> ----- 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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