Spectrum Projections in Musical-Mathematical Analysis


Dragan Latinčić




The text describes the method of rhythmic projections of the spectrum of harmonics, as well as the application of one of the most important isometric transformations to the projected metro-rhythmic entities of individual harmonics of the spectrum. It is a direct isometry called central rotation. The central rotation conditions the hemiol structuring of the meter. Hemioles are identified with regular and irregular geometric figures (primarily triangles) through the partition and composition (index) number of a specific spectral harmonic. The partition and composition of numbers dealt with by discrete mathematics, on the one hand, and the technique of horizontal hemioles, characteristic of the polyphony of the sub-Saharan region, on the other hand, served as a means of realizing the method by which the isometric transformation of the central rotation would be realized in (musical) time.