Welcome to the Piano World Piano Forums
Over 2.5 million posts about pianos, digital pianos, and all types of keyboard instruments
Join the World's Largest Community of Piano Lovers (it's free)
It's Fun to Play the Piano ... Please Pass It On!

SEARCH
Piano Forums & Piano World
What's Hot!!
Posting Pictures on the Forums
-------------------
Forums RULES & HELP
-------------------
ADVERTISE on Piano World
(125ad)
Piano Life Saver - Dampp Chaser
Dampp Chaser Piano Life Saver
(ad)
Piano Buyer Guide
Piano Buyer Fall 2017
Who's Online Now
59 registered members (Agent88, Bill McKaig,RPT, Axel Ramge, barbaram, ando, 9 invisible), 1,684 guests, and 1 spider.
Key: Admin, Global Mod, Mod
(ad)
Estonia Pianos
Estonia Pianos
Quick Links to Useful Piano & Music Resources
Our Classified Ads
Find Piano Professionals-

*Piano Dealers - Piano Stores
*Piano Tuners
*Piano Teachers
*Piano Movers
*Piano Restorations
*Piano Manufacturers

Quick Links:
*Advertise On Piano World
*Free Piano Newsletter
*Online Piano Recitals
*Piano Recitals Index
*Piano & Music Accessories
*Live Piano Venues
*Music School Listings
* Buying a Piano
*Buying A Acoustic Piano
*Buying a Digital Piano
*Pianos for Sale
*Sell Your Piano
*How Old is My Piano?
*Directory/Site Map
*Virtual Piano
*Music Word Search
*Piano Videos
*Virtual Piano Chords & Scales
Previous Thread
Next Thread
Print Thread
Page 3 of 4 1 2 3 4
#2673862 - 09/08/17 07:14 PM Re: C.HA.S. equal temperament [Re: alfredo capurso]  
Joined: Nov 2013
Posts: 3,335
prout Offline
3000 Post Club Member
prout  Offline
3000 Post Club Member

Joined: Nov 2013
Posts: 3,335
Southwestern Ontario
Originally Posted by alfredo capurso

Originally Posted by prout
Originally Posted by BDB
Originally Posted by prout
Every octave, whether or not within the temperament setting area, should sound as clean as is possible, and that depends on the relative amplitudes of the various coincident partials of the unisons that make up the octave.
I bet you cannot demonstrate how or why that is the case.
I can measure the relative amplitudes of the partials (as can many ETDs upon which many professional tuners rely) and aurally and subjectively compare the various partial combinations relative to the measured results. Since you do not believe that partials exist, there is no possibility of you accepting the demonstration, so there seems to be no point.

Originally Posted by BDB
Originally Posted by prout
The temperament has nothing to do with octaves, IMNSHO.
Even if it is a temperament based on something other than octaves being pure, which some people espouse?
I have already answered this . You should actually read what I have written. "iH overwhelms C.HA.S." If you want to tune octaves so they audibly beat, just like a 'nice' M3, go ahead. If you want to tune wide octaves on a pipe organ, be my guest, just not on any instrument I will play.


Hi prout,

I remember that you had already questioned the Chas "raw" frequency values, and that Kent Swafford - three years ago - had provided a neat and clear interpretation of Modern ET models, explaining how they may reveal their value.

That thread started with some usual insults and depreciation from the usual posters, but it became more and more interesting as Kent went deeper and deeper into his own observations. At one point, prout, I thought you had understood.

For those who like this subject, here is the link:

http://forum.pianoworld.com/ubbthreads.php/topics/2194834/1.html

Kind regards,

Alfredo
Good evening Alfredo. I greatly respect your investigations into temperaments. I reviewed the thread you posted above from 2014. In it I found the same reservations then that I have now regarding tempering the octave. I stated then that the inherent inharmonicity of the piano, at least in my case, requires, in order to create a 'harmonious' tuning, that the octave be stretched considerably beyond the mathematical value you determine for C.HA.S. That is, of course, also the case for every other possible 12 tone temperament on my piano.

I cannot form an opinion on stretching octaves on a non-inharmonic instrument, other than to say that my preference has always been for the past 50 years to tune the instruments that I did play (not the piano) to as close to 'just' as was possible for the repertiore I was playing. I tune my clavichords to a Kirnberger meantone variant. I now tune my piano to Young 1799 when my wife is not around, EVBT III sometimes when she is, and ET, as determined from the physical iH measurement of the first 32 partials of the bass and tenor strings of my piano, and as many partials as exist below 20kHz in the rest of the piano.

Essentially, I want pure, non-beating intervals, if possible. A pure, beatless Major 3rd is a thing of beauty. There is a calmness that is simply not possible in ETs. I don't mind the 'swirling' resonances of the inharmonic partials and the out-of-tune beatings of piano when tuned in some ET, but it is not calm. It is like always hearing singers producing vibrato, 'leaving the listener in doubt as to just what pitch is being aimed for', as opposed to a men and boys cathedral choir singing in just, vibrato less harmony, and using vibrato as an ornament, not the 'main course'.

(ad 800)
PTG Journal
PTG Journal
#2673864 - 09/08/17 07:29 PM Re: C.HA.S. equal temperament [Re: Toni Goldener]  
Joined: Jul 2007
Posts: 1,403
alfredo capurso Offline
1000 Post Club Member
alfredo capurso  Offline
1000 Post Club Member

Joined: Jul 2007
Posts: 1,403
Sicily - Italy
Hi prout,

I would never discuss your own preferences. You say.. "..A pure, beatless Major 3rd is a thing of beauty", I may say that to me it sounds purely colorless, dull, lifeless, but that is not the point I was addressing. Here you mentioned the Chas "raw" values for octaves stretch, remember? And so, I meant to re-address you to other observations.

