Reconstructing MOS

It seems trivial that taking every other note of a ten note MOS
results in a pentatonic. But I was looking at the 7L3s MOS, and
noticed that every other note is 'the' pentatonic one would
derive in meantone. However, 7L3s is the next MOS step after
4L3s, which is not in the meantone family and actually has all
kinds of quasi-'Eastern' intercals. The 'classic' pentatonic
only appears after reconstruction (and, I have not proved it in
any mathematical sense).

What is suggested is that 7L3s has a "chord scale" system
analagous to building chords on scale degrees in traditional scales,
but each chord is a pentatonic in some inversion. Whether pleasant
harmonization of unfamiliar melodies is useful or not is up to the
individual pracitioner, I'm just pointing out the curious fact that
its there.

0 1 2 3 4 5 6 7 8 9
L L s L L s L L s L

degree pentatonic (new L=2L from 7L3s, new s=L+s from 7L3s)
0 LssLs
1 sLssL
2 ssLsL
3 LssLs
4 sLsLs
5 ssLsL
6 LsLss
7 sLsLs
8 sLssL
9 LsLss

Here are some cents values for a few EDOs, check out every other value.

17 141 282 352 494 635 705 847 988 1058
24 150 300 350 500 650 700 850 1000 1050
27 133 267 355 489 622 711 844 978 1067
31 155 310 348 503 658 697 852 1006 1045
34 141 282 353 494 635 706 847 988 1058

It is equally trivial to say that if you go down far enough, you
can reconstruct anything. But 7L3s is not so deep to be playing with
individual cents.

On Thu, Jun 16, 2011 at 10:00 AM, bobvalentine1 <bob.valentine@...> wrote:
>
> It seems trivial that taking every other note of a ten note MOS
> results in a pentatonic. But I was looking at the 7L3s MOS, and
> noticed that every other note is 'the' pentatonic one would
> derive in meantone. However, 7L3s is the next MOS step after
> 4L3s, which is not in the meantone family and actually has all
> kinds of quasi-'Eastern' intercals. The 'classic' pentatonic
> only appears after reconstruction (and, I have not proved it in
> any mathematical sense).

This is what we typically call "mohajira," sometimes referred to as
"hemififths." The generator is a neutral third which is mapped to
11/9, and two of them make a fifth. Then, four fifths get you to 5/1,
so mohajira is an extension of meantone that has half the generator.
By taking every other note, you end up with meantone[5], which is what
you've noticed above.

> What is suggested is that 7L3s has a "chord scale" system
> analagous to building chords on scale degrees in traditional scales,
> but each chord is a pentatonic in some inversion. Whether pleasant
> harmonization of unfamiliar melodies is useful or not is up to the
> individual pracitioner, I'm just pointing out the curious fact that
> its there.
>
> 0 1 2 3 4 5 6 7 8 9
> L L s L L s L L s L

Man, what a fantastic idea. You've taken mohajira[10] and
deconstructed it into pentads. Just like 1-3-5 provides the base triad
for meantone[7], 1-3-5-7-9 can provide a base pentad for mohajira[10].
I'll have to take a look at this more.

-Mike

Mike Battaglia <battaglia01@...> wrote:

> This is what we typically call "mohajira," sometimes
> referred to as "hemififths." The generator is a neutral
> third which is mapped to 11/9, and two of them make a
> fifth. Then, four fifths get you to 5/1, so mohajira is
> an extension of meantone that has half the generator. By
> taking every other note, you end up with meantone[5],
> which is what you've noticed above.

Somebody (maybe Yasser) suggested that the Arabic rast
scale grew out of the classic pentatonic by equally dividing
the minor thirds (the larger step size). Mohajira is a
structure that's related to that rast scale and a rast is
present in the 10 note Mohajira MOS.

If you divide the minor thirds unequally, you get the usual
diatonic (sometimes also related to rast). Hence
pentatonics are the key to all mysteries.

Graham