re: Good 5-limit scale generators (was: More on composing in X...)

>I was mistaken in calling it a MOS, but it _is_ proper. Note that the
>generator here can be either a fifth or a major third. They end up as the
>same 8 note scale. In 12-tET it is 12121212. Outside of 12-tET the minor
>thirds must stay at 300 cents but you are free to narrow the fifths to
>improve the major thirds.

Aha! Thanks. So we can describe the octatonic scale as two chains of
minor thirds a fifth apart. Any improvement over 12-tET is going to be
very small.

>Here's the 9 note proper scale with 12 triads, based on 3 chains of fifths
>(or minor thirds) 1/3 octave apart. In 12-tET it's 121121121. The major
>thirds are stuck at 400 cents but you can widen the fifths to improve the
>minor thirds. If you lose an outside note you lose 3 triads. Lose a second
>note on the same side and you only lose another 2 triads, leaving 7 triads
>in 7 notes.

Wild. Unfortunately, neither the major or minor versions of this 7-note
structure are anywhere near proper, and their triads do not occur on a
regular pattern of scale steps.

>Do these symmetrical 8 and 9 note scales have standard names?

I am not familiar with the 9-note, but the 8-note one is commonly
called the "octatonic" scale. Messiaen is known for using it and
writing about it, but Stravinsky also used it extensively, and I
believe Rimski-Korsakov was the first to use it.

>By the way, why is this stuff in a thread called "more on composing in X
>tuning"? It doesn't seem to have anything to do with composing per se.
>"Good 5-limit scale generators" seemed like a perfectly good title to me.

I have no idea. I changed it back.

-Carl

--- In tuning@egroups.com, Carl Lumma <CLUMMA@N...> wrote:

http://www.egroups.com/message/tuning/13926

>
> I am not familiar with the 9-note, but the 8-note one is commonly
> called the "octatonic" scale. Messiaen is known for using it and
> writing about it, but Stravinsky also used it extensively, and I
> believe Rimski-Korsakov was the first to use it.

And Bartok excessively... correct (??)
_________ ___ __ _ _
Joseph Pehrson