Galileo Galilei observed in 1623 that the entire universe "is written in the language of mathematics", and it is remarkable the extent to which science and society are governed by mathematical ideas. It is perhaps even more surprising that music, with all its passion and emotion, is also based upon mathematical relationships. Such musical notions as octaves, chords, scales, and keys can all be demystified and understood logically using simple mathematics.

In fact there is a lot of scientific basis to the practice of music. Though what sounds melodious, or harmonious, or tuneful, must ultimately be regarded as a subjective matter, there seem to be physical justifications for the things in music which appeal aesthetically to most people. Much of music consists of melodic and rhythmic patterns put together in an orderly, but creative manner. The ‘scientific’ approach to music reached its height in the Baroque, and it’s greatest proponent was Johann Sebastian Bach (1685 – 1750).


Bach made use of a number of formal mathematical patterns when he composed his majestic organ fugues. Bach used, for example, the "golden section" as well as the Fibonacci succession (1, 1, 2, 3, 5, 8, 13 etc., in which each number in the succession is the sum of the two previous ones). In many ways he worked like an architect, joining the two different parts of a musical piece into one harmonious whole before the actual process of composition started.

Bach believed that a well-proportioned fugue would provide a guaranteed basis for a successful composition. This, of course, created favourable conditions for numerologists in their search for the ideal form, according to Andreas Haug who is professor at the Centre for Medieval Studies at NTNU (Norwegian University of Science and Technology). He was referring to the polyphonic choral work which the Renaissance composer Guillaume Dufay (c. 1400-74) composed for the consecration of the cathedral in Florence in 1436. It has been claimed that the form this motet takes mirrors the architectonic number symbolism of the cathedral and that Dufay was portraying the proportions of the church in his music. Some interpretations of the work go as far as analysing all notes and textual syllables in the motet so as to make the composition correspond to individual parts of the building.