More about miracle

"I just wish Icould wrap my head around what miracle -is-, rather than just a neat way to get arbitrarily close to JI."

The secor is small, so miracle divides various 11-limit consonances into equal parts. In particular, the fifth is six secors, and so gets divided into two, giving a 1-11/9-3/2 neutral triad, and into three, giving a 1-8/7-21/16-3/2 chord. 12/7 is divisible into eight and hence parts, leading to a 1-8/7-21/16-3/2-12/7-2 chord. 11/4 is divisible into 15 parts, and hence 5 and 3, leading to 1-11/9-3/2-11/6-9/4-11/4 chords.

Something I find useful in a miracle MOS is to arrange the tetrads/pentads into a line. If 1-5/4-3/2-7/4 is a major tetrad in root position and 1-6/5-3/2-12/7 a minor tetrad in root position, then you can arrange them as major tetrad on 1/1, minor tetrad on 5/4 (root up a major third) major tetrad on a secor (root down 7/6) and repeat, up and down, until you reach the limits of the MOS. Adjacent tetrads share two notes and hence an interval, and movement by a step gives good voice-leading properties.

On Fri, Sep 10, 2010 at 5:47 PM, genewardsmith
<genewardsmith@...> wrote:
>
> "I just wish Icould wrap my head around what miracle -is-, rather than just a neat way to get arbitrarily close to JI."
>
> The secor is small, so miracle divides various 11-limit consonances into equal parts. In particular, the fifth is six secors, and so gets divided into two, giving a 1-11/9-3/2 neutral triad, and into three, giving a 1-8/7-21/16-3/2 chord. 12/7 is divisible into eight and hence parts, leading to a 1-8/7-21/16-3/2-12/7-2 chord. 11/4 is divisible into 15 parts, and hence 5 and 3, leading to 1-11/9-3/2-11/6-9/4-11/4 chords.
>
> Something I find useful in a miracle MOS is to arrange the tetrads/pentads into a line. If 1-5/4-3/2-7/4 is a major tetrad in root position and 1-6/5-3/2-12/7 a minor tetrad in root position, then you can arrange them as major tetrad on 1/1, minor tetrad on 5/4 (root up a major third) major tetrad on a secor (root down 7/6) and repeat, up and down, until you reach the limits of the MOS. Adjacent tetrads share two notes and hence an interval, and movement by a step gives good voice-leading properties.

I see. I just loaded up blackjack and started messing around - I get
the pattern now. So the 33-cent interval functions as the chromatic
interval here, even though it's so small. So the distinction between
"chromatic" and "diatonic" breaks down with something like miracle,
since you need to be chromatic to make consonant tetrads work at all.

As an aside, I also have a feeling that words like "diatonic" and
"chromatic" are really discrete quantizations of an underlying
continuous function. The same applies to "chord tones," "non-chord
tones," "avoid notes" for a certain chord, etc.

-Mike