G. Bulancea
Friday 9 November 2018 by Libadmin2018


The current study carries further the research initiated in another article published in 2010, entitled Mathematical models for analysing diatonic modes. This research naturally completes the other by the supplementary approach of the chromatic musical modes. Only one of the two analysis models presented then will be selected, the latter one. The former model employed in the previous study does not display any applicability when it comes to chromatic modes. The latter model, which was initially applied only to diatonic tetrachords, will be extended this time to cover all nine tetrachords known to musical practice, 5 diatonic and 4 chromatic. [1] If we consider all nine tetrachords as the elements of a multitude, we will notice the specificity of this method of analysis which resides in making arrangements of two out of the total nine elements of that particular multitude. [2] Since our study focuses only on the chromatic modes, the tetrachords will be juxtaposed in such a manner that there is at least one chromatic tetrachord. Thus, there will be musical structures of octaval type which juxtapose a chromatic tetrachord with a diatonic one or even two chromatic tetrachords. Their juxtaposition is done at an interval of semitone (st), tone (T) and major second (2+) so as we are able to tackle with all possibilities that musical theory and practice offer. [3] To all these results we will also add those situations where the juxtaposition of two diatonic modes through a major second generates another musical mode of a chromatic type.

Keywords: musical modes, tetrachords, musical structures, mathematical formulas, mathematical models

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