Tempérament parfait

My ears and technical understanding are too limited to appreciate this information, but it sounded so fascinating to me that I couldn't resist making a quick translation of it for the non-French speaking forum dwellers.  The additions in [square brackets] are my guesses, for clarification.  Hope this helps!  Chris

----

Perfect Temperament

The just fifths equal temperament will make your piano perfectly tuned (of course, with a Western, contemporary tuning).

I did not invent this temperament, but have found the formula to apply it in Pianoteq. Mr. Serge Cordier is the one who explored, explained and defined this temperament. It simply consists in making the fundamentals of each fifth, just. When one makes the octaves just, the fifths are necessarily lowered, which makes the fifths "cry" and creates fake [artificial] beats throughout the piano. Of course, by making the fifths just, the octaves are widened [stretched], but this would already be the case anyway for the bass and treble [strings] in the temperament that a tuner would create.

When you try this temperament, you will initially notice that the thirds don't "ring" as usual, but you will then discover that your entire piano opens up in an extraordinary way. This may require a bit of time to appreciate, but after a few minutes, you will never want to hear a different tuning again. This may sound pretentious, but you have nothing to lose.

The formula is: "Flat" temperament + 1.23 Stretching

Enjoy the music.

Yes, it is flat, not equal,  at 1.23 stretch.  To make the rights thing, you must tune the piano at 439.85 hz,  not 440.00 hz.   Try to play Pianotq at this temperament with another instrument of your choice or with a CD you like.  All the range of the keyboard sound great.  My book of Serge Cordier is wright in french.  The name of the book is called  "Piano bien tempéré et justesse orchestrale", (Le tempérament équal à quintes juste).  Editor, "Buchet/Chastel  18,rue de Condé-75006 PARIS".  That book was wright in 1982, that's not a new book.

I think you mean "written" rather than "wright". Since it took me a while to guess I wanted to share it so others understand.

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

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

The problem, for me, is partly just setting the bearing. From what I can tell, Cordier doesn't just set all of the intervals in the center so that the 5ths are just, or adhere to ET in the bearing and then make the fifth of every note just.

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.

Bill Bremmer has continued his translation of the Cordier tuning sequence with information about tuning the octaves and the 12ths:

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

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

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

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.)

Please elaborate!

(sans rancune Stéphane ;-) )