Re: Sesquisexta tuning (Pythagorean manuals a 7:6 apart)

Hello, there, and I'd like to propose a name for my "two Pythagorean
manuals a 7:6 apart" tuning described in a longer post, if it hasn't
already been used and documented. If it has, I might with due caution
present my suggestion as an "alternative" name to be used along with
the established one.

Accordingly, I here propose the name _Sesquisexta_, the Latin name for
the proportion or ratio 7:6, literally "and again a sixth" -- or
"again a sixth part of the whole."

This name is intended especially to honor Jacobus of Liege, who in his
_Speculum musicae_ (c. 1325), Book Four, specifically mentions
sesquisexta or 7:6 as a superparticular ratio forming part of the
series intervening between the usual Pythagorean ratios of
_sesquitertia_ or 4:3 (the fourth) and _sesquioctava_ or 9:8 (the
whole-tone). He concludes that these intervening ratios are not used
because they do not fit the regular system of tones and semitones, but
notes that such ratios do occur in Greek theory. He also describes and
demonstrates the 64:63 septimal comma as well as the 81:80 syntonic
comma.

Briefly, Sesquisexta is a tuning of two 12-note Pythagorean manuals in
standard Eb-G# tunings at the distance of a pure 7:6 (~266.87 cents),
making available pure sonorities of 12:14:18:21 or 14:18:21:24 (the
neo-Gothic "7-flavor") in 11 locations.

At the same time, of course, all of the usual Pythagorean steps and
sonorities are available on either keyboard.

The keyboard layout invites stunning forms of "21st-century
fauxbourdon" involving parallel 7-flavor sonorities, maybe recalling
at once Dufay and Debussy. It might be taken as an offshoot on the
late medieval English technique of "sights" in improvised discant, a
point I'd like to research and explore further.

Anyway, "Sesquisexta" seems to me a propitious name, whether as one of
first impression, or as another synonym for a tuning which for me has
a most transporting character.

Most appreciatively,

Margo Schulter
mschulter@value.net