Cheers

Last edited by alfredo capurso; 09/08/17 07:31 PM.

alfredo
#2674048 - 09/09/17 06:48 PM Re: C.HA.S. equal temperament [Re: Toni Goldener]  
Joined: Mar 2009
Posts: 2,548
rXd Offline
2000 Post Club Member
rXd  Offline
2000 Post Club Member

Joined: Mar 2009
Posts: 2,548
Originally Posted by Jake Jackson
Originally Posted by rXd
Originally Posted by Jake Jackson
Originally Posted by Chris Leslie
Originally Posted by prout
Alfredo suggests an octave stretch of 2.0005:1. This results in a 0.43 cent stretch, which is well below the stretch I require on A3/A4 (~2.5 cents) to accomodate for iH on my BB......iH overwhelms C.HA.S.


I don't know how Alfredo can suggest such a restriction when the variation of a nice A3/A4 octave can have such variation from piano to piano. 2.5 cents at A3/A4 though seems very wide. What octave type does that correspond to on the BB?


Is he using the A3 second partial and A4 first partial set to 2.0005:1?


smile Surely this would be glaringly obvious from the clip that you posted earlier?


If not, why not? :😳


My untrained ear may have something to do with the problem. smile

Originally Posted by TheTuner
Does the octave stretch not come from the first tuned fourth e4-a4 and from the fifth a3-e4?
I don't tune the first octave a3-a4, it happens.


That was me being a little too acerbic and you both missed my point.,a point I, and others have been attempting to make in the last few posts. Come to think of it, all three of you missed it.

"A tuning that beautiful must be close to c.a.H.s". -Alberto

Hilariously arrogant but

It is.

When you leave an octave to chance like that and it ends up .00063, that's close enough.

The addition of unison strings made it .9987.


Amanda Reckonwith
Concert & Recording tuner-tech, London, England.
"in theory, practice and theory are the same thing. In practice, they're not." - Lawrence P. 'Yogi' Berra.


#2674266 - 09/10/17 01:59 PM Re: C.HA.S. equal temperament [Re: Toni Goldener]  
Joined: Mar 2009
Posts: 2,548
rXd Offline
2000 Post Club Member
rXd  Offline
2000 Post Club Member

Joined: Mar 2009
Posts: 2,548
OK. Already I feel like I've trodden in more than I can chew.
Now that Toni has penetrated the smoke screen and attempted the initial moves in establishing chas. can Alfredo give us a constructive critique of his single string temperament that he so kindly and courageously published so that we all can have a starting point in order to understand this thing in a practical way?

The way Toni seems to be understanding it would result in a quite narrow temperament octave on pretty much every piano. I have no problem with this, there's lots of precedent for heading in this direction to a certain extent. (Narrow middle octaves enabling more stretch in the outer octaves without going outside the realms of rationality where collaborating musicians are involved is not unheard of).

There must be very little that's totally new in piano tuning.

If you really have anything to say in plain language ...

......we're listening.


Amanda Reckonwith
Concert & Recording tuner-tech, London, England.
"in theory, practice and theory are the same thing. In practice, they're not." - Lawrence P. 'Yogi' Berra.


(ad)
Piano & Music Accessories
piano accessories music gifts tuning and moving equipment
#2674523 - 09/11/17 03:38 PM Re: C.HA.S. equal temperament [Re: rXd]  
Joined: Jul 2007
Posts: 1,403
alfredo capurso Offline
1000 Post Club Member
alfredo capurso  Offline
1000 Post Club Member

Joined: Jul 2007
Posts: 1,403
Sicily - Italy
Originally Posted by rXd
OK. Already I feel like I've trodden in more than I can chew.
Now that Toni has penetrated the smoke screen and attempted the initial moves in establishing chas. can Alfredo give us a constructive critique of his single string temperament that he so kindly and courageously published so that we all can have a starting point in order to understand this thing in a practical way?

The way Toni seems to be understanding it would result in a quite narrow temperament octave on pretty much every piano. I have no problem with this, there's lots of precedent for heading in this direction to a certain extent. (Narrow middle octaves enabling more stretch in the outer octaves without going outside the realms of rationality where collaborating musicians are involved is not unheard of).

There must be very little that's totally new in piano tuning.

If you really have anything to say in plain language ...

......we're listening.


Hi rxd,

You are correct, in regard to tuning practice I haven't done much, I have just worked out some interval checks that interlace 4ths and 5ths, and enable me to set the premises for aiming at my favorite tuning curve, reproducing it with a satisfactory degree of exactitude.

Perhaps you have already looked at the sequence flowchart I am sharing, there I mention the first five intervals of the sequence and their beat-rate proportion. It is not much, but it gives me the possibility to place the beat rate of the other SBIs in between, and have the thirds and sixths progression ready for the expansion.

I am not sure of what you mean when you say " ..can Alfredo give us a constructive critique of his single string temperament..", perhaps you can re-word that question?

Also when you say "..it would result in a quite narrow temperament octave..", I an not sure I understand, do you hear A3-A4 narrow, there?

Regards, a.c.

Last edited by alfredo capurso; 09/11/17 03:41 PM.

alfredo
#2674567 - 09/11/17 06:53 PM Re: C.HA.S. equal temperament [Re: Toni Goldener]  
Joined: Nov 2013
Posts: 3,335
prout Offline
3000 Post Club Member
prout  Offline
3000 Post Club Member

Joined: Nov 2013
Posts: 3,335
Southwestern Ontario
Ok, I am in the process of reading the original 2009 paper on C.HA.S.

If I am correct in my interpretation of the English translation of the original Italian, C.HA.S. is entirely based on the inharmonicity of the piano. It is dynamic. That is, Alfredo has essentially created a two octave structure in which there is beat synchronicity between the 12th and 15th partials, with the 12th being narrow and the 15th being equally wide. This 'zero sum' is expanded through out the compass as the inharmonicity changes. Notice that I said 'partials', not intervals. There is no static interval width.

