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.