generating principle for Young's well temperament

hello all,

just a very quick question from a quiet lurker...

i'm giving an introductory talk on historic tunings to some music
history classes here at the university of akron-- i was wondering if
someone on the list (i'm sure you can) can give me the generating
principle for young's well temperament. i've had no problem finding
theone for werckmeister III (incomplete 1/4 comma pythagorean
meantone), but i haven't been able to find young's.

many thanks,

Bill Sallak
University of Akron
<sallak@uakron.edu>

>just a very quick question from a quiet lurker...

Hiya Bill!

>i'm giving an introductory talk on historic tunings to some music
>history classes here at the university of akron-- i was wondering if
>someone on the list (i'm sure you can) can give me the generating
>principle for young's well temperament. i've had no problem finding
>theone for werckmeister III (incomplete 1/4 comma pythagorean
>meantone), but i haven't been able to find young's.

All historical well temperaments I've seen can be seen as methods
of unevenly distributing the *pythagorean comma* between fifths.
It happens that the *syntonic comma* (81:80) is close in size to
the pythag. comma, which is why doing this improves the thirds.

Young has 6 pure fifths, and 6 fifths flattened by 1/6th of a
pythag. comma each.

Usually in these temperaments there are two kinds of fifth, and
they are placed in two groups on the chain of fifths. This is
the case with Young.

Anton Kellner's proposed 'JS Bach' temperament has two kinds of
fifth (seven pure and five 1/5th P. flat), but the tempered fifths
do not all occur together on the chain. C-G-D-A-E are tempered,
E-B is pure, B-F# is tempered, and then F#--C are pure. This
pattern is found on Bach's seal, according to Kellner's web site.

More than you asked, I realize,

-Carl