The formula, once understood, uses the variable iH (interpreted either aurally, or with an ETD) to produce an equal beating temperament.

I have not finished the paper yet, but so far, with careful reading, it entirely makes sense. It is an ET with minimal or no stretch beyond what the piano wants. This is potentially very cool, though I think it is only one of many ways in which a fine aural tuner hears the instrument. It does, however, have great potential for a software based algorithmic approach in which iH is measured, plugged into Alfredo's formula, and a very fine tuning produced.

I would like to apologize publicly to Alfredo for misinterpreting my first reading and discussion of his temperament. I thought it was 'classical', that is to say, a mathematical formula that existed without concern for the instrument on which it is tuned. That is clearly not the case.

#2674609 - 09/11/17 10:56 PM Re: C.HA.S. equal temperament [Re: prout]  
Joined: May 2010
Posts: 2,444
DoelKees Offline
2000 Post Club Member
DoelKees  Offline
2000 Post Club Member

Joined: May 2010
Posts: 2,444
Vancouver, Canada
Originally Posted by prout
Ok, I am in the process of reading the original 2009 paper on C.HA.S.

If I am correct in my interpretation of the English translation of the original Italian, C.HA.S. is entirely based on the inharmonicity of the piano. It is dynamic. That is, Alfredo has essentially created a two octave structure in which there is beat synchronicity between the 12th and 15th partials, with the 12th being narrow and the 15th being equally wide. This 'zero sum' is expanded through out the compass as the inharmonicity changes. Notice that I said 'partials', not intervals. There is no static interval width.

The formula, once understood, uses the variable iH (interpreted either aurally, or with an ETD) to produce an equal beating temperament.

I have not finished the paper yet, but so far, with careful reading, it entirely makes sense. It is an ET with minimal or no stretch beyond what the piano wants. This is potentially very cool, though I think it is only one of many ways in which a fine aural tuner hears the instrument. It does, however, have great potential for a software based algorithmic approach in which iH is measured, plugged into Alfredo's formula, and a very fine tuning produced.

I would like to apologize publicly to Alfredo for misinterpreting my first reading and discussion of his temperament. I thought it was 'classical', that is to say, a mathematical formula that existed without concern for the instrument on which it is tuned. That is clearly not the case.


Equal beating 12ths and 15ths have been advocated by Bill Bremmer for a long time.

Kees

#2674617 - 09/12/17 12:49 AM Re: C.HA.S. equal temperament [Re: Toni Goldener]  
Joined: Jul 2007
Posts: 1,403
alfredo capurso Offline
1000 Post Club Member
alfredo capurso  Offline
1000 Post Club Member

Joined: Jul 2007
Posts: 1,403
Sicily - Italy

Hi Prout,

Thank you for your comment.

Let me clarify one thing, you wrote "..with the 12th being narrow and the 15th being equally wide..", and perhaps that terminology is confusing.

Perhaps it is more correct .."..with the 12ths and the 15ths that diverge equally from their pure ratio..". In fact, "beating" might be a slightly different thing.

More later.

Regards, a.c.


alfredo
#2674751 - 09/12/17 02:14 PM Re: C.HA.S. equal temperament [Re: DoelKees]  
Joined: Nov 2013
Posts: 3,335
prout Offline
3000 Post Club Member
prout  Offline
3000 Post Club Member

Joined: Nov 2013
Posts: 3,335
Southwestern Ontario
Originally Posted by DoelKees
Originally Posted by prout
Ok, I am in the process of reading the original 2009 paper on C.HA.S.
... It is an ET with minimal or no stretch beyond what the piano wants. This is potentially very cool, though I think it is only one of many ways in which a fine aural tuner hears the instrument. It does, however, have great potential for a software based algorithmic approach in which iH is measured, plugged into Alfredo's formula, and a very fine tuning produced.
...

Equal beating 12ths and 15ths have been advocated by Bill Bremmer for a long time.

Kees
Yes. I mentioned in my post that C.HA.S, aurally tuned, is much like most fine tunings, in that the iH of the piano must be considered at the root of any possible tuning. I could see C.HA.S. as an overlay on the basic iH.

prout

#2674822 - 09/12/17 06:28 PM Re: C.HA.S. equal temperament [Re: Toni Goldener]  
Joined: Jul 2007
Posts: 1,403
alfredo capurso Offline
1000 Post Club Member
alfredo capurso  Offline
1000 Post Club Member

Joined: Jul 2007
Posts: 1,403
Sicily - Italy

Hi Prout,

I need to say that this morning, reading that you could go through the Chas paper and appreciate the content made me very happy. That paper becomes incomprehensible for some expert readers, thank you, as you are helping me with that.

This model needed to be "dynamic" and needed to represent different "s" tuning curves, even beyond the basic inharmonicity.

With s = 1 the stretch is minimal, as you say.

Yes, every aural tuner will hear the "instrument" differently, and perhaps the instrument behaves differently, depending on the tuner smile

As for the "equal beating 12ths and 15ths", I myself have been a source of confusion, that is probably why Kees pops up. And perhaps I need to say again that the Chas ET model is not a "method" for expanding a tuning, as described by Bill Bremmer eight years ago:

Re: CIRCULAR HARMONIC SYSTEM - CHAS - #1198042 - May 12, 2009 08:38 PM

"The idea which I called "mindless octaves" is a very simple one indeed. At one PTG Convention, I observed Steve Fairchild RPT demonstrate it but I really didn't understand what he was doing at the time. Only later did I realize that the concept I had hit on purely by trial and error was what Steve had been doing.
//Snip//
The "mindless octaves" idea is nothing more than making an exact compromise between the double octave and the octave and 5th (12th). I use the sostenuto pedal to do it. When I used the idea, I heard clarity and beauty that I had never heard before and the feedback from customers kept me at it. To me, it was such a simple technique that it became habitual, within my muscle memory to perform, I didn't really have to concentrate when doing it, I could be thinking about something else, it was just mindless yet the technique yielded such consistent and perfected results each and every time. I later discovered that the aural technique could be as accurate and consistent as any ETD would provide. I use it today when I set up a custom ETD program and when I conduct a PTG Exam Master Tuning."

