Rameau's names for 5-limit intervals under 100 cents

Here's an addendum to my last post, which should
have been included in its tables: Rameau's names
for the small 5-limit intervals.

cents prime-factor Rameau's term

92 3^ 3 * 5^ 1 mean semitone
71 3^-1 * 5^ 2 minor semitone (theory), aug. unison (practice)
63 3^ 4 * 5^-4 least semitone
49 3^-4 * 5^ 3 major diesis
41 5^-3 minor diesis (or enharmonic)
22 3^ 4 * 5^-1 comma
20 3^-4 * 5^-2 diminished comma

Note that 5^-3 [= 125:128 = ~41 cents] was called 'minor
diesis' by Rameau and 'Great Diesis' by Ellis. (These two
different terms were noted by Paul Erlich in the posting
I quoted.)

Also note that 3^4*5^-4 [= 625:648 = ~63 cents] was called
'least semitone' by Rameau and 'major diesis' by Erlich
(and I presume Keenan).

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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