept clear, for me, you and our readers.

Is Chas Tuning esoteric? These are the common meanings:

(http://www.thefreedictionary.com/esoteric)
(http://www.answers.com/topic/esoteric)

1 Intended for or understood by only a particular group
2 Of or relating to that which is known by a restricted number of people.
3 Confined to a small group
4 Not publicly disclosed; confidential.
5 Restricted to or intended for an enlightened or initiated minority, esp because of abstruseness or obscurity
6 Difficult to understand; abstruse
7 Not openly admitted; private
8 Beyond the understanding of an average mind

These are my points and comments:

1 Yes, it is intended for tuners and musicians.
2 No, it is not restricted to aural tuners and musicians.
3 Large or small, it depends on what you compare the group with.
4 No comment needed.
5 Chas Theory and Tuning is not restricted nor exclusive at all.
6 How difficult to understand is subjective, it may also depend on knowledge, personal interest and prejudices.
7 No comment needed.
8 I never think in terms of average mind, in my opinion each single mind can open to new scenarios, then it may depend on the “key” and personal experiences, targets and chances.

Now, what does a tuner or a musician need to open to Chas “in tune” ET Temperament Theory and practice? He/She needs to acknowledge about:

-3 (optional) Partial lengths of a vibrating string
-2 (optional) Prime numbers and partials conflict (commas)
-1 (optional) Geometric progression (in relation to our aural system and the scale incremental ratio)

±0 Scale intervals and constants, i.e. Chas system's rule
+1 Piano adjustment following strings tensions and loading
+2 Strings adjustments following piano playing
+3 A method (any method) that uses both SBI and RBI to gain progressive SBI, RBI, progressive octaves and the two Chas system’s constants, i.e. 12ths and 15ths opposite equal beating all along the keyboard.

Now, consider what Bill Bremmer publicly reports:...“In the end, ET cannot exist either. The theoretical specification for each pitch is an irrational number which can never really be tuned. We have to round it off somewhere. The limitations of the piano and inharmonicity together with human variation and perception render every temperament inherently unequal.”

Consider also that the common approach to tuning enumerates these all variable factors:

The way the piano sounds (piano quality)
The acoustic of the room (air pressure)
The kind of music you play
Melodic and harmonic personal preferencies
Piano scaling and inharmonicity issues
Changes in climat

And that, due to these factors, we (aural tuners) could not share a reliable and practicable model*, I may ask you and all Colleagues to simply compare: which approach would you say is “esoteric”? Which approach ends up being more mysterious, or arcane or inscrutable?

*How do you tune 4ths and 5ths? How do you tune octaves? How do you tune 12ths and 15ths on 88 keys?

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
.

What I wrote in November 12, 2009:

..."Where to go then to oxygenize this discussion? This are my proposals:

a) Let’s distinguish the general meaning and relevance of a temperament theory, what Chas ET-EB is, from what piano tuning’s issues are

b) Let’s analyse what logic is behind each one considered theory

c) Let’s separate iH issues from beats-control and tuning-form issues

d) Let’s see if we can address aural piano tuners towards a more reliable and practicable model

e) Let’s try to clear up how octaves, SBI and RBI intervals should go, and get rid of all misteries

f) Let’s evaluate if today there is a way to reduce approximations relative to iH and piano scaling"...

I still think this is what we could well do, we all together, by using our best intensions and by giving up all dogmas, all absolutist positions and all kind of prejudicial aversions.

This is amongst my hopes for the coming time. To All

-(-------------------------2009 * HAPPY NEW YEAR * 2010

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Hello, I hope you all have had a good time!

Bill,

today I read your Topic "Aural Octave Tuning" where you write:

..."Sharpen F5 slightly until both the double octave and the octave and fifth have virtually the same quality. Neither interval will have much of any audible beat. They will both sound apparently or very nearly beatless yet the double octave will be slightly wide and the octave and fifth will still be slightly narrow. You can continue this very same procedure to C8….You may continue comparing the double octave and octave and fifth all the way to A0."...

