Pelog (was: RE: Re: salendro: nothing equal about it!)

<< , but the scales sure sound good in Blackwood's piece [in 23-tET]! >>

>Yes, but they sound nothing like slendro or pelog.

9-tET gives a much closer approximation of some actual pelog tunings: it's
"like" a major scale with a "whole step" of 133 cents and a "half step" of
267 cents, giving a scale of
0, 133, 267, 533, 667, 800, 933;
and a typical scale drawn from this tuning is "like" the pentatonic scale
drawn from the major scale:
0, 133, 267, 667, 800
which can be found in three transpostions in the scale above. It is no
wonder that Western texts (from guitar magazines to Persichetti's _Twentieth
Century Harmony_) often give the "pelog" scale as C Db Eb G Ab, but that is
of course a great distortion.

Wilson speaks of notational systems of 9 nominal symbols as
"Blasquintenzirkel systems, appropriate to Pelog" and has used them in
connection with linear temperaments of 9, 16, and 23 tones per octave.
Sounds like a reference to the circle of "blown fifths" I mentioned earlier.
Anyone know more?

16-tET provides a compromise between the 9-tET and 23-tET versions; I
believe Herman Miller has used 16-tET in this connection . . .

I don't mean to suggest that any of these equal temperaments play any role
whatsoever in the way the musicians conceptualize or hear their tunings.
Most likely the two operative factors are (1) an idiomatically and perhaps
timbrally motivated flattened fifth/sharpened fourth, and (2) some
categorically-perceived step sizes (perhaps more than two but almost
certainly fewer than seven). It's just that 9-tET is a very easy tuning to
play around with on a standard keyboard and one can modulate and also use
the very convincing-sounding symmetrical hexatonic scale.

Paul!
Wilson would not suggest the use of an equal temperment for either pelog or
slendro. nor would he suggest a just solution. He has pointed out that these
tunings if you face them head on avoid both. He has done some extensive work on
these which awaits some polishing before he goes public. That certain pelogs
could be extended to 9,16, & 23 tones he has suggested as a possibly but has
observed pelogs that cycle through other cycles 13, or 14 for that matter.
Possibly pelog includes a family of scales. Kunst got the idea "blown fifths"
from Hornbostel but there is neither evidence of tubes being used by tuners nor
actual measurements that match in any convincing way. It is all too common for
cultural artifacts from around the world to be placed in a western reference
even when it doesn't apply. If another culture mentions a flood there are those
who start talking about arks! I'm back but i don't know for how long.

"Paul H. Erlich" wrote:

>
>
> Wilson speaks of notational systems of 9 nominal symbols as
> "Blasquintenzirkel systems, appropriate to Pelog" and has used them in
> connection with linear temperaments of 9, 16, and 23 tones per octave.
> Sounds like a reference to the circle of "blown fifths" I mentioned earlier.
> Anyone know more?
>
> \

-- Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com

[Paul H. Erlich:]
>it's "like" a major scale with a "whole step" of 133 cents and a
"half step" of 267 cents, giving a scale of 0, 133, 267, 533, 667,
800, 933; and a typical scale drawn from this tuning is "like" the
pentatonic scale drawn from the major scale

I've used the 2L 5s mapping (where the generating fifth lies inside
the 1/14 between 4/7 and 1/2):

4/7 1/2
5/9
9/16 6/11
13/23 14/25 11/20 7/13
17/30 22/39 23/41 19/34 16/29 17/31 13/24 8/15

(etc.)

to facilitate the combining and bridging of a variety of EDOs... and
here that has usually been using 20e (and its L=5 & s=2) as the
target, or primary point of (compositional) focus.

And while the theoretical borders of the fifth size are anywhere <4/7
and >1/2, I'd tend to map this as something on the order of (where as
a general rule of thumb, s & L-s are >1/35):

[2][4][6] 1 3 5 [7]
9 11 13 [8][10][12][14]
16 18 20 15 17 19 21
23 25 27 22 24 26 28
30 32 34 29 31 33 35

(etc.)

This way the EDOs that lie on the borders, and those that fall outside
them, are also easily seen... I also like to see the reducible EDOs as
I'm generally not only interested in the exact scale mapping (in fact
I'm generally only using them as a motific "in," or path).

I've also experimented a bit with running these mappings through a
variety of meantonesque temperings - The 7-out-of-16 flip-flopped
"major" scale as a ((LOG(7/1)/LOG(2))/5*1200), 0 148 295 526 674 821
969 1200, for instance...

Dan