RE: Sauveur and (hepta)merides

This message is in MIME format. Since your mail reader does not understand
this format, some or all of this message may not be legible.

------ =_NextPart_000_01BDAB55.ECC61EBE
Content-Type: text/plain

>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.

That was a very important consideration at the time. However, at least
as important was the fact that the base-10 log of 2 is .3010, and since
in Sauveur's day everyone was working with tables of logs rather than
computers or calculators, heptamerides turned out to be very convenient.
Just look up a ratio on a table of logs, multiply by 1000, and that's
how many heptamerides it is!

------ =_NextPart_000_01BDAB55.ECC61EBE
Content-Type: application/ms-tnef
Content-Transfer-Encoding: base64
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------ =_NextPart_000_01BDAB55.ECC61EBE--

On Thu, 9 Jul 1998, Paul H. Erlich wrote:
> I thought the duodenarium was a 12-tone scale, Euler's 3^3.5^2 genus. I
> guess I was wrong. Please straighten me out.

As best I can interpret Ellis, he seems to use "duodene" to refer to the
12-tone Euler genus Paul E. describes, and "duodenarium" to the infinite
plane that results when you tile a bunch of these together--in other
words, the 3-5 harmonic lattice.

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