I’m glad you are opening to the Chas ET "mathematical rule", opposite 12ths and 15ths equal beating all along the keyboard, from A0 to C8.

This somehow repays my efforts and my attempt to share what I think is the most natural and practicable ET scientif model. I dear to say “natural”, in that Chas resolves mathematically the age-old conflict amongst all partials, and I say “practicable” in that Chas is the result of a new theoretical approach and research, what took me to my practical tunings.

You talk about EB 12ths and 15ths as a "mindless procedure", so you write: ...“you CAN continue this very same procedure to C8”...

Chas research report describes how EB 12ths and 15ths can produce a perfectly resonant, stable and symmetric beating-whole. So I can write: My aim is Chas “optimum”, and I gain it by adopting a preparatory tuning. For me this is "mindful ET tuning", and maybe this is today a part of the distance between us.

I'm sure you will soon acknowledge that 12ths and 15ths never need to invert, that 5ths never need to become wide, that octaves need to be progressive and are strictly tied up (also) with the first octaves we tune.

I hope it will not take long for the PTG to acknowledge Chas ET scientific relevance, as I would really like to share this discovery with aural tuners first, i.e. our Colleagues first, all over the world.

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

.

Hello Alfredo,

I have tried to make a temperament and tune a few octaves with your method , and could not get thru.

Something I don't get with the size of the octave probably.

Which interval is determining the size of the first octave, is it the 4th/5th of the first step ? this will vary depending of the piano (as always)

what you call octave "barely beating is tested with which intervals ?)

the 4th and its relation to the 12th above is driving the tuning I suppose, then may be you should propose some checks that could be used as soon as possible to ascertain the primarly interval size (octave and 4th I suppose again).

Usually the iH tend to lower the speed of the thirds in the low temperament zone. it also may make the 5ths slower, I am unsure to understand if the inversion of the fifths beats relate to that or not.

I wonder also something, are you tuning pianos actually ?

If so ,could you post some recordings of the tunings (I mean intervals, not just music played as on your sample).
Even if you could record yourself tuning your temperament I am pretty convinced that it would be a big help in understanding. Do you have a little recorder ? (I have a Zoom H2 which is not expensive and is sufficient for that kind of thing )

BTW I dont understand which is that "grandpianoman" tuning of your sample. did you tune that piano yourself ?

Sorry but I am a little lost with the instructions.

I'll give another try when I'll be more sure to do what you propose.

Happy New year to you also, BTW !

Best

Hello Bernhard,

I have been looking for your temperament instructions , while I seem to have it at some moment, I cant find it actually.

Do you know a link where it is explained ?

I recall trying to tune based on pure twelves, (3:1) and I liked the 3-4 medium octaves, then I had problems to keep the progression and have the usual amount of stretch, or the relation with the medium disturbed me.

Thanks for the link, if any.

Best wishes for 2010

Isaac OLEG

Isaac, i don´t want to hijack this thread, which is related to Chas.
Please mail me a pm.
regards,

Bernhard

OK sorry, I did not realize !

Your explanations make sense, I did not understood the formulas in the Chas paper, but I understand your criticism if it rely to what is expressed in that paper.

I guess that wanting to mathematically put in formula what the tuner is doing is probably very difficult, and that beauty may be hidden in the contortions we do to get rid of that pythagorean thing (with the help of the instrument hopefully).

On more pure instruments as harpichords, or guitar, expressing differntly ET may well be interesting, as may be for low iH pianos.

I am pretty sure that the "Railsback curve only or mostly used Steinway's as references. As I tuned with an EDT many years I have seen the cts value of the notes, being the center octaves or the bass or high treble, always computed with the same model. They vary wildly as long as you want to keep the same beats relations.

Difficult to have the high treble of a Fazioli at more than 25cts or the one of a Bechstein at less than 35 cts.

Then, when tuning aurally, the 3 different kind of instruments will be tuned completly differently in fact, one with a large octave in the temperament, the other with a very tight octave because it get harsh very soon if not.

