! Dimitrov.scl
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Latchezar Dimitrov 2020 Moyen half tone equal temperament
12
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100.27124
200.54248
300.81373
401.08497
501.35622
601.62746
701.94696
802.16995
902.44119
1002.7123
1102.9836
1203.2548

I was thinking, not clearly, that wide fifths would mean that other intervals would be wide, but the opposite has to happen, or the octave would get too wide.

Yes, it is flat, not equal,  at 1.23 stretch.

Please elaborate!

(sans rancune Stéphane ;-) )

(..) I do worry that the thirds are going to be awfully wide.

Indeed!

I don't. I briefly browsed the Internet with keywords "cordier piano enregistrement" (or "record" or "recording"), but did not find any relevant reference.

In passing, I found an interesting (I mean scientifically conducted ;-) ) experimental study to be presented at "10ème Congrès Français d'Acoustique, Lyon 12-16 April 2010":
Objectivation de la perception du tempérament : l'accordage du piano
Unfortunately, there is no English translation of this paper (not even its summary!).

In a few words, those blindfold tests (made with an acoustic piano, tuned according to standard equal temperament, then Cordier's temperament) show Cordier tuning was mostly preferred on recorded samples of  Rachmaninov, Debussy and even Bach short pieces. Standard equal temperament was never significantly preferred.

[EDIT] Thanks to Pianoteq's Scala import function + A/B switching, it is easy for each of us to compare Alfredo's and Cordier's temperaments! Personally, my first attempts tend to favor Alfredo...

I'll have to check the Scala file later, but I do worry that the thirds are going to be awfully wide. That's one thing I like about Alfredo's slightly narrow, consonant 12ths across the keyboard--they keep the thirds from getting too far out of control.

In fact, I've been going in another direction, experimenting with temperament ordinaire as outlined by Rousseau--a departure from meantone that seems to have a wolf on close voiced chords that include an Ab (if I'm tuning it correctly), but which has great thirds and fifths and brings out some interesting resonances if I spread it from the center with 12ths similar to Alfredo's. I'll post a file once I'm more sure I have it right. But let's hope we can get Cordier set up to have a listen.

Do you know of recordings in Cordier? (With CHas, the recordings let us know what we were after.)

Here is the frequency scale given in the fr.wikipedia.org I quoted above - obviously, the perfect fifth is divided into 7 equal parts, so that a semitone interval is 1.5^(1/7)

We can check this formula is consistent with the Scala file cordier.scl :

 Serge Cordier, piano tuning, 1975 (Piano bien tempéré et justesse orchestrale)

  0:          1/1               0.000  unison, perfect prime
  1:        100.279 cents     100.279
  2:        200.559 cents     200.559
  3:        300.838 cents     300.838
  4:        401.117 cents     401.117
  5:        501.396 cents     501.396
  6:        601.676 cents     601.676
  7:          3/2             701.955  perfect fifth
  8:        802.234 cents     802.234
  9:        902.514 cents     902.514
 10:       1002.793 cents    1002.793
 11:       1103.072 cents    1103.072
 12:       1203.351 cents    1203.351

Also, we can notice its stretching is much wider than in CHas:

CHas s=1
  0:          1/1               0.000  unison, perfect prime
  1:        100.038 cents     100.038
  2:        200.077 cents     200.077
  3:        300.115 cents     300.115
  4:        400.153 cents     400.153
  5:        500.192 cents     500.192
  6:        600.230 cents     600.230
  7:        700.268 cents     700.268
  8:        800.307 cents     800.307
  9:        900.345 cents     900.345
 10:       1000.383 cents    1000.383
 11:       1100.422 cents    1100.422
 12:       1200.460 cents    1200.460

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

And he's planning to record some things with the tuning soon, it seems.

The second question for MODARTT: what is the unit (or scale) used for the stretch value? The manual simply says:

"When the octave stretching parameter is set to 1, the stretching follows the natural inharmonicity of the strings (depending on the string length), so there still is a slight stretching. If you want no stretching at all, then use the flat temperament."

Knowing the answer to the latter, computing the answer to the former is straightforward, I believe!

More generally, is there a document that gives the units used in Pianoteq configuration parameters (taken apart obvious ones in dB or %)?

Alain

Alain, there is no unit for the stretch, it is just a percentage of a default deviation (that can vary from one piano to another). This approach (percentage of a given default value) is also used for some other parameters, it is quite a direct and intuitive approach where dB would not be very relevant.

Concerning tuning, the best solution for achieving a given precise temperament is to use the detune NOTE EDIT (TUNING panel, diapason menu, clicking at the bottom on "Detune notes" gives you access to the detune NOTE EDIT). Here the deviation is in the standard "cent" unit, a hundreth of a semitone.

At least we'll eventually get a cents deviation chart to give us an estimate of the pitches.

Here is the frequency scale given in the fr.wikipedia.org I quoted above - obviously, the perfect fifth is divided into 7 equal parts, so that a semitone interval is 1.5^(1/7) :

    * 1.0
    * 1.059634
    * 1.122824
    * 1.189782
    * 1.260734
    * 1.335916
    * 1.415582
    * 1.5
    * 1.589451
    * 1.684236
    * 1.784674
    * 1,891101
    * 2,003875

But S. Cordier and his adepts did or do not use electronic tuners, and it is likely their "beating method" yields sligtly different values.

Also, there are often confusions between pure, perfect (just) and "no beat" fifths!

To be frank, being an "ordinary" pianist, I did not study Cordier's detailed method ;-)

And I'm immediately lost when I try to follow the instructions for setting the bearing: I can't begin to measure "0.8 beats per second wide,"
and "1.7 beats per second wide." Looking forward to hearing from people who can. At least we'll eventually get a cents deviation chart to give us an estimate of the pitches.

Not that I doubt you--it's just that it seems too simple. 

Things are not that simple, I fear!
What I understand at the moment - please correct me wherever I'm wrong:

According to the classic theory, octave stretching is required because of higher string inharmonicity in the piano (not in other instruments e.g. organs). It is not a linear stretching: specific stretching for lower wound strings, small stretching for medium strings, maximum stretching for short strings. In Pianoteq, this stretching is automatically set with "stretching" = 1.

If we increase "string length" to 10 m, inharmonicity becomes negligible for all strings, so  stretching is no longer necessary.

Cordier's temperament is unrelated to inharmonicity: it may be superimposed to it (or vice-versa ;-) ). Hence, I doubt this combination can be accurately obtained in Pianoteq with a simple "stretching" change!

Cordier's temperament has been applied to organs

Wikipedia references:

Tempérament égal à quintes justes

This article was not translated into English, but it was briefly summarized in
Equal temperament

(Is this accurate? Does using the flat setting and putting the stretch at 1.23 actually create the Cordier temperament?)

One question for Stéphane : how did you estimate this 1.23 stretch value ?

The second question for MODARTT: what is the unit (or scale) used for the stretch value? The manual simply says:

"When the octave stretching parameter is set to 1, the stretching follows the natural inharmonicity of the strings (depending on the string length), so there still is a slight stretching. If you want no stretching at all, then use the flat temperament."

Knowing the answer to the latter, computing the answer to the former is straightforward, I believe!

More generally, is there a document that gives the units used in Pianoteq configuration parameters (taken apart obvious ones in dB or %)?

Alain

http://www.pianoworld.com/forum/ubbthre...74/42.html

I haven't had the chance to see how this matches up with setting the stretch to 1.23 in PianoTeq, and I really don't trust myself to count the beats correctly. (I can count off a second, and I can count beats, but doing both at the same time is a skill I am still trying to learn...)

Merci pour cette information, j'ai hate d'essayer.