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Ombak and octave stretching in Balinese gamelan
Journal of Mathematics and Music ( IF 0.5 ) Pub Date : 2020-09-20 , DOI: 10.1080/17459737.2020.1812128
William A. Sethares 1 , Wayne Vitale 2
Affiliation  

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.



中文翻译:

巴厘岛加麦兰的 Ombak 和八度音阶伸展

巴厘岛加麦兰演奏实践中的主要美学是ombak(印度尼西亚语中的wave),它体现在音乐形式、表演和调音上。ombak出现在配对调音系统中,其中两种乐器(或乐器组)的相应同音被调到稍微不同的频率,一个更高一个更低,以产生节拍。音高等级不一定要以精确的 2:1 频率比调整到八度音阶;相反,八度音阶经常被拉伸或压缩。本文讨论了ombak速率和八度回火之间的关系,并证明了打浆率与所选的八度音调策略相结合,可以使用回火参数进行建模这决定了拉伸或压缩的量。然后使用该模型分析九个完整加麦兰的调优数据。

更新日期:2020-09-20
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