Re: Review of 53-tET

Hello, there, Joe.

You remind me of a discussion we once had: 53-note Pythagorean is itself a
circulating tuning, or "loop," as you very aptly called it -- not quite a
mathematically closed circle (one fifth is narrow by about 3.62 cents,
with all the rest pure). You cleverly proposed that "loop" was a bit like
the French for "wolf," and suggests an "odd" fifth a bit different from
the others, but still quite musically interchangeable (as in unequal
well-temperaments also).

One distinction is that 53-EDO is slightly more accurate as a 5-limit
approximation (since the fifths are very slightly narrower than pure, as
also in a 3-5 schismic temperament like that of Helmholtz or Sabat), while
Pythagorean is more accurate for ratios of 2-3-7-9.

Most appreciatively,

Margo Schulter
mschulter@value.net

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:

/tuning/topicId_40150.html#40150

> Hello, there, Joe.
>
> You remind me of a discussion we once had: 53-note Pythagorean is
itself a
> circulating tuning, or "loop," as you very aptly called it -- not
quite a
> mathematically closed circle (one fifth is narrow by about 3.62
cents,
> with all the rest pure). You cleverly proposed that "loop" was a
bit like
> the French for "wolf," and suggests an "odd" fifth a bit different
from
> the others, but still quite musically interchangeable (as in unequal
> well-temperaments also).
>
> One distinction is that 53-EDO is slightly more accurate as a 5-
limit
> approximation (since the fifths are very slightly narrower than
pure, as
> also in a 3-5 schismic temperament like that of Helmholtz or
Sabat), while
> Pythagorean is more accurate for ratios of 2-3-7-9.
>
> Most appreciatively,
>
> Margo Schulter
> mschulter@v...

***Thank you so *very* much, Margo, for refreshing my memory on
this. Of course, *now* I remember the difference between Pythagorean
53 and 53-tET... I seem pretty good at coming up with some terms (I
did "bicycle chain" too!) but then am busy forgetting all the rest!

I think it's better "embedded" *this* time!

Thanks again!

Joe Pehrson