If that comma is solved on a larger distance, it decompress the ih of the piano and the eveness is easier to attain, but we are use to that high treble artificial stretch not for the piano acoustical reasons but because of our ears. SO to me, a good method may prepare the instrument to accept the stretch of the high treble so it is there while not too much out of justness with the center.

I cant understand how mathematically we can include that.

is not the spectra of the piano progressing more or less unevenly and asking for many compromising while tuning ?

As promised, more critical reviewing of Chas statements:

1. - Falsification of the evidence of Chas equal beating double octave - duodecimes (twelfths) equal temperament form over other equal temperament forms:

In section four of the Chas research report, difference quotients are calculated from differences of Chas octaves series which are compared with the harmonic octave series.
Other partial series like 3,9,27... are left out from the difference calculations, only partials related to the octaves are taken into account, so one can say "filtered" data has been used, to evidentiate the model.

Chas model compromises the pythagorean comma equally between the double octaves and duodecimes. That means octaves are half weighted by pythagorean comma distribution than duodecimes. Saying a natural interval ratio like 9/8 (which contains 2 duodecimes, (3^2) and three octaves (2^3)) is closer to the Chas ratio than to other ratios, does not mean more than saying the 12th root of two temperament is better than 19th root of three, because the octaves are better in 12th root of two.

The evidence of Chas equal beating form over other forms of equal temperament fails by taking differences of multiples of other harmonic series like 3,4,5… instead of only the second partial. In fact, some intervals are closer to the natural ratio in one equal temperament, while other intervals are closer to the natural ratio in other temperaments. This is all not new and also not solved with the Chas equal beating temperament.

2. Falsification of the statement (section 4.6) "This inversion* is determined by the s variable unique to this model"
(* inversion of interval progression, as observed by the Chas author when tuning real pianos, and "predicted" by the Chas model)

The s-variable has no evidence at all for this statement here, as the complete presented data tables presented in the Chas paper where this statement relates to, are all based on the harmonic case, where the s variable has a value of 1. Chas ratios for all intervals remain constant over the whole keyboard and do not "invert" somewhere when the s variable is 1 as with the presented data.

In fact, the predicted inversions are caused due to a wrong method to determine interval ratios by multiplying their numerator alone with the multiples of the second harmonic. To determine interval ratios an octave higher on the scale, one has to multiply the numerator AND denominator of an interval by two, not the numerator alone for example.

3. Falsification of the statement (section 4.5) "If in a different logarithmic scale, we wanted to favour partial 3 we would have to take value 3 and position 12+7 = ordinal 19, so the formula will be 3^(1/19) = 1.059526065... This ratio, too, in distances of octaves, (3*2)^(1/31), (6*2)^(1/43) etc, modifies towards 2^(1/12)."

Calculating higher harmonic degrees of an interval by multiplying with multiples of the second harmonic does not correspond to the interval ratios of a tuning at higher scale position. The correct formula for the 31st step is 3^(31/19) and not (3*2)^(1/31), and therefore does not modify towards 2^(1/12) but remains constant for the harmonic case. Same is for the wrong statement relating the partial 5 temperament.

Hello Kamin, you kindly ask:

..."Which interval is determining the size of the first octave, is it the 4th/5th of the first step ? this will vary depending of the piano (as always)...

...what you call octave "barely beating is tested with which intervals ?)"...

In the first four steps I determine the relations between two 4ths (A3-D4 and E4-A4), two 5ths (A3-E4 and D4-A4) and A3-A4 octave. So, all together they determine each other. In midrange iH is very low so it is no problem.

...the 4th and its relation to the 12th above is driving the tuning I suppose,"...

Going up, from A4, I use 4ths (going wider), 5ths (less and less narrow) and octaves (slowly progressive). On C#5, I can check five progressive octaves, fiths progression (less and less narrow) and the first 10th (A3-C#5). Then I use all intervals, slow and fast beating intervals.

..."then may be you should propose some checks that could be used as soon as possible to ascertain the primarly interval size (octave and 4th I suppose again)."...

