Topic by Jake Johnson

  • Avatar
  • Jake Johnson
  • Member
  • Offline
  • From: Atlanta
  • Registered: 04-05-2007
  • Posts: 4,501

Topic: Returning to the CHas

Alfredo (who developed the CHas temperament, recall) apparently created this page some time ago, but I just now ran across it:

http://www.chas.it/ContentPartViewer.aspx?ID=confronto

The audio files compare chords in ET and CHas, but don't use a piano. This page, about halfway down, of an extended, heated, thread at PW explains which chords are used in each recording:

http://www.pianoworld.com/forum/ubbthre...30/20.html

(page 20 of this thread, in case the url sends you to the first page)

Strangely, on Alfredo's page, if you click on the british flag for an English translation, the links to the audio files disappear. However, more reference materials appear at the bottom of the page, including his tuning sequence prior to fine tuning.

The essential principle seems to be that 12ths are kept narrow to the same degree that 15ths are kept wide, usually by 1 beat, but always on a 1-to-1 basis. The 3rd partial is used to tune the 12th. The 4th partial is used to tune the 15th.

Last edited by Jake Johnson (10-11-2010 01:58)

Reply by Jake Johnson

  • Avatar
  • Jake Johnson
  • Member
  • Offline
  • From: Atlanta
  • Registered: 04-05-2007
  • Posts: 4,501

Re: Returning to the CHas

Alfredo has just posted some more instructions for tuning to CHas on the PianoWorld forum:

http://www.pianoworld.com/forum/ubbthre...UNING.html

He's responding to a posted recording, critiquing problems with its attempt at CHas, so a few more details slip out. (In saying that A4 should be sharp, I believe he means that A3 should be lowered to create a wider octave--A4 is thus sharp in terms of the octave, not raised above 440. EDIT: It occurs to me, however, that his A4 may be the A above A440.)

I'll take a run at this with the new Pianoteq D4 later this week, but I hope someone with more experience with setting temperaments beats me to it. Philippe.....??? Joe.....??? Gilles....???

Last edited by Jake Johnson (08-06-2012 14:42)

Reply by jcfelice88keys

  • Avatar
  • jcfelice88keys
  • Member
  • Offline
  • Registered: 22-09-2008
  • Posts: 1,149

Re: Returning to the CHas

Jake Johnson wrote:

Alfredo has just posted some more instructions for tuning to CHas on the PianoWorld forum:

http://www.pianoworld.com/forum/ubbthre...UNING.html

He's responding to a posted recording, critiquing problems with its attempt at CHas, so a few more details slip out. (In saying that A4 should be sharp, I believe he means that A3 should be lowered to create a wider octave--A4 is thus sharp in terms of the octave, not raised above 440. EDIT: It occurs to me, however, that his A4 may be the A above A440.)

I'll take a run at this with the new Pianoteq D4 later this week, but I hope someone with more experience with setting temperaments beats me to it. Philippe.....??? Joe.....??? Gilles....???

Hello Jake,

I did listen to the original mp3 file, and am prepared to state that CHas is a "cure without a disease."  To my ears (albeit with absolute pitch whose resolution has been verified to measure accurately to within one twelfth of a semitone in repeated double blind tests), the piano sounded as though it was tuned in equal temperament.  Some of the unison strings were out of tune at the time of the mp3 audio recording, as well.

Of course my statement will be chided by the CHas believers, but here are my reasons for the above:

The 5'11" Steinway used in the recording had worn (i.e., flattened) hammers over essentially the entire keyboard's range.  This is because many of the individual notes had overly prominent 2- and 3-octave high overtones -- a "zinging" (not singing) quality about them (because the flattened hammers' contact areas were larger and more "grooved"  than they should have been).  Personally, I believe this particular quality about the hammers imparting high zinging harmonics to each tone -- is what most CHas adherents believe is the result of the CHas tuning.  This is simply untrue.


Now, do you want to hear the truth???
CHas tuning is so extremely similar to equal temperament that it is within 0.1Hz of Equal Temperament between A0 (27.5 Hz) and D#5 (622.3Hz).  The two tunings diverge by only one-tenth Hertz beginning at note E5 (659.3 versus 693.4Hz), when both tunings each center themselves at A-440 Hz.  The first note that Equal Temperament and CHas diverge by one Hertz (1cps) occurs at F6 (1397Hz vs. 1398Hz).  The first note that ET and CH diverge by only 2Hz comes at the highest C# on the piano!!! They diverge by 3Hz at the highest G# on the piano, and they diverge by only 4Hz at the highest C8 on the piano!!!

