|A Universal Property of Musical Scales|
|Living - The Dialogue|
|TS-Si News Service|
|Saturday, 26 March 2011 14:00|
Amsterdam, The Netherlands. There is a universal property of musical scales that makes it possible to recognize the music in very different groups of sounds produced by many different cultures around the world.
Scientists find patterns throughout nature, but biology shows that humans are themselves part of nature and produce artifacts, such as poetry and music, that can be examined in view of their fundamental and universal patterns. Music lovers often cite the universality of music as a means by which disparate cultures can find a basis for common understanding.
Almost all music compositions in the world are based on an underlying scale. At a superficial level, a scale consists of an ascending or descending sequence of tones where the initial and final tones are separated by an octave, which means the frequency of the final tone is twice that of the initial tone (the fundamental).
Convex Structures. The many hundreds of scales in existence seem to possess a deeper commonality.
If their tones are compared in a two- or three-dimensional way by means of a coordinate system, they form convex or star-convex structures.
Click Pic for DetailsIn Western music, the major scale (do-re-mi-fa-sol-la-ti-do) is the best known. However, many other scales are in use (such as the minor and the chromatic scale). Besides these well-documented traditional scales, modern composers, particularly those from the twentieth century on, have devised a wide variety of artificial scales.
Dr. Aline Honingh and Prof. Rens Bod are from the Institute for Logic, Language and Computation (ILLC) at the University of Amsterdam. They compared nearly 1,000 scales from all over the world, from Japan to Indonesia and from China to Greece.
The researchers found scales can be studied as multidimensional objects by placing them in a coordinate system (eg., Euler lattice). Their findings appear in the Journal of New Music Research (JNMR).
Until recently it seemed that the octave was the only thing musical scales have in common. It turns out there is a deeper commonality in the many hundreds of scales: if you use a coordinate system, and compare their tones in a two- or three-dimensional way, they form convex or star-convex structures. Such structures are basic patterns without indentations or holes, such as a circle, square or oval.
To their surprise, the researchers discovered that all traditional scales produced star-convex patterns. This also was the case with almost 97% of non-traditional, scales conceived by contemporary composers who often state they have designed unconventional scales.
The percentage in either case is very high, because the probability that a random series of notes will produce a star-convex pattern is very small.
Honingh and Bod try to explain the phenomenon of a universal property by using the notion of consonance (harmony of sounds). They connect their research results with language and visual perception where convex patterns have also been detected, possibly indicating a cognitive universal (a general cognitive property) among humans.
ParticipationThe research is part of the Vici programme Integrating Cognition of the Netherlands Organisation for Scientific Research (NWO) led by Rens Bod.
CitationIn search of universal properties of musical scales. Aline Honingh and Rens Bod. Journal of New Music Research 2011; In press.
Musical scales have both general and culture-specific properties. While most common scales use octave equivalence and discrete pitch relationships, there seem to be no other universal properties. This paper presents an additional property across the world’s musical scales that may qualify for universality. When the intervals of 998 (just intonation) scales from the Scala Archive are represented on an Euler lattice, 96.7% of them form star-convex structures. For the subset of traditional scales this percentage is even 100%. We present an attempted explanation for the star-convexity feature, suggesting that the mathematical search for universal musical properties has not yet reached its limits.
|Last Updated on Saturday, 26 March 2011 23:13|