Sauveur and (hepta)merides

On Wed, 8 Jul 1998, John Chalmers wrote:
> Helmholtz (p.421) proposed 24 tones of JI, then expanded the series to 28
> or 30 notes (p.422). His translator, Ellis, suggested 27 tones of meantone
> or Pythagorean (p.433-434) and it was he who named the 1/8th skhisma tuning
> after Helmholtz (p.435). On page 437, Ellis says it is audibly equivalent to
> Sauveur's theoretical cycle of 301 tones/octave (heptamerides).

Reading this, I wondered where Sauveur came up with 301, and Ellis tells
me it is a 7-way subdivision of his cycle of 43 merides (hence,
heptamerides, duh). However, what is his reasoning for choosing 43? I
quite figure out much that's very noteworthy about 43 except that it's
very close to 1/5-comma meantone. And 301's not bad, but in that same
neighborhood 270 is much better for anything under the 17-limit.

--pH http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
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NOTE: dehyphenate node to remove spamblock. <*>

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End of TUNING Digest 1469
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