You wrote: ..."I thought it was 'classical', that is to say, a mathematical formula that existed without concern for the instrument on which it is tuned. That is clearly not the case."

Thanks for reading that paper carefully.

Regards, a.c.
.


alfredo
#2674855 - 09/12/17 08:48 PM Re: C.HA.S. equal temperament [Re: Toni Goldener]  
Joined: May 2010
Posts: 2,444
DoelKees Offline
2000 Post Club Member
DoelKees  Offline
2000 Post Club Member

Joined: May 2010
Posts: 2,444
Vancouver, Canada
For those new to the topic this thread will be interesting:
http://forum.pianoworld.com/ubbthreads.php/topics/2659720/1.html

Kees

#2674870 - 09/12/17 10:26 PM Re: C.HA.S. equal temperament [Re: prout]  
Joined: May 2010
Posts: 2,444
DoelKees Offline
2000 Post Club Member
DoelKees  Offline
2000 Post Club Member

Joined: May 2010
Posts: 2,444
Vancouver, Canada
Originally Posted by prout
Originally Posted by DoelKees
Originally Posted by prout
Ok, I am in the process of reading the original 2009 paper on C.HA.S.
... It is an ET with minimal or no stretch beyond what the piano wants. This is potentially very cool, though I think it is only one of many ways in which a fine aural tuner hears the instrument. It does, however, have great potential for a software based algorithmic approach in which iH is measured, plugged into Alfredo's formula, and a very fine tuning produced.
...

Equal beating 12ths and 15ths have been advocated by Bill Bremmer for a long time.

Kees
Yes. I mentioned in my post that C.HA.S, aurally tuned, is much like most fine tunings, in that the iH of the piano must be considered at the root of any possible tuning. I could see C.HA.S. as an overlay on the basic iH.

prout

Not sure how your reply is a reply to my post, but it is of course obvious that the iH of the piano must be considered for not just most, but all tunings, and not just "fine" ones, but even rough ones.

Stopper advocates pure 12ths across the board (not sure which 12ths in the bass, not 3:1 for sure) and Alfredo advocates equal beating 12ths and 15ths across the board (not sure which 12ths and 15ths in the bass, not 3:1 and 4:1 probably)

There, now I've explained C.HA.S.^(R) and Stopper's stretch schemes for ET in one sentence. smile

Kees

#2674894 - 09/13/17 01:41 AM Re: C.HA.S. equal temperament [Re: DoelKees]  
Joined: Jul 2007
Posts: 1,403
alfredo capurso Offline
1000 Post Club Member
alfredo capurso  Offline
1000 Post Club Member

Joined: Jul 2007
Posts: 1,403
Sicily - Italy

Originally Posted by DoelKees
For those new to the topic this thread will be interesting:
http://forum.pianoworld.com/ubbthreads.php/topics/2659720/1.html

Kees


Thank you, Kees, in my previous post I had forgotten to copy the relative link:

http://forum.pianoworld.com/ubbthreads.php/topics/1213402/2.html.

As I mentioned, Chas represents 12ths and 15ths that deviate numerically from their pure value of the same amount.

Regards, a.c.
.


alfredo
#2674906 - 09/13/17 04:31 AM Re: C.HA.S. equal temperament [Re: DoelKees]  
Joined: Sep 2008
Posts: 277
Bernhard Stopper Offline
Full Member
Bernhard Stopper  Offline
Full Member

Joined: Sep 2008
Posts: 277
Germany
Originally Posted by DoelKees
Originally Posted by prout
Originally Posted by DoelKees
Originally Posted by prout
Ok, I am in the process of reading the original 2009 paper on C.HA.S.
... It is an ET with minimal or no stretch beyond what the piano wants. This is potentially very cool, though I think it is only one of many ways in which a fine aural tuner hears the instrument. It does, however, have great potential for a software based algorithmic approach in which iH is measured, plugged into Alfredo's formula, and a very fine tuning produced.
...

Equal beating 12ths and 15ths have been advocated by Bill Bremmer for a long time.

Kees
Yes. I mentioned in my post that C.HA.S, aurally tuned, is much like most fine tunings, in that the iH of the piano must be considered at the root of any possible tuning. I could see C.HA.S. as an overlay on the basic iH.

prout

Not sure how your reply is a reply to my post, but it is of course obvious that the iH of the piano must be considered for not just most, but all tunings, and not just "fine" ones, but even rough ones.


thumb

[/quote]
As I mentioned, Chas represents 12ths and 15ths that deviate numerically from their pure value of the same amount.

Regards, a.c.
[/quote]
.

Just to complete the list (ET size expressed in size of octaves, as this gives more feel for the "stretch" than the halftone step factor or the pure interval base):

Pure 26ths ET (aka Bremmers mindless octaves (publication date?), equivalent to CHAS) represents 12ths and 15ths (two 8ths) that deviate numerically from their pure value of the same amount, resulting in an octave width of 1200.54 cents without iH.

Pure 19ths ET represents 12ths and 8ths that deviate numerically from their pure value of the same amount, resulting in an octave width of 1200.76 cents without iH.