You'll find that written in the sequence.

..."Usually the iH tend to lower the speed of the thirds in the low temperament zone. it also may make the 5ths slower, I am unsure to understand if the inversion of the fifths beats relate to that or not."...

I tune with 2:1, 3:2, 4:3, 3:1, 4:1, 5:2, 5:1 ratios, and iH has never been a problem. Remember that 5ths inversion is established on centre strings, so that A3-E4 is narrower than D4-A4, little less than 2/3 bps Vs 1/3.5 bps. I mute from mid-bass strings crossing up to C6.

..."I wonder also something, are you tuning pianos actually? If so, could you post some recordings of the tunings (I mean intervals, not just music played as on your sample).
Even if you could record yourself tuning your temperament I am pretty convinced that it would be a big help in understanding. Do you have a little recorder ? (I have a Zoom H2 which is not expensive and is sufficient for that kind of thing )"...

I may be in Paris by the end of this month, I'll let you know...would you be there? It would be much easyer to directly show you the procedure.

..."BTW I dont understand which is that "grandpianoman" tuning of your sample. did you tune that piano yourself ?"...

Yes, I tuned that Steinway s in front of our colleague Alessandro Petrolati, he could then play and record the piano. Grandpianoman was so kind to make an MP3 available, out of Chas Tuning .rar original version. This is why I mention him.

Best regards, a.c.

Bernhard Stopper,

I’m very happy with what I have described in Chas research report. Also I’m quite happy with your fast acknowledgement of Chas model’s relevance. In fact, only seven months ago you dared to write:

Bernhard Stopper on Chas Topic, 06/09/09:

...“My model has perfect symmetry in abscence of inharmonicity, while CHAS or other ET solutions have not.

...“You WILL find symmetries of highest degree in the resulting beat tables, which are not present in other ET solutions (including yours). And THAT is a discovery (discovered in 2004, as is wrote in an earlier post of this thread).

...“Such relations are apparent in many ET solutions, but only in the case of 19th root of three this is true for all combinations of octaves fifths and fourths (with distances of octaves, fourths and fifths between them) etc.

...“The point is, that the acoustic effects caused by the outstanding symmetry of the 19th root of three ET can still be preserved with proper consideration of inharmonicity.

Two months ago you could write:

Bernhard Stopper on Chas Topic 12/11/09:

...“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.”...

What is new is that from Chas equation you can gain any ET scale's ratio and correction, and now you can “understand” that. Last month you wrote:

Bernhard Stopper on Chas Topic 12/17/09:

...”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..."...

You see Stopper, now you “understand” Chas mathematical validity. Soon you will also “understand” Chas model’s maximum coherence and congruence. I simply believe Time is enough to defeat your malignity and you yourself confirm that.

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 miss some substantial defense on my falsifcations of your paper.

I think you are missing your brain, Stopper, something you will not find in this thread.

Well, this clinches it for me, Alfredo. You are interested in appearance not substance. But then you are not alone.

You continue to expect acceptance, and yet you also continue to become abusive when questioned.

It is tempting to respond to you in the same manner as you yourself just responded. Time for me instead to simply log off.

We probably have a different perception of the reality regarding this.
Relevance and validity are two slightly different things.


You can gain this with Mazzola's general tuning formula as i mentioned already.
Again, Chas model is valid here, but not relevant as new.


That´s what i was saying already. Valid yes, new or relevant no.

I figured out too, that the model of the natural form of the fifth circle equation i am using to illustrate my tuning model can exactly take the Chas model form for the harmonic case. By replacing the constants with variables (which is equivalent to Mazzolas general model) every inifinite scale can be done as with Chas.


I have falsified your statements regarding this and your are obviously not able to defend against these falsifications.


No comment.

Jeff, try to be happy with what follows and try to refrain from such comments: "You are interested in appearance not substance."...

You have had almost 8 months of "substance".

Kent, you write:

...“You continue to expect acceptance, and yet you also continue to become abusive when questioned.”...

