Ombak and octave stretching in Balinese gamelan

A primary esthetic in the performance practice of Balinese gamelan is the ombak (Indonesian for wave), which is manifest in musical form, performance, and tuning. The ombak arises in a paired tuning system in which corresponding unisons of two instruments (or instrumental groups) are tuned to slightly different frequencies, one higher and one lower, to produce beats. Pitch classes are not necessarily tuned to octaves in an exact 2:1 frequency ratio; instead, octaves are often stretched or compressed. This paper discusses the relationship between the ombak rate and octave tempering, and demonstrates that the beating rate, combined with the octave tuning strategy chosen, can be modeled using a tempering parameter that determines the amount of stretching or compression. This model is then used to analyze tuning data of nine complete gamelan.