5 and 7

On Wed, 17 Mar 1999, Paul H. Erlich wrote:
> On Tue, 16 Mar 1999, Carl Lumma wrote:
>> MOS does do one thing that nothing else I know of does. It explains why 5
>> or 7 but not 6.
>
> Bah! Tetrachord/trichord theory explain that very well! Even propriety,
> if you're talking about a chain of fifths.

Recently I posted to the list derivations of 5 and 7 using Fokker's
method, starting with 81:80 (the smallest 5-limit quaternary interval)
as a commatic interval, and completing the matrix with 25:24 (-1 2) or
16:15 (-1 -1), the two smallest 5-limit secondary intervals, as
chromatic intervals.

Using the 81:80 as a comma, of course, tends to imply chain-of-fifths,
so it's not entirely unrelated.

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "How about that? The guy can't run six balls,
-\-\-- o and they make him president."

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