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Brats and fractions of a comma

🔗Gene Ward Smith <gwsmith@svpal.org>

8/26/2005 2:10:46 PM

Here are some meantone fifths which have a nearly small-ratio brat.

1/11 comma 12/7
1/10 comma 7/4
1/9 comma 9/5
1/7 comma 2
1/6 comma 9/4
2/11 comma 5/2
1/5 comma 3
2/9 comma 9/2
1/4 comma infinity
3/11 comma -3
2/7 comma -3/2
3/10 comma -3/4
1/3 comma 0

A brat of 12/7 would probably not be useful for tuning 1/11 comma,
but the fifth, the positive real root of 3x^4 + 70x - 120 = 0, is of
size 699.994 cents, which certainly would allow it to be used for
tuning equal temperament if it was useful. The 1/7 comma brat of 2 is
more likely to be interesting. 1/5 comma at +3 and 3/11 comma at -3
also look plausible.