Muzikologija 2020 Issue 28, Pages: 205-234
https://doi.org/10.2298/MUZ2028205L
Full text ( 1625 KB)
Central rotation of regular (and irregular) musical poligons
Latinčić Dragan (Department of Composition, Faculty of Music, University of Arts, Belgrade, Serbia)
The text describes 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.
Central rotation conditions the hemiola structuring of the meter. Hemiolas
are identified with regular and irregular geometric figures (primarily
triangles) by means of a partition and the composition (index) number of a
particular spectral harmonics. The partition and composition of numbers,
which are dealt with in discrete mathematics, on the one hand, and, the
technique of horizontal hemiolas, characteristic of the polyphony of the
sub-Saharan region, on the other, served as a means of creating methods by
which the isometric transformation of central rotation would be realized in
(musical) time.
Keywords: rhythm, lambdoma, polygonal number, isometric transformations, central rotation, spectrum, triangle, hemioles, discrete mathematics, partition of numbers, polyphony of the Sub-Saharan region