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

> ----- Original Message -----
> From: Joe Monzo <joemonz@yahoo.com>
> To: <tuning-math@yahoogroups.com>
> Sent: Wednesday, May 30, 2001 10:36 AM
> Subject: [tuning-math] Re: [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)?
>
>
> 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,

I realize that the only way to accurately analyze the similarites
between one tuning system and another is to compare their interval
matrices. But I thought it would be "fun" (and historically
informative?) to present this simplified comparison anyway:

55-EDO 2/11-comma meantone

degrees exponent of approximate 3:2
between degrees ~cents =(3^x)/((81/80)^((2/11)*x)) ~cents

0 0 0 0
5
50 1090.909091 5 1090.223832
9
41 894.5454545 3 894.1342992
9
32 698.1818182 1 698.0447664
9
23 501.8181818 -1 501.9552336
5
18 392.7272727 4 392.1790656
9
9 196.3636364 2 196.0895328
9
0 0 0 0

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

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