Re: [tuning-math] Digest Number 497

Gene asked:

>Has anyone paid attention to scales which have a number of steps a
>multiple of a MOS? They inherit structure from the MOS, and using a 2MOS
>or a 3MOS seems like a good way to fill in those annoying gaps.

I think most of Messiaien's "Modes of Limited Transposition" in 12-tet
are multiple MOS's of 3, 4 and 6-tet. I don't have a list handy on this
computer to check, unfortunately. IIRC, William Lyman Young (in his
"Report
to the Swedish Royal Academy of Music" etc.) proposed a decatonic scale
in
24-tet which was two 5-tone MOS's of 12 (2322323223) and a 14-tone scale
of 2 sections of the 7-tone diatonic sequence as 22122212212221 in
24-tet.
He considered these as generated from cycles of half-fourths or
half-fiths.

I suspect that some of Wyschnegradski's scales might be multiple MOS's
too,
but I don't have a list either.

--John

--- In tuning-math@y..., John Chalmers <JHCHALMERS@U...> wrote:
> Gene asked:
>
> >Has anyone paid attention to scales which have a number of steps a
> >multiple of a MOS? They inherit structure from the MOS, and using a 2MOS
> >or a 3MOS seems like a good way to fill in those annoying gaps.

Thanks for your reply, which was interesting. I seem to have sowed confusion with my question, however, so let me give an example.

Orwell has a 13-tone MOS which in its 19/84 version is

[3, 8, 8, 3, 8, 8, 3, 8, 8, 3, 8, 8, 8]

It also has a 22-tone MOS,

[3, 3, 5, 3, 5, 3, 3, 5, 3, 5, 3, 3, 5, 3, 5, 3, 3, 5, 3, 5, 3, 5]

This is all well an good, but what if you want a scale of consecutive generators right in the middle of this fairly large gap?

Consider the 9-tone MOS:

[11, 8, 11, 8, 11, 8, 11, 8, 8]

If we replace every "11" by a "3, 8" and every "8" by a "3, 5" we get the 18-tone 2MOS:

[3, 8, 3, 5, 3, 8, 3, 5, 3, 8, 3, 5, 3, 8, 3, 5, 3, 5]

This, it seems to me, is slightly but discernably more regular than its neighbors, of 17 and 19 generators.

17: [3, 8, 3, 5, 3, 8, 3, 5, 3, 8, 3, 5, 3, 8, 8, 3, 5]

19: [3, 3, 5, 3, 5, 3, 8, 3, 5, 3, 8, 3, 5, 3, 8, 3, 5, 3, 5]

I would say it also is more regular than the 3MOS of 15 tones or the 4MOS of 16 tones.

15: [3, 8, 3, 5, 3, 8, 8, 3, 8, 8, 3, 8, 8, 3, 5]

16: [3, 8, 3, 5, 3, 8, 3, 5, 3, 8, 8, 3, 8, 8, 3, 5]

--- In tuning-math@y..., John Chalmers <JHCHALMERS@U...> wrote:
> Gene asked:
>
> >Has anyone paid attention to scales which have a number of steps a
> >multiple of a MOS? They inherit structure from the MOS, and using
a 2MOS
> >or a 3MOS seems like a good way to fill in those annoying gaps.
>
> I think most of Messiaien's "Modes of Limited Transposition" in 12-
tet
> are multiple MOS's of 3, 4 and 6-tet. I don't have a list handy on
this
> computer to check, unfortunately. IIRC, William Lyman Young (in his
> "Report
> to the Swedish Royal Academy of Music" etc.) proposed a decatonic
scale
> in
> 24-tet which was two 5-tone MOS's of 12 (2322323223) and a 14-tone
scale
> of 2 sections of the 7-tone diatonic sequence as 22122212212221 in
> 24-tet.
> He considered these as generated from cycles of half-fourths or
> half-fiths.
>
> I suspect that some of Wyschnegradski's scales might be multiple
MOS's
> too,
> but I don't have a list either.
>
> --John

john, most of these scales are themselves MOSs. what gene was after,
i think, was multiple-MOSs that are not themselves MOSs, such as a 24-
note meantone or pythagorean chain.