RE: Re: Woolhouse's derivation of 7/26-comma 'optimal' m eantone

Joe Monzo wrote,

>Manuel and Wim:

>Thanks, Manuel. The tuning you gave Wim is fine for
>experimenting on a 12-tone keyboard.

>But you're missing a very important point of Woolhouse's
>theory.

>He plainly advocated 12-EDO for the 'common keyboard' and
>other 'usual' instruments.

If a Renaissance piece had 12 or fewer written pitches in a chain of fifths,
Woolhouse would have surely advocated retuning to 7/26-comma meantone.
Woolhouse advocated 12-tET for the 'common keyboard' only because most
post-Renaissance pieces use more than 12 written pitches in a chain of
fifths, e.g., they typically use both G# and Ab or at least one similar
enharmonic pair, and would thus need extra keys to be able to play this
music in 7/26-comma meantone.

>The reason he went thru the
>trouble to calculate the 7/26-comma meantone and to advocate
>its close EDO approximations of 50-EDO and 19-EDO, was to
>be able to have *two* different sizes of semitone, one
>'diatonic' and one 'chromatic'

That's a weird way of putting it, but anyway, you still get two different
sizes of semitone, even with only 12 notes in a chain of fifths.
Specifically, you get 7 diatonic semitones, and 5 chromatic semitones.