Bellissima, Fabio (Author)
Bollettino di Storia delle Scienze Matematiche
Volume: 31
Issue: 2
Pages: 177-216
A music interval is perceived like a distance - and therefore like a difference - between two sounds. But to equal intervals correspond equal ratios, not equal differences. Then, there exists a distortion (an anamorphism) in the way the intervals are perceived. To solve this distortion, logarithms are needed (and indeed they were immediately applied to music theory as soon as they were invented). But Greeks did not have them. So, this distortion caused difficulties not only to the music theory but also to the theory of proportions (which, among Pythagoreans, was born principally in the field of the music theory). The division between Pythagoreans and Aristossenians and the errors made by Ptolemy in assigning numbers to the Aristossenians scales are the most visible effects. On the other hand, the possibility offered by the logarithmic anamorphism of interpreting multiplicative results in additive terms may have helped the discovery of some elementary properties of the proportions.
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