source file: m1349.txt
Date: Mon, 9 Mar 1998 15:34:16 -0500

Subject: 1/3-comma meantone

From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>

>}Third-comma meantone uses a fifth tempered down by 1/3 of a comma
>}so that the submediant (e.g. A in the key of C) has a 5:3 ratio relative to
>}the tonic rather than 27:16 as you would get if you were to use exact 3:2
>}perfect fifths.
>
>I think that's a poor justification for 1/3-comma meantone. The real reason
>is so that all minor thirds will have an exact 6:5 ratio (and, of course, all
>major sixths will have an exact 5:3 ratio). If, say, a two-voice invention
>uses a preponderance of minor thirds and major sixths as consonant harmonies,
>then the best tuning for it is something like 1/3-comma meantone. This has
>nothing to do with the submediant, or the mediant in minor, except when that
>scale degree happens to be played along with the tonic degree in harmony.
>
>The same goes for 1/4-comma meantone and major thirds and minor sixths. For a
>style that uses complete triads, something between 1/4- and 1/3- comma, but
>closer to 1/4- comma, is best. But many people have a hard time adjusting to
>flat major thirds, so perhaps 1/4-comma is an upper limit on meantone
>tempering for modern ears.