Centaur/Indian_12 in Bigler marvel

Recall that both Grady's 7-limit scale Centaur and the 5-limit scale
Indian_12 become the same scale when tempered via marvel. This
includes tempering via Kurt Bigler's marvel tuning of a sqrt(225/224)
flattening of the fifth--the 1/2-kleismic-fifth marvel which wants to
mutate into meantone.

When we temper using Bigler marvel, Centaur and Indian_12 do in fact
warp into an irregular 12 note meantone scale. This has the wolf fifth
of Meantone[12] and nine Bigler fifths of 698.1 cents, but also two
flat fifths of 692 cents. It has seven pure major thirds and a 392.4
cent major third, and then the usual four sharp thirds of meantone, of
which one is slightly less sharp. The result is like a warped version
of 1/4-comma meantone. The warpage from 1/4-comma is not random; it
allows for two pure 7/4 intervals plus five pure 7/5 intervals and one
flat by six cents; in this way we get two pure 1-5/4-7/4 chords, two
pure 1-7/5-7/4 chords, two pure two pure 1-7/5-8/5 chords and two pure
1-5/4-10/7 chords.

This is actually an interesting scale!

hi Gene,

wow, now *this* sounds like an interesting lattice!
can you give me the data (scale members and unison-vectors)
in monzos?

-monz

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> Recall that both Grady's 7-limit scale Centaur and the 5-limit scale
> Indian_12 become the same scale when tempered via marvel. This
> includes tempering via Kurt Bigler's marvel tuning of a
sqrt(225/224)
> flattening of the fifth--the 1/2-kleismic-fifth marvel which wants
to
> mutate into meantone.
>
> When we temper using Bigler marvel, Centaur and Indian_12 do in fact
> warp into an irregular 12 note meantone scale. This has the wolf
fifth
> of Meantone[12] and nine Bigler fifths of 698.1 cents, but also two
> flat fifths of 692 cents. It has seven pure major thirds and a 392.4
> cent major third, and then the usual four sharp thirds of meantone,
of
> which one is slightly less sharp. The result is like a warped
version
> of 1/4-comma meantone. The warpage from 1/4-comma is not random; it
> allows for two pure 7/4 intervals plus five pure 7/5 intervals and
one
> flat by six cents; in this way we get two pure 1-5/4-7/4 chords, two
> pure 1-7/5-7/4 chords, two pure two pure 1-7/5-8/5 chords and two
pure
> 1-5/4-10/7 chords.
>
> This is actually an interesting scale!

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> hi Gene,
>
>
> wow, now *this* sounds like an interesting lattice!
> can you give me the data (scale members and unison-vectors)
> in monzos?

I can give Centaur as a 7-limit scale, and Indian_12 as a 5-limit
scale, but to give the Biglerized version would require monzos with
rational number coefficients. Do you want to graph that?

I still think the 31-note scale I gave would be interesting.