2011-03-28

Universal Property of Music Discovered

Cognitive universal for scales : Compute Scotland


Researchers at the Institute for Logic, Language and Computation (ILLC) of the University of Amsterdam have discovered a universal property of scales: 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.

 


By placing scales in a coordinate system (‘Euler lattice’) they can be studied as multi-dimensional objects.

Dr Aline Honingh (left) and Prof. Rens Bod (right) from the ILLC did this for nearly 1,000 scales from all over the world, from Japan to Indonesia and from China to Greece.


Universal property of music discovered


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. (Credit: Image courtesy of Universiteit van Amsterdam (UVA))


1000 scales

By placing scales in a coordinate system (an ‘Euler lattice’) they can be studied as multidimensional objects. Dr. Aline Honingh and Prof. Rens Bod from the ILLC did this for nearly 1,000 scales from all over the world, from Japan to Indonesia and from China to Greece. To their surprise, they discovered that all traditional scales produced star-convex patterns. This was also the case with almost 97% of non-traditional, scales conceived by contemporary composers, even though contemporary composers often state they have designed unconventional scales. This percentage 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 this phenomenon 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).

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