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Margoized 1/4-comma meantone

🔗Gene Ward Smith <gwsmith@svpal.org>

3/16/2003 9:14:45 PM

I was about to do this after my "a funny thing happened" post, when a
funny thing happened, namely more computer weirdness. However, here at
last it is.

If m=5^(1/4) is the meantone fifth, then we can make a circle of fifths
by [m, m, m, m, m, m, m, 56/55*m, m, m, m, 176/175*m] and another by
[m, m, m, m, m, m, m, 176/175*m, m, m, m, 56/55*m]. The major thirds
corresponding to the first circle are [5/4, 5/4, 5/4, 5/4, 14/11,
14/11, 14/11, 14/11, 44/35, 44/35, 44/35, 44/35] and to the second
circle are [5/4, 5/4, 5/4, 5/4, 44/35, 44/35, 44/35, 44/35, 14/11,
14/11, 14/11, 14/11]. If we follow Robert's principles, the second
version would be preferred, as we have four pure thirds followed by
four 396 cent thirds; the last of which goes with a sharp fifth
5^(1/4) 176/175 of 706.44 cents.