It is nearly impossible for a piano tuner to tune to an accuracy within one-tenth of a Hertz for the middle four octaves of a piano.  One would have to hear a "beat" frequency lasting a whole 10 seconds(!), by which time the sound has decayed almost to inaudibility in the middle octaves.


* * * * * * * * *

The following paragraph summarizes the mathematical comparison between equal temperament and the CHas tuning schemes: 
The ratio of frequencies from one semitone to another in equal temperament is 1.05946309; the ratio of frequencies from one semitone to another in CHas tuning is 1.05948654.  You will notice the ratios are essentially the same number, at least out to five significant figures.  Piano tuners are not robots; our limits of tuning are not as accurate as the divergence of Equal Temperament from CHas tuning.

When one reads in the Pianoworld forum how the octaves are no longer in exact tune in CHas tuning, people are confusing what they hear with their ears, and the mathematical equations they see with their eyes, carried out beyond the fourth decimal place.

* * * * * * *

My final statement about the similarities between the ET and CH tuning schemes is this:  Normal stretch tuning, performed aurally by a competent piano tuner, imparts more differences than these two tuning schemes.  End of story.


Cheers,

Joe

Last edited by jcfelice88keys (10-06-2012 01:51)

Reply by Jake Johnson

  • Avatar
  • Jake Johnson
  • Member
  • Offline
  • From: Atlanta
  • Registered: 04-05-2007
  • Posts: 4,501

Re: Returning to the CHas

Joe,

Two questions:

Did you see that Alfredo responded to the mp3 by saying that it was not correct?

When you speak of the CHas as being indistinguishable from ET, are you speaking of the mp3 or of the ideal Chas tuning as laid out by Alfredo? (I thought that we had determined that there was more of a difference than what you are finding. Alfredo was setting the temperament across two octaves and paying a lot of attention to the 12ths across the stretch. Have you listened to any of his tunings? The mathematical theory has caused a lot of debate, but the sound he gets, even if it is very close to ET, is clearly good. Damned good ear, the man has.)

Regardless, it would be good to hear a piece performed with a good ET tuning and then performed with CHas to let us hear any differences.

Reply by jcfelice88keys

  • Avatar
  • jcfelice88keys
  • Member
  • Offline
  • Registered: 22-09-2008
  • Posts: 1,149

Re: Returning to the CHas

Jake Johnson wrote:

Joe,

Two questions:

Did you see that Alfredo responded to the mp3 by saying that it was not correct?

When you speak of the CHas as being indistinguishable from ET, are you speaking of the mp3 or of the ideal Chas tuning as laid out by Alfredo?  [...]

Hello again Jake,

My listening comments were made on the approximately 11 minute mp3 snippet of Alfredo playing various pieces, including the Ravel Forlane.  I mistakenly read this as being a 5'11 Steinway, such as a model L, whereas it seems it was a 5'1" Model S.  If in fact his actual proposed tuning is different from what was posted in the mp3, then I may stand corrected. 

The mathematical calculations I made were based on a comparison of the ratio of a tone to its next semitone higher (or lower), comparing Equal Temperament versus CHas calculations of pitch, each starting from A440 and calculating upwards and downwards from that standard starting pitch.

If I am able to find the exact deviations in cents from Equal Temperament, throughout the piano's normal 88-note range, I will be glad to make the pitch assignments, myself, and then present a recording of the two pitches, superimposed.  Personally, I do not expect to find much, if anything, different between the two tuning schemes.  I will be fair and let one's ears (and oscilliscope) decide.

Cheers,

Joe

Reply by Gilles

  • Avatar
  • Gilles
  • Member
  • Offline
  • From: Québec, QC
  • Registered: 18-07-2008
  • Posts: 3,344

Re: Returning to the CHas

Hello Jake and Joe,

Since I was mentioned as having had in interest in CHAS tuning before (not sure how to capitalize it correctly...), I thought I might add something here. Jake's interest is probably in trying to hand tune each note with pianoteq PRO using real instrument tuning instructions. I also think as does Joe that it is probably very hard to do since it is almost equal temperament.

