Oxford Dict Temperament Diagrams

Hello, all. In the Oxford Dictionary of Music & Musicians in the
section titled "Well Tempered Clavier" there is a Fig. 1 that shows
hexachord diagrams for a number of temperaments such as ET, Vallotti,
Werckmeister, and Temperament Ordinaire. According to the text the
units shown with each diagram are in units of 1/12 Pythagorean comma.
The diagrams are supposed to show how the triadic concords are tempered
as well as the size of semitones. The text walks you through the
Vallotti (Fig. 1(b)) temperament but I find that compounds my
confusion.

I understand the mathematics of meantone and irregular (well)
temperaments and the usual 3 x 5 diagrams that are often employed. I
cannot, however, arrive at the numbers given in the diagrams in Fig. 1.
Any help would be greatly appreciated. Sincerely,

> From: <arl_123@hotmail.com>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, June 06, 2001 5:04 AM
> Subject: [tuning] Oxford Dict Temperament Diagrams
>
>
> Hello, all. In the Oxford Dictionary of Music & Musicians in the
> section titled "Well Tempered Clavier" there is a Fig. 1 that shows
> hexachord diagrams for a number of temperaments such as ET, Vallotti,
> Werckmeister, and Temperament Ordinaire. According to the text the
> units shown with each diagram are in units of 1/12 Pythagorean comma.
> The diagrams are supposed to show how the triadic concords are tempered
> as well as the size of semitones. The text walks you through the
> Vallotti (Fig. 1(b)) temperament but I find that compounds my
> confusion.
>
> I understand the mathematics of meantone and irregular (well)
> temperaments and the usual 3 x 5 diagrams that are often employed. I
> cannot, however, arrive at the numbers given in the diagrams in Fig. 1.
> Any help would be greatly appreciated. Sincerely,

If you would scan the pages from the ODM and upload them to the
"files" section, I'll take a look and see what I can figure out.

BTW, 1/12 Pythagorean comma is called a "grad":
http://www.ixpres.com/interval/dict/grad.htm

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

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