Pure 12ths ET (Stopper 1988) represents 8ths and 5ths that deviate numerically from their pure value of the same amount, resulting in an octave width of 1201.23 cents without iH.
http://www.piano-stopper.de/dl/EUROPIANO_3_88_STOP.pdf

Pure 16ths ET represents 12ths and 5ths that deviate numerically from their pure value of the same amount, resulting in an octave width of 1201.80 cents without iH.

Pure 20ths ET represents 12ths and two 5ths that deviate numerically from their pure value of the same amount, resulting in an octave width of 1202.13 cents without iH.

(....this list can be extended by any number of combinations of twelfths, octaves or fifths and fourths which are just fractions of twelfths and octaves)

Pure 5ths ET, (Kolinski 1959), resulting in an octave width of 1203.35 cents without iH.

Any real number value (Geometrie der Töne, G. Mazzola 1990), resulting in an octave width of any real number value cents without iH.

Not to forget Haye Hinrichsen who came up with his own octave size for lowest entropy he calculated for a group of 88 notes with a harmonic power spectrum (no iH) to be 1200.6 cents. link:
http://www.scielo.br/scielo.php?scr...11172016000100410&lng=en&tlng=en

My calculations for lowest entropy tend to pure 12ths ET, when not throwing only 88 harmonic spectrum tones into the equation, but including inharmonic spectrum tones also.

Anyway, the generally observed pure effect of pure 12th ET is mainly caused by an at the same time synchronous effect of a large number of slow beating intervals having quasi perfect interval ratios, coupled with an asynchronous effect influencing fast and slow beating intervals by the slight offsets in the octaves, reducing the perception of those beats (even of the major thirds, which are slightly faster than in standard ET) significantly. Another important effect is the melodic correction for the high treble and low bass: Standard ET usually hangs in the treble and creates basses that are too high. In pure 12th ET, the two notes of an octave sound "the same" when played successively.

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

Bernhard Stopper






Last edited by Bernhard Stopper; 09/13/17 05:07 AM.
#2674946 - 09/13/17 09:24 AM Re: C.HA.S. equal temperament [Re: DoelKees]  
Joined: Nov 2013
Posts: 3,335
prout Offline
3000 Post Club Member
prout  Offline
3000 Post Club Member

Joined: Nov 2013
Posts: 3,335
Southwestern Ontario
Originally Posted by DoelKees
Originally Posted by prout
Originally Posted by DoelKees
Originally Posted by prout
Ok, I am in the process of reading the original 2009 paper on C.HA.S.
... It is an ET with minimal or no stretch beyond what the piano wants. This is potentially very cool, though I think it is only one of many ways in which a fine aural tuner hears the instrument. It does, however, have great potential for a software based algorithmic approach in which iH is measured, plugged into Alfredo's formula, and a very fine tuning produced.
...

Equal beating 12ths and 15ths have been advocated by Bill Bremmer for a long time.

Kees
Yes. I mentioned in my post that C.HA.S, aurally tuned, is much like most fine tunings, in that the iH of the piano must be considered at the root of any possible tuning. I could see C.HA.S. as an overlay on the basic iH.

prout

Not sure how your reply is a reply to my post, but it is of course obvious that the iH of the piano must be considered for not just most, but all tunings, and not just "fine" ones, but even rough ones.

Stopper advocates pure 12ths across the board (not sure which 12ths in the bass, not 3:1 for sure) and Alfredo advocates equal beating 12ths and 15ths across the board (not sure which 12ths and 15ths in the bass, not 3:1 and 4:1 probably)

There, now I've explained C.HA.S.^(R) and Stopper's stretch schemes for ET in one sentence. smile

Kees
Both of my comments above were, in part, the result of a wine induced fog. Sorry.

I am not sure why I comment on ET tunings. Perhaps because, while I abhor ET, I am forced to employ it in my work. There is something always disturbing when playing Chopin, Debussy, Ravel, whomever, and landing on a interval that is meant to be the tension resolution of a phase, only to find it beating like some superannuated soprano. It is my opinion, obviously not shared by others, that these composers did not intend this to be the case, though they may have suffered under the same disability.

#2674980 - 09/13/17 10:48 AM Re: C.HA.S. equal temperament [Re: prout]  
Joined: Sep 2008
Posts: 277
Bernhard Stopper Offline
Full Member
Bernhard Stopper  Offline
Full Member

Joined: Sep 2008
Posts: 277
Germany
Quote

There is something always disturbing when playing Chopin, Debussy, Ravel, whomever, and landing on a interval that is meant to be the tension resolution of a phase, only to find it beating like some superannuated soprano. It is my opinion, obviously not shared by others, that these composers did not intend this to be the case, though they may have suffered under the same disability.


I would not be sure that you are in good society with these composers, Chopin for example preferred Montal as tuner, who deliberately tuned ET and not one of the well temperament or meantone/meantone derivative temperament tuners who were en vogue in academic circles at this time (most of them promoting their own holy grail of temperament).

Bernhard Stopper

#2675004 - 09/13/17 12:28 PM Re: C.HA.S. equal temperament [Re: Bernhard Stopper]  
Joined: Nov 2013
Posts: 3,335
prout Offline
3000 Post Club Member
prout  Offline
3000 Post Club Member

Joined: Nov 2013
Posts: 3,335
Southwestern Ontario
Originally Posted by Bernhard Stopper
Quote

There is something always disturbing when playing Chopin, Debussy, Ravel, whomever, and landing on a interval that is meant to be the tension resolution of a phase, only to find it beating like some superannuated soprano. It is my opinion, obviously not shared by others, that these composers did not intend this to be the case, though they may have suffered under the same disability.


I would not be sure that you are in good society with these composers, Chopin for example preferred Montal as tuner, who deliberately tuned ET and not one of the well temperament or meantone/meantone derivative temperament tuners who were en vogue in academic circles at this time (most of them promoting their own holy grail of temperament).

