Re: Digest Number 137

[Rousseau:]
> The reasoning in my last post was valid <snip>

Yes, absolutely. I should have said so myself.

> Was Euler looking for a tuning in which 36/35 = 0 steps?
> Do you think he would have been favorable to 12TET?

Definitely not.

Again from my notes, at the end of the same paper,
[_Conjecture_] Euler suggests that the music of his
time had already replaced Leibniz's 2/3/5 basis
with 2/3/5/7.

If he wanted 7-limit ratios to be distinct he would
have had to go with an ET higher than 22 degrees.
But did hid advocate ET? That I don't know.

In a much later paper, Euler described relative
consonance as a continuum based on the complexity
of the rational numbers, much as Schoenberg, Partch
and myself do. So he was perhaps willing to admit
higher odd- or prime-limits in music. I don't know
about this either.

> 22TET could be a good alternative to 12. I have not tested
> it, how well does it approximate the different genus?

Paul Erlich likes 22-ET a lot, partly because it is
consistent in the 7-limit. He would certainly be able
to say more about it.

And Ivor Darreg was a big advocate of 17-ET, also in your
list of ETs with consistent 64:63.

-monzo

|\=/|.-"""-. Joseph L. Monzo....................monz@juno.com
/6 6\ \ http://www.ixpres.com/interval/monzo/homepage.html
=\_Y_/= (_ ;\
_U//_/-/__/// |"...I had broken thru the lattice barrier..."|
/monz\ ((jgs; | - Erv Wilson |

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