Central rotation of regular (and irregular) musical poligons

• Main Author: Latinčić Dragan
• Format: Article
• Language: English
• Published: Serbian Academy of Sciences and Arts - Institute of Musicology of Serbian Academy of Sciences and Arts 2020-01-01
• Series: Muzikologija
• Subjects: rhythm; lambdoma; polygonal number; isometric transformations; central rotation; spectrum; triangle; hemioles; discrete mathematics; partition of numbers; polyphony of the sub-saharan region
• Online Access: http://www.doiserbia.nb.rs/img/doi/1450-9814/2020/1450-98142028205L.pdf

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.