Researchers at the Institute for Logic, Language and Computation (ILLC) of the University of Amsterdam have discovered a universal property of musical scales.
Until now it was assumed that the only thing scales throughout the world have in common is the octave.
The many hundreds of scales, however, 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. Convex structures are patterns without indentations or holes, such as a circle, square or oval.
Almost all music in the world is based on an underlying scale from which compositions are built. In Western music, the major scale (do-re-mi-fa-sol-la-ti-do) is the best known scale. However, there are many other scales in use, such as the minor and the chromatic scale. Besides these ‘traditional’ scales there are also artificial scales created by modern composers. At a superficial level, scales consist 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).