Fwd: Nueva escala temperada From Mario Pizarro

I don't think this is really new, but it may not be widely known as a stretched 12-EDO.

John: He derivado la nueva escala temperada donde las 12 frecuencias son:.

C = 1

C# = (3/2)^(1/7)

D = (3/2)^(2/7)

Eb = (3/2)^(3/7)

E = (3/2)^(4/7)

F = (3/2)^(5/7)

F# = (3/2)^(6/7)

G = (3/2)

Ab = (3/2)^(8/7)

A = (3/2)^^(9/7)

Bb = (3/2)^(10/7)

B = (3/2)^(11/7)

2C = (3/2)^(12 /7)=2.00387547381

PLEASE SEND THIS NEW TO TUNING YAHOOGROUPS. ALSO TO MIKE BATTAGLIA AND KEENAN PEPPER, I CAN NOT SEND TO TUNING DIRECTLY BECAUSE MY EQUIPMENT IS UNABLE TO CONECT THEM. MY AUTHORIZED EMAIL IS OUT OF SERVICE
THANKS
MARIO

> C = 1
> C# = (3/2)^(1/7)
> D = (3/2)^(2/7)
> Eb = (3/2)^(3/7)
> E = (3/2)^(4/7)
> F = (3/2)^(5/7)
> F# = (3/2)^(6/7)
> G = (3/2)
> Ab = (3/2)^(8/7)
> A = (3/2)^(9/7)
> Bb = (3/2)^(10/7)
> B = (3/2)^(11/7)
> 2C = (3/2)^(12 /7)=2.00387547381...

Hola Mario,

that old tuning idea agrees excatly with the specification of Serge Cordier's 1946 re-invention:

http://fr.wikipedia.org/wiki/Temp%C3%A9rament_%C3%A9gal_%C3%A0_quintes_justes http://fr.wikipedia.org/wiki/Temp%C3%A9rament_%C3%A9gal_%C3%A0_quintes_justes
"
Pour bien comprendre de quoi il s'agit, voici les rapports d'intervalles dans l'espace d'une octave : 1,0 1,059634 1,122824 1,189782 1,260734 1,335916 1,415582 1,5 1,589451 1,684236 1,784674 1,891101 2,003875for further discussion en detail see also in:

http://www.forum-pianoteq.com/viewtopic.php?id=1307 http://www.forum-pianoteq.com/viewtopic.php?id=1307
quote:
"
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

Please remember,
that you wrote about that way alredy here in that group,
about ~10 years ago:

https://groups.yahoo.com/neo/groups/TUNING/conversations/messages/97636 https://groups.yahoo.com/neo/groups/TUNING/conversations/messages/97636
"Miss Margo Schulter informed that Mr. Cordier presented exactly the same
scale in Paris in 1946."as in an older meassages from August 2001

https://groups.yahoo.com/neo/groups/tuning/conversations/topics/27517 https://groups.yahoo.com/neo/groups/tuning/conversations/topics/27517

Manuel included that in his 'scala'-archive back in November 2000

https://groups.yahoo.com/neo/groups/tuning/conversations/topics/15925 https://groups.yahoo.com/neo/groups/tuning/conversations/topics/15925
quote
"
This tuning (7th root of 3/2) is in the scale archive.
It has been invented by at least three people:
Augusto Novaro, Mieczyslaw Kolinsky and Serge Cordier.
The files are cordier.scl and kolinsky.scl.
"
Content:
https://searchcode.com/codesearch/view/4845917/ https://searchcode.com/codesearch/view/4845917/

Finally see Patrizio Barbieri's
http://www.patriziobarbieri.it/pdf/temperaments.pdf https://www.fastbot.de/red.php?red=3225972633904755179+http://www.patriziobarbieri.it/pdf/temperaments.pdf
historically review, on page 9,
quote:
'.... The problem was completely solvd by
a method now occasionally used,
referred to as "equal temperament by pure 5ths";
it was rediscoverd about 1959-1974 by
Mieczyslaw Kolinsky & Serge Cordier,
but was alreday known in the 19th-century as the
"Pleyel-Method".
Its slightly sharp "physiological octaves are also in perfect
agreement with the problems of string inharmonicicty
and ear nonlinarity, both aspects alredy noticed in the
mid 18th-century..."

Hence we may conclude,
the composer and piano-builder:

http://en.wikipedia.org/wiki/Ignaz_Pleyel http://en.wikipedia.org/wiki/Ignaz_Pleyel

was probably one among of the earliest independent inventors
of the above scale:

(3/2)^(n/7) with runinng n=0,1,2,3,...,12.

bye
Andy