Hi gang.

Just a short not to let you know I am lurking.

John Starrett

--- In tuning-math@y..., "John Starrett" <jstarret@c...> wrote:
> Just a short not to let you know I am lurking.
>
> John Starrett

Hi John!

Dear Graham and Dave,

What we need is a really user-friendly, _practical_ guide to a bunch
of the new temperaments and their MOSs (and ideally, tetrachordal
alterations of those MOSs in cases like 10-of-22 and 22-of-46).

If one of you does this, you'll be a real hero.

My only other plead would be to please optimize for all saturated
chords (especially the 9-limit ones) and not just for all complete
chords, through some limit. I want to see Margo's Wonder scale
(generator = 2*MIRACLE generator) in there.

Hey, my ~22-tET decatonics made the rankings for 7-limit, didn't
they? How about 9-limit?

-Paul

--- In tuning-math@y..., "Paul Erlich" <paul@s...> wrote:
> Dear Graham and Dave,
>
> What we need is a really user-friendly, _practical_ guide to a bunch
> of the new temperaments and their MOSs (and ideally, tetrachordal
> alterations of those MOSs in cases like 10-of-22 and 22-of-46).
>
> If one of you does this, you'll be a real hero.
>
> My only other plead would be to please optimize for all saturated
> chords (especially the 9-limit ones) and not just for all complete
> chords, through some limit. I want to see Margo's Wonder scale
> (generator = 2*MIRACLE generator) in there.
>
> Hey, my ~22-tET decatonics made the rankings for 7-limit, didn't
> they? How about 9-limit?
>
> -Paul

It's all yours Graham.

> --- In tuning-math@y..., "Paul Erlich" <paul@s...> wrote:
> What we need is a really user-friendly, _practical_ guide to a
bunch
> of the new temperaments and their MOSs (and ideally, tetrachordal
> alterations of those MOSs in cases like 10-of-22 and 22-of-46).

Are "tetrachordal alterations" only possible when the interval of
repetition is some whole-number fraction of octave?

How do you do them, in general?

What would be a "tetrachordal alteration" of Blackjack?

-- Dave Keenan

--- In tuning-math@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> > --- In tuning-math@y..., "Paul Erlich" <paul@s...> wrote:
> > What we need is a really user-friendly, _practical_ guide to a
> bunch
> > of the new temperaments and their MOSs (and ideally, tetrachordal
> > alterations of those MOSs in cases like 10-of-22 and 22-of-46).
>
> Are "tetrachordal alterations" only possible when the interval of
> repetition is some whole-number fraction of octave?

In an MOS, the interval of repetition is _always_ some whole-number
fraction of the interval of equivalence.
>
> How do you do them, in general?

I don't know if there's a general way, but you understand what
omnitetrachorality is, right? "Alteration" simply means re-shuffling
the step sizes in an MOS or hyper-MOS.
>
> What would be a "tetrachordal alteration" of Blackjack?

Don't know if there is one! Can you make a blackjack-like scale
omnitetrachordal?