Re: Just "pelog-style pentatonic"

Hello Margo, your "human-style" is suave.

Thanks also Paul for your comments. We could eventually talk about the tetrachordality
which, from the gammier theory perspective, is almost an obligation in pentatonic.

In http://www.aei.ca/~plamothe/indextg.htm I wrote in French, in august 2000, vis-à-vis penta-9
It seems there exist only four great natural pentatonic genus.The eight first pentatonic gammiers
belong to these four genus. The next pentatonic gammier, in the canonical order of gammiers,
implies a new genus, using the harmonic 23. That's the gammier number 237. I don't know if
there exist modes approaching. If a musician tried to explore that gammier, I would be curious
to know his impressions.
I had forgotten that when I wrote my precedent message asking to Margo an advice about
the style pelog or japanese of her pentatonic scale. Reading anew this message, I was
struck to read the last sentence:
It seems that the approximative Harrison 1 6 3 1 6 - (in 17-tET) is nearest from
Japanese than from Pelog. Or, would have to correct my styles?
The 1 6 3 1 6 is justly the good caracterization of penta-9 as I used it in
http://www.aei.ca/~plamothe/gammes-gsp.htm

Verifying that, it was yet more astonishing: the distance between the gammier
<3 7 9 27>
which gives the scales of Harrison and Margo, and penta-9 is the half-syntonic
comma 162/161. The scale corresponding to the Harrison's one
1 24/23 4/3 3/2 36/23 2
belongs to the gammier <1 3 9 23> while <3 9 23 27> gives yet this scale and also
the scale corresponding to the Margo's one
1 27/23 4/3 3/2 36/23 2
what is easily shown by
(161/162) 24/23 = 28/27
(161/162) 27/23 = 7/6
(161/162) 36/23 = 14/9.
More generally the operator
T : 7 --> 81/23
transforms one gammier to another
T <3 7 9 27>
= <3 81/23 9 27>
= <1 27/23 3 9>
= <27/27 27/23 27/9 27/3>

= <3 9 23 27>
The gammier <3 7 9 27> is simpler than <3 9 23 27> but it's clear it has the
style of the penta-9 <1 3 9 23>.
http://www.aei.ca/~plamothe/gam/tg237-penta9.gif
This simple remark is not a proposition to define or name a category. It's just to
signal a proximity resulting from duality in the gammier generation.

I wrote "I would be curious to know his impressions" for I don't have any idea about the
perceptive possiblity of the harmonic 23. Without a good color difference between
the 17-tET tuning (slightly favorizing harmonic 23) and the 36-tET tuning of these
scales, maybe we could have serious doubt on that possibility.

Happy holidays!

Pierre