Bernhard Stopper
I am not suggesting that any composer I mentioned preferred a WT over a ET. Chopin's preferred tuner, like all tuners, could not produce an ET on any piano, since the physics of the instrument prevents the tuner from so doing. It is quite possible that Montal's 'ET' used the iH of Chopin's instruments in a way that made Chopin's use of 'remote' keys very calm, or, that because they were calm, Chopin chose to write in those 'remote' keys. We can never know.

But I do know that the underlay of constant beating inherent in an inharmonic instrument adds a veil of haze to the purity of the potential sound that is then made worse by the use of any temperament that elevates the idea that all intervals should beat, whether or not that beating has musical value, as opposed to just being accepted as a necessary compromise in tuning.

I am forced by my work to play in all keys. For me, an on-the-fly just intonation would be fun to use. There was (is?) a company based in Vancouver in the early 1990s called Justonic Tuning Inc. that provided software to do this on digital keyboards.

#2675022 - 09/13/17 02:00 PM Re: C.HA.S. equal temperament [Re: prout]  
Joined: Jun 2003
Posts: 25,548
BDB Offline
Yikes! 10000 Post Club Member
BDB  Offline
Yikes! 10000 Post Club Member

Joined: Jun 2003
Posts: 25,548
Oakland
First you say that you do not like equal temperament on pianos, and then you say that equal temperament cannot be tuned on pianos. So since you have never heard equal temperament on pianos, how do you know you do not like it?


Semipro Tech
#2675025 - 09/13/17 02:22 PM Re: C.HA.S. equal temperament [Re: prout]  
Joined: Sep 2008
Posts: 277
Bernhard Stopper Offline
Full Member
Bernhard Stopper  Offline
Full Member

Joined: Sep 2008
Posts: 277
Germany
Originally Posted by prout

Chopin's preferred tuner, like all tuners, could not produce an ET on any piano, since the physics of the instrument prevents the tuner from so doing.

The tuners of today and the past (including Montal) could indeed tune ET on any piano. ET on pianos (ih involved) is defined as progressively (as progressive as iH allows) increasing interval beatings along the scale, in most cases keeping a base interval aurally as pure as possible (even in CHAS were Alfredo claims no interval is pure, the 26ths are pure (exactly pure in case of no iH and aurally pure as possible with iH)). As long as everything is in a tolerable tolerance, pro tuners classify such progressive intervals as ET.

Originally Posted by prout
It is quite possible that Montal's 'ET' used the iH of Chopin's instruments in a way that made Chopin's use of 'remote' keys very calm, or, that because they were calm, Chopin chose to write in those 'remote' keys. We can never know.



No this is not possible. I am pretty sure from what i read from your posts so far you are informed enough about iH that it is by definition impossible to calm remote keys by iH with progressively tuned intervals. Maybe another wine fog? wink

Bernhard Stopper

Last edited by Bernhard Stopper; 09/13/17 02:42 PM.
#2675035 - 09/13/17 03:03 PM Re: C.HA.S. equal temperament [Re: BDB]  
Joined: Nov 2013
Posts: 3,335
prout Offline
3000 Post Club Member
prout  Offline
3000 Post Club Member

Joined: Nov 2013
Posts: 3,335
Southwestern Ontario
Originally Posted by BDB
First you say that you do not like equal temperament on pianos, and then you say that equal temperament cannot be tuned on pianos. So since you have never heard equal temperament on pianos, how do you know you do not like it?
You're funny! Thanks for that.

What I do know is that I really do not like ET on an organ, which is possible, frequent, and I spent too many decades fighting.

No one has ever heard ET on a piano, including you as a member of the set. What I do not like is the attempt at approximating ET on a piano. It is ever so much easier to tune a UT and know that intentionally, some intervals will sound harsh and some will sound sublime. When the harsh and sublime intervals are crafted into a beautiful piece of music, the result is a musical experience beyond a level that is obtainable when every interval is, more or less, sort of, hopefully, evenly harsh, or, dare I say it, out-of-tune.

I know my opinion is not main stream, and I am happy to bow out and let the ET proponents bask in harsh glare of their temperament.

I remain,

PRO UT

#2675038 - 09/13/17 03:06 PM Re: C.HA.S. equal temperament [Re: Bernhard Stopper]  
Joined: Nov 2013
Posts: 3,335
prout Offline
3000 Post Club Member
prout  Offline
3000 Post Club Member

Joined: Nov 2013
Posts: 3,335
Southwestern Ontario
Originally Posted by Bernhard Stopper
Originally Posted by prout
It is quite possible that Montal's 'ET' used the iH of Chopin's instruments in a way that made Chopin's use of 'remote' keys very calm, or, that because they were calm, Chopin chose to write in those 'remote' keys. We can never know.


No this is not possible. I am pretty sure from what i read from your posts so far you are informed enough about iH that it is by definition impossible to calm remote keys by iH with progressively tuned intervals. Maybe another wine fog? wink

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

#2675049 - 09/13/17 04:14 PM Re: C.HA.S. equal temperament [Re: prout]  
Joined: Sep 2008
Posts: 277
Bernhard Stopper Offline
Full Member
Bernhard Stopper  Offline
Full Member

Joined: Sep 2008
Posts: 277
Germany
Originally Posted by prout
Originally Posted by Bernhard Stopper
Originally Posted by prout
It is quite possible that Montal's 'ET' used the iH of Chopin's instruments in a way that made Chopin's use of 'remote' keys very calm, or, that because they were calm, Chopin chose to write in those 'remote' keys. We can never know.