Kent, I’m not expecting acceptance, I’m hoping to share Chas ET Theory and its tuning model, i.e. an ET temperament where octaves are a little wider than 2:1.

You say I become abusive when questioned but sorry, I can not agree, if anything the opposite is true. Chas Topic is full of examples where I’ve been questioned in abusive terms, nevertheless – to a certain extent – I’ve replied as usual.

This is so evident that I find difficult to justify your comment. Actually, since you could check what I’m stating - by simply reading this Topic - I would kindly and respectfully ask you to refrain from passing easy or superficial judgements. Otherwise, you could start a dedicated Topic.

In my opinion, and personally speacking, Stopper’s case is quite unusual. Leave all style factors aside, leave his off-putting manners aside (educational, cultural, moral barrier?), Stopper has been trying to banalize Chas ET Theory right from his first “cello” post, insinuating that Chas research report may be a scientific hoax. Read Stopper (05/07/09, page 1):...“Well observed Jeff. Maybe a kind of scientific hoax of the category "cello scrotum"...”.

Why in my opinion Stopper may be missing his brain (missing his elaborations) is quite simple: Stopper contradicts himself. Just read, this is not maths, but basic English:

STOPPER on Chas Topic 06/09/09:...“You WILL find symmetries of highest degree in the resulting beat tables, which are not present in other ET solutions (including yours). And THAT is a discovery (discovered in 2004, as is wrote in an earlier post of this thread).

The same day:..."Such relations are apparent in many ET solutions, but only in the case of 19th root of three this is true for all combinations of octaves fifths and fourths (with distances of octaves, fourths and fifths between them) etc...

..."My model has perfect symmetry in abscence of inharmonicity, while CHAS or other ET solutions have not.

So, that was Stopper and his "...highest degree...",and "...only in the case of 19th root of three this is true..." and "...perfect symmetry...".

Now read this, STOPPER on Chas Topic 12/17/09:

...”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...”...

Even if I leave Stopper’s contradictions and style aside, there are three more points that reveal such a conversation partner’s unreliability.

1. Refuting Chas ET model’s maths and numerical evidences.
2. Confusing Chas approach and ET Theory with a technique to expand a temperament.
3. Claiming about who is first and what is new.

About point one, you may understand that Chas model’s maths is not different from any geometrical progression’s maths. Maybe you, Kent, do not know enough but Stopper may well know.

About point two, a technique can help you to get by, a solid and reliable ET Theory can represent a rational and precise reference. Again, you Kent may not be familiar with this, but Stopper may well be.

About point three, I have well explained what is new about Chas, and it is listed in my first post (page 1). But what is more important about Chas is the approach to what is Not New:

a) stretched octaves
b) stretch curves
c) pure intervals

Other models have already stretched octaves, nothing new.

What is new is the approach to the temperament and the resulting Chas "scale ratio": the reason for a mild (read mild) octaves stretch curve resulting from the interrelation of all partials.

Chas model theorizes a synchronic beating whole, where no interval is pure (sorry?). All intervals are stretched.

Then, all intervals can have their proportional beat curve, a proportional beat curve that you can aim at in practice, as it is drawn in theory. Difficult? Maybe you, Kent, could not realize but Stopper may well do.

For what is written above, I had already declared my lack of interest in discussing with Stopper, what I consider a perfectly admissible personal position. And please, do not take all this as a justification because I should not need any, take this as a mere description, my personal description. Then, stop insinuating, stop threatening, stop insulting, and if you have some spare time...enjoy yourself.

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 don't see a point where I contradicted myself. I did not took back any of my statements regarding the higher degree of symmetry which is causing purity in tempered chords in the temperament I prefer. (a purity you are avoiding in your form). Beside that I always said there is an infinite number with mathematical valid equal temperaments including yours possible. Where do you see a contradiction when I am falsifying the arguments you give to make your temperament more evident than others?

What caused me to assume your paper to be a scientific hoax where the sheer numbers of wrong statements inside your report (see my falsifications).