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Imperfect fifths pack into musical scales.
John M. McBride,Tsvi Tlusty +1 more
TL;DR: This work assimilates data from diverse ethnomusicological sources into a cross-cultural database of scales and generates populations of scales based on proposed and alternative theories and assess their similarity to empirical distributions from the database.
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Abstract: Musical scales are used in cultures throughout the world, but the question as to how they evolved remains open. Some suggest that scales based on the harmonic series are inherently pleasant, while others propose that scales are chosen that are easy to sing, hear and reproduce accurately. However, testing these theories has been hindered by the sparseness of empirical evidence. Here, to enable such examination, we assimilate data from diverse ethnomusicological sources into a cross-cultural database of scales. We generate populations of scales based on proposed and alternative theories and assess their similarity to empirical distributions from the database. Most scales can be explained as tending to include intervals roughly corresponding to perfect fifths ("imperfect fifths"), and packing arguments explain the salient features of the distributions. Scales are also preferred if their intervals are compressible, which could facilitate efficient communication and memory of melodies. While no single theory can explain all scales, which appear to evolve according to different selection pressures, the simplest harmonicity-based, imperfect-fifths packing model best fits the empirical data.
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Vocal imprecision as a universal constraint on the structure of musical scales
TL;DR: In this article , the authors conducted a large-scale computational analysis of vocal pitch-class properties and their implications for scale structure and found that vocal imprecision fundamentally constrains the formation of musical scale structure: it provides a lower limit on the spacing between adjacent scale tones and thus an upper limit of the number of scale tones that an octave can contain.
References
The motor origins of human and avian song structure
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Vocal mistuning reveals the origin of musical scales
TL;DR: In this article, the authors analysed the tuning of sung musical intervals from a familiar song, doing so across both trained and untrained singers, and found that sung intervals (unlike those of instruments) showed marked overlap with neighbouring interval categories.
African tone-systems-a reassessment
Abstract: There is an extensive literature on “African scales”, but only rarely is it reported what the internal order of the tone material is in the minds of the musicians themselves. Only in a few works can one find direct quotations from the musicians in their own vocabulary. One famous example is Klaus Wachsmann's documentation of the tuning process of an amadinda xylophone in Uganda, and the critical remarks made in Luganda by the two royal musicians, Mr. Evaristo Muyinda and Mr. Baziwe, while they were tuning their instruments. Simultaneously, the process of tuning was measured “live” with a Stroboconn pitch-measuring machine. Wachsmann writes (1957:14-15): “Strictly speaking there is no scale which one could describe in unambiguous terms of physical definition, but there are tuning processes in the course of which corrections are made. Their trend can be described, and in favourable circumstances one can form a realistic picture of the pattern in the mind of the tuner.”
Temperament in Tuning Systems of Southeast Asia and Ancient India
Rolf Bader
- 01 Jan 2019
TL;DR: In this article, the authors present examples from fieldwork in Southeast Asia between 1999 and 2014, and often find musicians wanting to get close to just intonation, but deviating from it mainly because of three constraints: the need to switch between different ensemble types, constraints of instrument building, and acoustical constraints.