No this is not possible. I am pretty sure from what i read from your posts so far you are informed enough about iH that it is by definition impossible to calm remote keys by iH with progressively tuned intervals. Maybe another wine fog? wink

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


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

#2675066 - 09/13/17 05:02 PM Re: C.HA.S. equal temperament [Re: Bernhard Stopper]  
Joined: Jun 2003
Posts: 25,548
BDB Offline
Yikes! 10000 Post Club Member
BDB  Offline
Yikes! 10000 Post Club Member

Joined: Jun 2003
Posts: 25,548
Oakland
I think at this point, there is no point discussing anything with Prout. He never explains anything, and makes claims about things that he cannot possibly know, like what people he has never met hear. It is time to dismiss him as a quack.


Semipro Tech
#2675087 - 09/13/17 06:23 PM Re: C.HA.S. equal temperament [Re: Bernhard Stopper]  
Joined: Jul 2007
Posts: 1,403
alfredo capurso Offline
1000 Post Club Member
alfredo capurso  Offline
1000 Post Club Member

Joined: Jul 2007
Posts: 1,403
Sicily - Italy
Originally Posted by prout
Originally Posted by Bernhard Stopper
Quote

There is something always disturbing when playing Chopin, Debussy, Ravel, whomever, and landing on a interval that is meant to be the tension resolution of a phase, only to find it beating like some superannuated soprano. It is my opinion, obviously not shared by others, that these composers did not intend this to be the case, though they may have suffered under the same disability.


I would not be sure that you are in good society with these composers, Chopin for example preferred Montal as tuner, who deliberately tuned ET and not one of the well temperament or meantone/meantone derivative temperament tuners who were en vogue in academic circles at this time (most of them promoting their own holy grail of temperament).

Bernhard Stopper
I am not suggesting that any composer I mentioned preferred a WT over a ET. Chopin's preferred tuner, like all tuners, could not produce an ET on any piano, since the physics of the instrument prevents the tuner from so doing. It is quite possible that Montal's 'ET' used the iH of Chopin's instruments in a way that made Chopin's use of 'remote' keys very calm, or, that because they were calm, Chopin chose to write in those 'remote' keys. We can never know.

But I do know that the underlay of constant beating inherent in an inharmonic instrument adds a veil of haze to the purity of the potential sound that is then made worse by the use of any temperament that elevates the idea that all intervals should beat, whether or not that beating has musical value, as opposed to just being accepted as a necessary compromise in tuning.

I am forced by my work to play in all keys. For me, an on-the-fly just intonation would be fun to use. There was (is?) a company based in Vancouver in the early 1990s called Justonic Tuning Inc. that provided software to do this on digital keyboards.




Hi Prout,

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

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

Originally Posted by Bernhard Stopper

Just to complete the list (ET size expressed in size of octaves, as this gives more feel for the "stretch" than the halftone step factor or the pure interval base):

Pure 26ths ET (aka Bremmers mindless octaves (publication date?), equivalent to CHAS) represents 12ths and 15ths (two 8ths) that deviate numerically from their pure value of the same amount, resulting in an octave width of 1200.54 cents without iH.

Pure 19ths ET represents 12ths and 8ths that deviate numerically from their pure value of the same amount, resulting in an octave width of 1200.76 cents without iH.

Pure 12ths ET (Stopper 1988) represents 8ths and 5ths that deviate numerically from their pure value of the same amount, resulting in an octave width of 1201.23 cents without iH.
http://www.piano-stopper.de/dl/EUROPIANO_3_88_STOP.pdf

Pure 16ths ET represents 12ths and 5ths that deviate numerically from their pure value of the same amount, resulting in an octave width of 1201.80 cents without iH.

Pure 20ths ET represents 12ths and two 5ths that deviate numerically from their pure value of the same amount, resulting in an octave width of 1202.13 cents without iH.

(....this list can be extended by any number of combinations of twelfths, octaves or fifths and fourths which are just fractions of twelfths and octaves)

Pure 5ths ET, (Kolinski 1959), resulting in an octave width of 1203.35 cents without iH.

Any real number value (Geometrie der Töne, G. Mazzola 1990), resulting in an octave width of any real number value cents without iH.

Not to forget Haye Hinrichsen who came up with his own octave size for lowest entropy he calculated for a group of 88 notes with a harmonic power spectrum (no iH) to be 1200.6 cents. link:
http://www.scielo.br/scielo.php?scr...11172016000100410&lng=en&tlng=en

My calculations for lowest entropy tend to pure 12ths ET, when not throwing only 88 harmonic spectrum tones into the equation, but including inharmonic spectrum tones also.

Anyway, the generally observed pure effect of pure 12th ET is mainly caused by an at the same time synchronous effect of a large number of slow beating intervals having quasi perfect interval ratios, coupled with an asynchronous effect influencing fast and slow beating intervals by the slight offsets in the octaves, reducing the perception of those beats (even of the major thirds, which are slightly faster than in standard ET) significantly. Another important effect is the melodic correction for the high treble and low bass: Standard ET usually hangs in the treble and creates basses that are too high. In pure 12th ET, the two notes of an octave sound "the same" when played successively.

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

Bernhard Stopper



Hi Bernard,

You wrote: .."Pure 26ths ET (aka Bremmers mindless octaves (publication date?), equivalent to CHAS) represents 12ths and 15ths (two 8ths) that deviate numerically from their pure value of the same amount, resulting in an octave width of 1200.54 cents without iH."..

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

..."...My calculations for lowest entropy tend to pure 12ths ET, when not throwing only 88 harmonic spectrum tones into the equation, but including inharmonic spectrum tones also."...

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

..."..Anyway, the generally observed pure effect of pure 12th ET is mainly caused by an at the same time synchronous effect of a large number of slow beating intervals having quasi perfect interval ratios,..."..

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

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

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

More tomorrow, as I had a long day.

Regards, a.c.