Our previous use of a scala file for doing this gave, to my ears, a rather pleasant sound for some music and I still use it, even though for professional tuners such as Joe and Philippe, it sounds flat at the top as it is not stretched afterwards (I hear that too, but it doesn't really bother me). What I like is the very slow beats introduced by the scala file method, beats that may be similar to what the real CHAS tuning tries to do.

We have found in the past that the mathematical justification of the method was dubious (I won't enter into that, though...) and I found myself that cumulative addition errors of the CHAS ratio were introduced in the values given for the CHAS file.

In short, two things remain for the scala file version: first only double octaves are beat free (instead of single ones) and the cumulative error is, to my ears, spread evenly in a two octave interval, in the same fashion as the equal temperament itself does over a single octave.

Now I am not a piano tuner and don't have absolute pitch, but I still can detect very small frequency differences (though I found that with a self administered test, and not double blind...) so I find the scala method does give a valuable approximation of what the "real" CHAS tuning tries to be.

As a demo, I uploaded the first 30 seconds of Ravel's Forlane, first with equal temperament, then with the scala file CHAS24.scl that I used in the past, then a difference of the two renderings, not all zeros as it would be if there were no audible difference. I used the stock D4 Intimate preset.

http://www.forum-pianoteq.com/uploads.p...d_CHas.mp3

I think probably, as does Joe, that CHAS tuning is a slight variant of the standard equal temperament but with a different way of spreading the errors, giving for some music a charming "nostalgic" sound. But then for somebody with absolute pitch, it might just sound wrong of course...

It may sound good for some music in a similar way different major or minor keys sounded so much different, or had different "personalities" before equal temperament tuning spread the error evenly.

Last edited by Gilles (11-06-2012 16:53)

Reply by Jake Johnson

  • Avatar
  • Jake Johnson
  • Member
  • Offline
  • From: Atlanta
  • Registered: 04-05-2007
  • Posts: 4,501

Re: Returning to the CHas

Thanks for posting that, Gilles. Again, your difference files reveal much. I do hear some differences--in that repeated Eb, particularly, which seems a little more mild in CHas, for better or worse.

Ultimately, I wish Alfredo would create the tuning in Pianoteq. Our attempts worry me.  We are not absolutely sure that we are getting the tuning correct, but are trying to judge its value. We're also not using his unison settings, and he writes at length about the importance of the unisons.

Joe, I do take your point about the very small hz differences. I'm not sure how Alfredo would respond. He's
tuned for decades---Bill Bremmer, Kamin, and others on the PW site have listened to at least one of his recorded tunings and praised it. Alfredo would surely understand that the small differences that you note shouldn't make an audible difference.

Last edited by Jake Johnson (12-06-2012 16:07)

Reply by alfredo capurso

  • Avatar
  • alfredo capurso
  • Member
  • Offline
  • Registered: 23-02-2010
  • Posts: 22

Re: Returning to the CHas

Jake Johnson wrote:

Thanks for posting that, Gilles. Again, your difference files reveal much. I do hear some differences--in that repeated Eb, particularly, which seems a little more mild in CHas, for better or worse.

Ultimately, I wish Alfredo would create the tuning in Pianoteq. Our attempts worry me.  We are not absolutely sure that we are getting the tuning correct, but are trying to judge its value. We're also not using his unison settings, and he writes at length about the importance of the unisons.

Joe, I do take your point about the very small hz differences. I'm not sure how Alfredo would respond. He's
tuned for decades---Bill Bremmer, Kamin, and others on the PW site have listened to at least one of his recorded tunings and praised it. Alfredo would surely understand that the small differences that you note shouldn't make an audible difference.

Hi Jake and All friends,

I hope you are fine. I'm glad I came around, perhaps I can answer some questions of yours.

About theoretical Hz differences, they seem to be small but, more important, those differences can stretch all intervals, and the stretch (in theory, and as we do in practice) can be variated.

About differences in practice, I cannot say how much different Chas may sound, that depends on both the listener and the tuning that is being compared with.

In my view (and my ears) Chas may not be "that" different from a good tuning, in terms of general intonation, and that is (possibly) because any sensitive aural tuner would/will target, in my opinion, a similar arrangement. In fact, I do not think I'm the only ear-equipped piano tuner.

