scale collection

Gene, you had also given Qm(2) previously (e=15, c=4).

What's this:

10-tone scale, e=24 c=4, in 72-tET
(0 5 14 19 28 33 42 49 58 63 72)

?

-Carl

Dave, this is one of yours:

!
Single-chain MOS of 7:4's in 41-tet.
11
!
204.878 !......7
234.146 !......8
439.024 !......15
468.293 !......16
673.171 !......23
702.439 !......24
907.317 !......31
936.585 !......32
1141.463 !.....39
1170.732 !.....40
1200.000 !.....41
!

I don't see any generators near 7:4 in the catalog. What is this?

-Carl

--- In tuning-math@y..., Carl Lumma <carl@l...> wrote:
> Dave, this is one of yours:
>
> !
> Single-chain MOS of 7:4's in 41-tet.
> 11
> !
> 204.878 !......7
> 234.146 !......8
> 439.024 !......15
> 468.293 !......16
> 673.171 !......23
> 702.439 !......24
> 907.317 !......31
> 936.585 !......32
> 1141.463 !.....39
> 1170.732 !.....40
> 1200.000 !.....41
> !

It's definitely not one of mine. What made you think it was?

> I don't see any generators near 7:4 in the catalog.

It might appear with a 7:8 generator in the catalog. But it doesn't
and shouldn't.

> What is this?

A mistake? It would take quite a stretch of my imagination to consider
the generator of this scale as a 4:7. It has a 32 cent error. If it
has a 7-limit mapping at all, it must be [2, -6, 1] in which case the
generator can be considered to be (the inversion of) half the pelogic
fifth. That temperament would be better represented in 37-ET, but 11
notes would no longer be MOS there. Even with the optimum generator
(259.64 cents) it has a max abs error of 28.5 cents.

>It's definitely not one of mine. What made you think it was?

I have it in my records as being yours. It might be my mistake; I
don't remember a source.

>A mistake? It would take quite a stretch of my imagination to consider
>the generator of this scale as a 4:7. It has a 32 cent error. If it
>has a 7-limit mapping at all, it must be [2, -6, 1] in which case the
>generator can be considered to be (the inversion of) half the pelogic
>fifth. That temperament would be better represented in 37-ET, but 11
>notes would no longer be MOS there. Even with the optimum generator
>(259.64 cents) it has a max abs error of 28.5 cents.

I'll delete it.

-Carl