Last edited by alfredo capurso; 09/13/17 06:47 PM.

alfredo
#2675105 - 09/13/17 08:01 PM Re: C.HA.S. equal temperament [Re: Toni Goldener]  
Joined: Nov 2008
Posts: 5,760
UnrightTooner Offline
5000 Post Club Member
UnrightTooner  Offline
5000 Post Club Member

Joined: Nov 2008
Posts: 5,760
Bradford County, PA
All:

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

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

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

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


Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?
#2675144 - 09/14/17 01:51 AM Re: C.HA.S. equal temperament [Re: UnrightTooner]  
Joined: Sep 2008
Posts: 277
Bernhard Stopper Offline
Full Member
Bernhard Stopper  Offline
Full Member

Joined: Sep 2008
Posts: 277
Germany
Originally Posted by UnrightTooner
All:

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

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

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

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


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

Last edited by Bernhard Stopper; 09/14/17 09:40 AM.
#2675148 - 09/14/17 02:57 AM Re: C.HA.S. equal temperament [Re: alfredo capurso]  
Joined: Sep 2008
Posts: 277
Bernhard Stopper Offline
Full Member
Bernhard Stopper  Offline
Full Member

Joined: Sep 2008
Posts: 277
Germany
Originally Posted by alfredo capurso

..."..Anyway, the generally observed pure effect of pure 12th ET is mainly caused by an at the same time synchronous effect of a large number of slow beating intervals having quasi perfect interval ratios,..."..

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


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

Last edited by Bernhard Stopper; 09/14/17 09:16 AM.
#2675321 - 09/14/17 05:31 PM Re: C.HA.S. equal temperament [Re: Bernhard Stopper]  
Joined: Jul 2007
Posts: 1,403
alfredo capurso Offline
1000 Post Club Member
alfredo capurso  Offline
1000 Post Club Member

Joined: Jul 2007
Posts: 1,403
Sicily - Italy
Originally Posted by Bernhard Stopper
Originally Posted by UnrightTooner
All:

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

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

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

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


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


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

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

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

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

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

Eight years have gone, one wouldn't say.

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

Well, here is what you were saying: "Pure 26ths ET (aka Bremmers mindless octaves (publication date?), equivalent to CHAS) represents 12ths and 15ths (two 8ths) that deviate numerically from their pure value of the same amount, resulting in an octave width of 1200.54 cents without iH."...

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

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

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

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

s-sure.

More tomorrow.

Regards, a.c.
.

Last edited by alfredo capurso; 09/14/17 06:04 PM.

alfredo
#2675417 - 09/15/17 05:26 AM Re: C.HA.S. equal temperament [Re: alfredo capurso]  
Joined: Sep 2008
Posts: 277
Bernhard Stopper Offline
Full Member
Bernhard Stopper  Offline
Full Member

Joined: Sep 2008
Posts: 277
Germany
Originally Posted by alfredo capurso

When dealing with numbers, I have to ask you to be rigorous, at least when you mention Chas.

Accepted.

Originally Posted by alfredo capurso

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


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

#2675428 - 09/15/17 06:39 AM Re: C.HA.S. equal temperament [Re: Bernhard Stopper]  
Joined: Jul 2007
Posts: 1,403
alfredo capurso Offline
1000 Post Club Member
alfredo capurso  Offline
1000 Post Club Member

Joined: Jul 2007
Posts: 1,403
Sicily - Italy
Originally Posted by Bernhard Stopper
Originally Posted by alfredo capurso

When dealing with numbers, I have to ask you to be rigorous, at least when you mention Chas.

Accepted.

Originally Posted by alfredo capurso

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


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


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

Last edited by alfredo capurso; 09/15/17 06:41 AM.

alfredo
Page 3 of 4 1 2 3 4

Moderated by  Piano World 

Piano Acc. & Gift Items in
Piano World's Online Store
In PianoSupplies.com ,(a division of Piano World)
our online store for piano and music gifts and accessories, Digital Piano Dolly, party goods, tuning equipment, piano moving equipment, benches, lamps Caster Cups and more.


Free Shipping* on Jansen Artist Piano Benches, Cocoweb Piano Lamps, Hidrau Hydraulic Piano Benches
(*free shipping within contiguous U.S. only)
(ad)
Pearl River & Ritmuller
Pearl River Pianos
(ad)
Pianoteq
PianoTeq 6 Out now
ad
Pierce Piano Atlas


New Topics - Multiple Forums
New Chinese made Baldwin 7 foot grand
by 7naturals. 11/22/17 01:23 AM
Moonlight Sonata Sostenuto
by Weiyan. 11/22/17 12:53 AM
Experience with Redbird, Concertpianos, and “Maestro”?
by Duke of Dunning. 11/21/17 06:26 PM
Forum Statistics
Forums44
Topics182,879
Posts2,673,446
Members89,168
Most Online15,252
Mar 21st, 2010
(ad)
Accu-Tuner
Sanderson Accu-Tuner
Check It Out!
There's a lot more to Piano World than just the forums.
Click Here to
Explore The Rest of Piano World!!
Visit our online store for gifts for music lovers


 
Help keep the forums up and running with a donation, any amount is appreciated!
Or by becoming a Subscribing member! Thank-you.
Donate   Subscribe
 
Our Piano Related Classified Ads
| Dealers | Tuners | Lessons | Movers | Restorations | Pianos For Sale | Sell Your Piano |

Advertise on Piano World
| Subscribe | Piano World | PianoSupplies.com | Advertise on Piano World |
| |Contact | Privacy | Legal | About Us | Site Map | Free Newsletter |


copyright 1997 - 2017 Piano World ® all rights reserved
No part of this site may be reproduced without prior written permission
Powered by UBB.threads™ PHP Forum Software 7.6.0