Re: [tuning] Making cents of JI, meantone, Werckmeister

If you take A=440 as a constant, Werckmeister's chromatic temperament comes
out as follows:

+12 +2 +4 +6 +2 +10 0 +8 +4 0 +8 +4
C C# D D# E F F# G G# A Bb
B Db Eb Gb Ab A#

Since there was no absolute measurement for pitch frequency in the Baroque,
the relationships between notes as expressed above could begin on most any
pitch frequency. Please note that all notes are sharp to conventional tuning
(except for A and F#).

Recently I noticed that the "Andy Gump" embouchure (or overbite embouchure)
for bassoon (fagot) traditional in Germany (and even the U.S.) before the
1940's aids in the accurate playing of the above scale. To the 12-TET
bassoonist, this embouchure was "sharp."

Johnny Reinhard
AFMM

Johnny Reinhard wrote,

>If you take A=440 as a constant, Werckmeister's chromatic temperament comes

>out as follows:

>+12 +2 +4 +6 +2 +10 0 +8 +4 0 +8 +4
> C C# D D# E F F# G G# A Bb

> B Db Eb Gb Ab A#

Johnny, if I wasn't already familiar with Werckmeister, I couldn't make
heads or tails out of this table. I can't tell which cents value is
associated with which note. It would probably help our readers if you
arranged it vertically.

Paul, too bad you didn't straighten it up...after all, my copy was straight
up. ;)

+12 +2 +4 +6 +2 +10 0 +8 +4 0 +8 +4
C C# D D# E F F# G G# A Bb
B
Db Eb Gb Ab A#

Hopefully, this will be better since I used tabs exclusively. If we could
send attachments there would be no problem.

Johnny Reinhard
AFMM

Johnny, tabs are the cause of problem -- each computer interprets them
differently.
By vertically I meant:

C
C#
D
Eb
E
F

etc.