RE: [tuning] Re: Neo-Gothic tunings (Part 1 of 2)

Margo wrote,

>"Exponential meantone" is defined as having a ratio between its
>whole-tone and diatonic semitone equal to Euler's exponential _e_,

Why call it a "meantone"? It's not a meantone temperament, even in the most
inclusive sense of that word.

>At 22-tet, the
>whole-tone has grown to ~218.18 cents and the diatonic semitone has
>contracted to ~54.54 cents, with R at 4. While this semitone --
>literally a "diatonic quartertone" -- may look very small on paper, I
>find that my ears can routinely accept it as a regular semitone.

One of the pieces I performed at the Microthon was a modal improv, where one
of the modes used was the neo-gothic aeolian mode of 22-tET. Characterized
by tonic, subdominant, and dominant triads all tuned approximately 6:7:9,
whole tones of 218.18 cents, and diatonic semitones of 54.54 cents, this
mode doesn't sound "microtonal" to most people -- it sounds comfortable and
familiar. Only in attempting to use one of the major triads of the mode do
we elicit reactions of unfamiliarity from most people.

>to tune 22-tet for Neo-Gothic music is likely more an
>expression of calculated xenharmonic zest.

Or perhaps someone might have a desire to use acoustically recognizable
intervals (6:7, 9:7, etc.) as the functional discords -- one could imagine
an "adaptive JI" version of a neo-gothic piece where subtle deviations from
22-tET allow all vertical intervals to be in JI, and 7-based ratios instead
of 5-based ratios become the target tunings for thirds and sixths.

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