Selecting sub-scales from larger DE / MOS scales

I'm starting to get the impression that selecting smaller scales from an MOS or DE scale by skipping steps in a symmetrical manner can result in some useful and interesting sub-scales for melodic and harmonic uses. As an example of what I'm talking about, take this 10-note DE scale from the "Nai Lemba" temperament <<6, -2, -2, -17, -20, 1]] that I've been playing with recently.

0 3 1 4 2 0 3 1 4 2 0 (generators)
A Ax B# C Db Dx E F Fx G# A

If you just consider this as a 10-note scale without paying attention to the different sizes of the steps, look at what you get when you alternately take 2-step and 1-step intervals:

0 1 4 0 3 4 2 0
A B# C Dx E Fx G# A

You can think of it as an equivalent of a 7-note MOS scale from 10-ET, with 3 large steps and 4 small steps, and a 3-step generator. It's a useful 7-note scale with both of the 7-limit tetrads (A C E Fx and B# Dx Fx A, in the 26-ET-inspired notation I'm using). You can also use it to play the melody from one of Bartók's Rumanian Folk Dances:

http://www.kunstderfuge.com/mid/bartok_roumanian_folk_dances_3_(c)pajares.mid

Now see what happens when you take the larger 16-note DE scale and construct a scale that looks like the 7-note pelog approximation in 16-ET:

0 3 6 1 4 7 2 5 0 3 6 1 4 7 2 5 0
A Ax B B# C CxDb D#Dx E ExF Fx G G# AbA

0 6 4 5 3 1 7 0
A B C D# E F G A

You end up with (what'd you expect?) a nice pelog scale in Lemba temperament!

I seem to recall some discussion about scale patterns like this from a while back, but I don't remember much about it. Is there a name for this kind of scale? It seems like a good way to make musically useful subsets from some of those larger scales.

Hello Herman!
This whole train of thought is exactly how i come up with most of my pitch
material. Double layers of patterns, are IMHO the best. I have ben finding it
true of other parameters also!
Erv used the term Binary Depth which I am sure was off the cuff, but seems to
work quite well!

Herman Miller wrote:

> I'm starting to get the impression that selecting smaller scales from an
> MOS or DE scale by skipping steps in a symmetrical manner can result in
> some useful and interesting sub-scales for melodic and harmonic uses. As
> an example of what I'm talking about, take this 10-note DE scale from
> the "Nai Lemba" temperament <<6, -2, -2, -17, -20, 1]] that I've been
> playing with recently.
>
> 0 3 1 4 2 0 3 1 4 2 0 (generators)
> A Ax B# C Db Dx E F Fx G# A
>
> If you just consider this as a 10-note scale without paying attention to
> the different sizes of the steps, look at what you get when you
> alternately take 2-step and 1-step intervals:
>
> 0 1 4 0 3 4 2 0
> A B# C Dx E Fx G# A
>
> You can think of it as an equivalent of a 7-note MOS scale from 10-ET,
> with 3 large steps and 4 small steps, and a 3-step generator. It's a
> useful 7-note scale with both of the 7-limit tetrads (A C E Fx and B# Dx
> Fx A, in the 26-ET-inspired notation I'm using). You can also use it to
> play the melody from one of Bart�3k's Rumanian Folk Dances:
>
> http://www.kunstderfuge.com/mid/bartok_roumanian_folk_dances_3_(c)pajares.mid
>
> Now see what happens when you take the larger 16-note DE scale and
> construct a scale that looks like the 7-note pelog approximation in 16-ET:
>
> 0 3 6 1 4 7 2 5 0 3 6 1 4 7 2 5 0
> A Ax B B# C CxDb D#Dx E ExF Fx G G# AbA
>
> 0 6 4 5 3 1 7 0
> A B C D# E F G A
>
> You end up with (what'd you expect?) a nice pelog scale in Lemba
> temperament!
>
> I seem to recall some discussion about scale patterns like this from a
> while back, but I don't remember much about it. Is there a name for this
> kind of scale? It seems like a good way to make musically useful subsets
> from some of those larger scales.
>
>
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-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> I seem to recall some discussion about scale patterns like this from a
> while back, but I don't remember much about it. Is there a name for
this
> kind of scale? It seems like a good way to make musically useful
subsets
> from some of those larger scales.

I discussed "muddles" some time back.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> I seem to recall some discussion about scale patterns like this
from a
> while back, but I don't remember much about it. Is there a name for
this
> kind of scale?

Lots of people have discussed these, for example Mats Oljare, who
called them 2nd order MOS or something like that.

> It seems like a good way to make musically useful subsets
> from some of those larger scales.

Indeed. One can derive them as Fokker periodicity blocks with all but
two of the defining unison vectors tempered out. Japanese scales like
1/1 16/15 4/3 3/2 8/5 can be understood as de-tempered Mavila
(formerly Pelogic) scales in this way, for a simple example.