Re: 9 toner in 22 EDO

Hi Paul, everyone,

yes I looked at the orwell info - graham gave me the link. Funny how 7/6
almost closes, yet the 9 tone generator is quite a few cents adrift, so
that it doesn't close. I'm wondering if the generator is some other ratio,
such that it has a comma after 22 steps (like the pythag one after 12 for
3/2)?

Mark

--- In tuning@yahoogroups.com, "Mark Gould" <mark.gould@a...> wrote:
> Hi Paul, everyone,
>
> yes I looked at the orwell info - graham gave me the link. Funny
how 7/6
> almost closes, yet the 9 tone generator is quite a few cents
adrift, so
> that it doesn't close.

the 9 tone generator? meaning 5/22 oct.?

> I'm wondering if the generator is some other ratio,
> such that it has a comma after 22 steps (like the pythag one after
12 for
> 3/2)?
>
> Mark

there isn't really a "22-tone comma" in this sense that's worth a
whole lot to tuning theory -- 22-equal is normally generated not one-
dimensionally, by a single comma which is the octave-reduced 22nd
power of some simple ratio, but rather by two, three, or four
different commas (for example, without going past prime 5, you can
use 250:243 and 2048:2025, or either of those and 3125:3072 -- just
as 12-equal, once you go past prime 3, can be defined by 81:80 and
128:125 or either of those and 2048:2025 -- if this doesn't make
sense to you, take a look at the "gentle introduction to fokker
periodicity blocks" and then get back to me) . . .

the closest thing to such a beast would almost certainly be the
result of raising 9:7 to the 22nd power (and octave-reducing), since
9:7 is only 1 cent off from 8/22 oct. . . . the trouble is, you
really only generate a doubled 11-equal in this way, and every other
note of 22-equal is left out entirely . . .

i probably misunderstood your question, so please clarify if
necessary . . .

cheers,
paul