Re: [tuning] Re: Teaching of Intonation After Mozart's Death

----- Original Message -----
From: Dave Keenan <D.KEENAN@UQ.NET.AU>
To: <tuning@yahoogroups.com>
Sent: Tuesday, May 29, 2001 4:46 PM
Subject: [tuning] Re: Teaching of Intonation After Mozart's Death

> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > Before Mozart -- Meantone temperament, specifically something close
> > to 55-tone equal temperament;
>
> So you mean somewhere between 1/6 and 1/5 comma, i.e. away from 1/4
> comma in the direction of 12-tET (1/11 comma)?
>
>

Hi Dave,

You're correct that it's in the *direction* away from 1/4-comma
and towards 1/11-comma, and your estimate of between 1/6- and
1/5-comma is very close.

But it's really extremely close to *2*/11-comma meantone.
Here are some more-exact figures:

2^(32/55), the "5th" in 55-EDO = ~698.181818... cents,

is equiavelent to that of ~0.175445544-comma meantone.

To describe it in terms of low-integer fractions of a comma,

that's less than 1/7 of a cent wider than
the 2/11-comma meantone "5th" = ~698.0447664 cents,

and even much closer (~1/46-cent wider) to
the 3/17-comma meantone "5th" = ~698.1597733 cents,

closer still (less than 1/100-cent narrower) to
the 7/40-comma meantone "5th" = ~698.1914002 cents,

and almost bang on (~1/6692-cent wider)
the 10/57-comma meantone "5th" = ~698.1819676 cents.

-monz
http://www.monz.org
"All roads lead to n^0"

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