RE: Oops... back to school for me

>I've obvioulsly got my hands full with 22, but I noticed the other day
>that (more or less) the 3/2 +/- 7 cents gives 19 & 22, +/- 5 cents
>gives 31 & 34 -- two meantone and two commaful temperaments, and that
>19 + 22 gives 41 and 31 + 34 gives 65, both with a 3/2 less than 0.5
>cents off just. What I've heard of 31 never "did" it for me, and I'll
>have to wait to get Neils new CD to hear 34.

Did you notice this:

The 3/2 in 22TET is off by .1308 degrees.
The 3/2 in 19TET is off by -.1143 degrees.
The 3/2 in 41TET (= 19+22) is off by .0165 (= .1308 - .1143) degrees.

I noticed this in 1991. More examples:

The 3/2 in 7TET is off by -.0947 degrees.
The 3/2 in 5TET is off by .0752 degrees.
The 3/2 in 12TET (= 5+7) is off by -.0196 (= -.0947 + .0752) degrees.

In 27TET, the 3/2 is off by .2060 degrees, and the 5/4 is off by .3079
degrees.
In 26TET, the 3/2 is off by -.2090 degrees and the 5/4 is off by -.3701
degrees.
In 53TET (= 26+27), the 3/2 is off by -.0030 (= .2060 - .2090) degrees,
and the 5/4 is off by -.0622 (= .3079 - .3701) degrees.

53 is also 31+22, 34+19, and 41+12, which shows that the errors in these
pairs of tunings are nearly equal and opposite when measured in degrees
of the tuning.


SMTPOriginator: tuning@eartha.mills.edu
From: alves@orion.ac.hmc.edu (Bill Alves)
Subject: Re: 22-tone equal, reply to Ehrlich
PostedDate: 12-12-97 19:56:33
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