ТРАГОМ ХЕТИТСКИХ РИТМОВА - ПРОЈЕКЦИЈЕ СПЕКТРА У МУЗИЧКО-МАТЕМАТИЧКОЈ АНАЛИЗИ
ON THE PATH OF HITTITE RHYTHMS - SPECTRUM PROJECTIONS IN MUSIC-MATHEMATICAL ANALYSIS

Summary/Abstract: The topic of the paper is related to the metro-rhythmic projection of the spectral sequence and its application in compositional work. The text explains how it is possible to observe the interval and chord funda of spectral sequence as metro-rhythmic schemes according to which the harmonics are superimposed. Their projections are realized by real metric platforms on which the distributivity and frequence of performances of projected rhythmic units (change of the same) as well as their change (change of different ones) can be monitored. Interval and chord funds are classified according to the reference systems of each harmonic separately. Spectral intervals and chords, by themselves, contain sets of harmonics. In order to make the classifications of interval and chord funds as clear as possible, the text explains the principle according to which the types of combinations and permutations with and without repetition of any of the elements from the sets of harmonics can be isolated. The continuation of the study includes practical (musical) examples and tables related to the application of projection, as well as the application of direct and indirect isometric transformations to the projected metro-rhythmic entities of individual harmonics of spectrum. These are direct isometries (central rotation and central symmetry), and, on indirect isometries (axial reflection). Since the central rotation also conditions the chemical structuring of the meter, the chemical groups are identified below with regular and irregular geometric figures (primarily triangles) by means of the partition and composition (index) number of a certain spectral harmonic. The partition and composition of numbers dealt with in discrete mathematics, on the one hand, and the technique of horizontal chemols, characteristic of the polyphony of the sub-Saharan region, on the other, served as a means of realizing methods by which isometric transformations would be realized in (musical) time. The author’s methodological approach conditions a less expected sequence of steps than the one primarily imposed during the compositional process, and is reflected in the choice of (mensural) metro-rhythmic, or non-mensural (aleatory) temporal components, as primary components, on which all other components of sound would depend. This method develops the awareness that a geometric figure, as a projected metro-rhythmic consequence of spectral proportions, becomes a means of composing a work, as temporal sign or symbol.

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