Re: [tuning] well-temperament wazoo

Paul writes:
<< There's a pattern to all the well-temperaments that deviate significantly

from 12-tET -- can anyone spot it? >>

Greetings,
no, I can't say I spot it, since the piles of numbers are somewhat
dazzling to me, but the obviously significant pattern of virtually all well
temperaments is the ascending amount of tempering in the tonic thirds as one
modulates by fifths from the key of C, reaching a maximum of 21.7 cents at
the top of the circle, then returning to a level of lower tempering upon
descending.
Was that in there?
Regards,
Ed Foote
Precision Piano Works
Nashville, Tn.

Ed Foote wrote,

> no, I can't say I spot it, since the piles of numbers are somewhat
>dazzling to me,

They were just circles of fifths -- I would have though you'd be quite
comfortable with that representation . . .

>but the obviously significant pattern of virtually all well
>temperaments is the ascending amount of tempering in the tonic thirds as
one
>modulates by fifths from the key of C, reaching a maximum of 21.7 cents at
>the top of the circle, then returning to a level of lower tempering upon
>descending.
> Was that in there?

That was in there (though the amount of temperament in the worst third is
often different than 21.7 cents); you can see how each circle of fifths has
a few wide fifths adjacent to one another, and those are the fifths you
would normally use around G#/Ab, resulting in the worst thirds coming up in
the key of F#/Gb. But there was another, subtler pattern that I was
referring to . . .