The gamelan pelog scale of Central Java as an example of a non-harmonic musical scale
A consequence of the mechanism of pitch extraction in the auditory midbrain is a high sensitivity for low-order frequency ratios in musical tone intervals, in particular for the ratios 4:3, 5:4, and 6:5.
Many music cultures have made use of these conditions. Some, however, have constructed musical scales without applying any low-order ratios, except for the octave (ratio 2:1). The most famous example is the gamelan music of Java and Bali.
The main instruments in gamelan music are various types of metallophones. The common characteristic of these instruments is a partly non-harmonic sound-spectrum for each single tone. Due to this fact, simultaneous tones always cause a strong component of dissonance in hearing sensation. A harmonic frequency ratio, say 5:4, between the pitch frequencies of two tones only has a small effect here, as compared to string and wind instruments, where the effect is large due to highly harmonic sound-spectra. Metallophones, and also xylophones, are well suited acoustically for trying out non-harmonic musical scales. This is what musicians in Java and Bali did for many centuries.
The two main scales in Java are slendro and pelog. Slendro is a five-tone scale that very roughly approaches equal-size intervals. The intervals vary within a given scale and across orchestras, but the underlying tuning concept can be considered as a rough five-tone equal temperament (5ET).
Pelog is a seven-tone scale, whose underlying tuning concept is less obvious. One possibility is that the tuning approaches a nine-tone equal temperament (9ET), using both single steps (133 Cent) and double steps (267 Cent) from an imagined 9ET scale, which is a particular element of the historical tradition of Javanese Music.
The tones of the pelog scale are called "bem-gulu-dada-pelog-lima-nem-barang-bem2"
An analysis of the tuning data of the 27 gamelan pelog orchestras measured by Surjodiningrat et al. (1972) revealed that in the main octave (corresponding to C4-C5 in European music) a conspicuously large number of the 22 investigated interval types show a close relation to the 9ET concept. The bias toward 9ET was found to be statistically significant on the 0.02 level. Four of the 22 interval types even showed a cluster of a relevant subset of the 27 specimens around the theoretical 9ET interval: gulu-dada (133 Cent), bem-dada (267 Cent), dada-nem (533 Cent), and gulu-nem (667 Cent).
Click interval types to see the 22 diagrams of the interval distribution across the 27 orchestras for each of the 22 interval types:
First-order intervals, like bem-gulu, gulu-dada, etc.
Second-order intervals, like bem-dada, gulu-pelog, etc.
Third-order intervals, like bem-pelog, gulu-lima, etc.
Fourth-order intervals, like bem-lima, gulu-nem, etc.
Literature: Surjodiningrat,W., Sudarjana, P.J., and Susanto, A. (1972) Tone measurements of outstanding Javanese gamelans in Jogjakarta and Surakarta, Gadjah Mada University Press, Jogjakarta 1972.
This is a small book of ca. 70 pages, ca. 10 tables and 20 figures in the text, and 12 tables in the appendix (containing all the raw data). The book is the English translation of the original Indonesian publication that appeared in 1969. The authors are physicists, who did part of their studies in the USA (1964-65), and at the time of the measurements (1968) they were lecturers at the Gadjah Mada University, Yogjakarta, in mathematics, acoustics, and electronics.
Added Aug 24, 2006: After publication of the present study I was
informed that Jay Rahn had earlier strengthened the 9ET hypothesis of
pelog by different mathematical techniques that he applied to the tuning
data of two high-quality pelog ensembles from Central Java: 'Javanese
Pélog Tunings Reconsidered.' Yearbook of the International Folk
Music Council 10 (1978): 69-82.
Pictures, sound samples from music recordings, and an appendix with pictures and descriptions of instrument types: Roger Vetter's brilliant site about gamelan music at the Kraton of Yogyakarta (whose instruments contributed to a major part of the tuning data presented here)