Then, if you ask me, the way the piano "sings" is very different, because "different" beat curves can determine an ambient (correct word?) which is totally harmonious, where tensions and sounds can intertwine and blend to a very high degree. And all intervals, all across the scale, are better defined (tension and "meaning"-wise), which translates in a much clearer "reading", particularly up from C6 and from C3 down, that is where tunings may easly get more untidy.

So, altogether, I'd say that Chas may well address tuners, in that this model can prove, beyond personal preferences, the coherence of one precise Form. As for listeners, that depends...

What is new, really, is that we now have a reliable theoretical and practical reference, and that we are enabled (to hope) to experience an absolute optimum.

Joe, you say "CHas is a "cure without a disease."...", and I wish I could agree. But... have a look at Chas thread in PW, see if you can confirm. Btw, are you an aural piano tuner?

I'll be happy to deepen on any other issue.

Thanks Jake.

Have a nice Sunday,

Alfredo

Last edited by alfredo capurso (17-06-2012 11:47)

Reply by jcfelice88keys

  • Avatar
  • jcfelice88keys
  • Member
  • Offline
  • Registered: 22-09-2008
  • Posts: 1,149

Re: Returning to the CHas

alfredo capurso wrote:

Joe, you say "CHas is a "cure without a disease."...", and I wish I could agree. But... have a look at Chas thread in PW, see if you can confirm. Btw, are you an aural piano tuner?

Alfredo


Hello Alfredo,

I shall have a look at the CHas thread in PW.  To answer your question, for the most part, I am an aural piano tuner.   Often times, I test myself by laying the bearings on a chromatic C scale, tuning C, then C#, D, etc., -- without making various checks -- and then check my work by sounding the various intervals.  As an example of a check, I sound G3 and C4, and listen for the concurrent G5 overtone to undulate at once every four seconds.


I do use an electronic tuning device (ETD) as a mediator, in the event that a particular chord or check does not seem to align itself properly.  In fact, I often use double octaves as an aural check, usually in smaller pianos, because of inharmonicity.

Cheers,

Joe

Reply by alfredo capurso

  • Avatar
  • alfredo capurso
  • Member
  • Offline
  • Registered: 23-02-2010
  • Posts: 22

Re: Returning to the CHas

To All, hello.

Yesterday, surfing the web, I've casually found one more work on Chas:

www.luciocadeddu.com/tesi/Cannas_triennale.pdf

Cagliari's is now the fourth Italian University (after Messina, Palermo and Milan's) involved with the divulgation of the Harmonic Temperament, and that is why I am very happy to share this news with you. For translating I often use Lexicool... In case, let me know if I can help.

Joe, you wrote: "CHas is a "cure without a disease."...".

Have you been able to have a look here:
http://www.pianoworld.com/forum/ubbthre...874/1.html

and here:
http://www.pianoworld.com/forum/ubbthre...184/1.html

Did you too get the (general) idea of how tuning and intonation is dealt with?

Regards, a.c.

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. - Department of Mathematics, University of Palermo - 2009, Italy:
http://math.unipa.it/~grim/Quaderno19_C...9_engl.pdf

Article by Professor Nicola Chiriano - published by P.RI.ST.EM (Progetto Ricerche Storiche E Metodologiche) - University "Bocconi" - Milano, 2010 - (Italian):
http://matematica.unibocconi.it/articol...pianoforte

Chas Tunings (piano solo):
http://www.chas.it/index.php?option=com...mp;lang=en

With orchestra:
http://www.youtube.com/watch?v=SQ9BYCbJOfs

Reply by Jake Johnson

  • Avatar
  • Jake Johnson
  • Member
  • Offline
  • From: Atlanta
  • Registered: 04-05-2007
  • Posts: 4,501

Re: Returning to the CHas

Nice video, Alfredo. It puts Rachmaninoff in a different light. The tuning gives him a different kind of forcefulness. (But I wanted all of those other people to stop playing so I could hear the piano.)

I hope you will post some videos of solo piano, close up, using CHas.

And, it's been a long time since we've heard from you. I'm glad to see that more people are exploring the harmonies that you are getting.

Last edited by Jake Johnson (15-12-2012 18:14)