A theory

Since 612 is the "tuning of schismas", any near-multiple of 612 will
be more likely to have the schisma vanish, and thus to do 5-limit
well, than non-near-multiple of 612. This is similar to how the
diatonic semitone produces a bit of periodicity in the smaller 5-
limit ETs, with peaks at 19 and 22, 31 and 34, 41 and 43, 53 and 55.

So . . . there must be some very significant 7-limit comma lurking at
about 1/1664 octave. This is the Breedsma, which equals exactly one
step of 1663.89978-tET.

--- In tuning-math@y..., "paulerlich" <paul@s...> wrote:

> Since 612 is the "tuning of schismas", any near-multiple of 612 will
> be more likely to have the schisma vanish, and thus to do 5-limit
> well, than non-near-multiple of 612.

It's not likely to have the schisma vanish; quite the reverse. What it *is* going to do is to represent the schisma as a certain number of steps with great accuracy.

> So . . . there must be some very significant 7-limit comma lurking at
> about 1/1664 octave. This is the Breedsma, which equals exactly one
> step of 1663.89978-tET.

You seem to be on to something, but why just the breedsma? This still seems to require more explanation.

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:
>
> > Since 612 is the "tuning of schismas", any near-multiple of 612 will
> > be more likely to have the schisma vanish, and thus to do 5-limit
> > well, than non-near-multiple of 612.
>
> It's not likely to have the schisma vanish; quite the reverse. What
it *is* going to do is to represent the schisma as a certain number of
steps with great accuracy.

Oops -- that's what I meant!

>
> > So . . . there must be some very significant 7-limit comma lurking at
> > about 1/1664 octave. This is the Breedsma, which equals exactly one
> > step of 1663.89978-tET.
>
> You seem to be on to something, but why just the breedsma? This
still seems to require more explanation.

You bet!