Pelog and "superpelog"

Pelog is an irregular 7-note scale used in the music of Indonesia. It resembles a 7-note subset of 9-ET, but most pelog scales (which vary from one ensemble to another) have steps of varying size. Within the same ensemble, such as a gamelan (a group of musicians playing tuned percussion instruments typically with metal bars, plus drums, cymbals, and sometimes flutes or other instruments), different instruments are detuned relative to other instruments to create a shimmering effect. Even the octaves are detuned.

"Superpelog" is my name for a 14-note tuning based on a specified period and generator, which includes a number of approximations of different pelog-like scales. It's a combination of two pelog approximations described by Erich von Hornbostel, extended to 14 steps to allow for modulation between keys. A nine-note subset of this scale also has a resemblance to a tuning used in the music of the Balinese gambuh theater, played on huge bamboo flutes. One version of this tuning, which in some ways might be said to be the "optimal" version (related to Paul Erlich's "Tenney-optimal" temperaments), has a generator of 260.76 cents and a period of 1206.55 cents. But since there's no one standard for pelog tunings, these numbers can be varied as desired to create a variety of pelog-like scales. Von Hornbostel's "type a" tuning (in the Scala archive as "pelog_pa.scl") has a generator of 522.0 cents, which when split in half results in a 261.0 cent generator for superpelog tuning (the same as the generator of his "type b" pelog tuning, "pelog_pb.scl"). Superpelog can also be tuned as a subset of 23-ET, with a generator of 5 steps (approximately 260.87 cents).

The steps of this scale can be named by specifying the number of generators it takes to reach each note. For convenience, a letter of the alphabet can be assigned to each note, corresponding to the generator iterations.

generators       0  5 10  1  6 11  2  7 12  3  8 13  4  9  0
note name        A  F  K  B  G  L  C  H  M  D  I  N  E  J  A
degree of 23-ET  0  2  4  5  7  9 10 12 14 15 17 19 20 22 23

Note that taking every other note of superpelog results in a 7-note scale of mavila temperament, which is what you get when you temper out the major chroma (or major limma) 135;128. So the superpelog scale contains two interleaved mavila scales.

A different pelog approximation is provided by taking nine iterations of the superpelog generator. While neither version of the scale is a very close approximation to any actual pelog, this one seems to sound closer to authentic scales than the mavila one. The basic scale can be described as "A F B G C H D I E", and bears a close resemblance to an actual tuning used in music of the gambuh theater (if "A" is set to approximately 400 Hz). Various five-note modes of this scale can be used; here are a few selected for similarity to modes used in gambuh music:

tetekep selisir  G C D E A
tetekep sunaren  E A F C H
tetekep baro     C H D A F
tetekep lebeng   H D I F B

Note that each of these modes can be transposed to seven or eight different "keys" by shifting the letters forward in the alphabet. "Tetekep baro", for instance (which sounds like a very typical 5-note pelog scale), can be spelled as "D I E B G", and so on, all the way up to "I N J G L". This convenience is the reason for the strange ordering of letter names.

But the superpelog scale is more than a set of pelog approximations; it also has a useful linear temperament mapping for 11-limit harmony. It's not a particularly accurate temperament (for instance, the same interval represents both 4:3 and 11:8), but it has some unexpected resources. The chord CKDAG, for instance, is a fairly good approximation of a 3:5:7:9:11 chord.

In 1987, Erv Wilson designed a layout for a generalized keyboard which fits the structure of this scale, having 23 keys per octave on a hexagonal grid. The central 9 notes of the scale were assigned the names "panelu", "singgul", "sorog", "kenong", "panangis", "galimer", "pamiring", "barang", and "liwong".

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