Equal temperament and Pythagorean tuning: a geometrical interpretation in the plane (Q1582668)

The author gives an interesting geometrical interpretation of Pythagorean tuning and equal temperament as discrete subsets of the Euclidean plane. For instance, he shows that there is a natural parallel projection between these tunings. This implies, in particular, that when performing a composition on two instruments simultaneously in both Pythagorean tuning and equal temperament, the so-called Garbuzov zones [see \textit{N. A. Garbuzov}, The zonal nature of the human aural perception (in Russian), Izd. Akad. Nauk SSSR, Moscow-Leningrad (1948)] can be considered as segments on parallel lines in the plane.