The symmetry of melodic structure


The tonal pitch as the most important acoustic property was first studied in the Pythagorean school (6th century B.C.). This marks the beginning of the mathematical study of the tonal pitch and its frequency as the function of a stretched string (with the use of the first acoustic apparatus, the monochord), or of the length of an air tube (Encyclopedia of Music, 1963, p. 705; Canak, 1985, 1987, 1988; Ghyka, 1987; Vinogradov and Krasovskaya, 1991).


Figure 3.1 Pythagoras' acoustic experiments.