Musical kaleidocycles: composition and analytical techniques

Abstract

Many composers of the 20th century used cyclic harmonic patterns, although they did not develop a unitary theory to systematize their use. An analysis of these patterns is particularly interesting as regards composition: the purpose of this article is to show how a reset of cyclic elements inherited from the tradition could be a starting point for a kaleidocyclic technique in musical composition. At the beginning of the 20th century, several composers were fascinated by cyclic chord relations, mainly at major/minor third, tritone and augmented triad. These relations allowed to break definitely with the tonal system, based on the fifth-relation, and to explore the features of interval relations dividing the octave into equal parts. Thus, specific sections of works based on such harmonic modules (Ravel, Stravinskij, Szimanowsky), two-part pieces with tritone repeat (Skrjabin) and also musical fugues with entries at third or tritone (Bartok) were composed. There were not strict cycles yet, but those works showed a tendency to periodical repetition of elements upon planned transposition levels, ending with the initial position, similarly to static progressions. From a historical point of view, the earliest general theories on the octave division into equal parts date back to the middle of the 19th century, but the topic started to be dealt with more systematically only at the beginning of the 20th century, with the disruption of the tonal system, and it was only at the beginning of the 1960s that its manifold implications started to be analyzed deeply, especially thanks to the techniques developed in the field of the American Set-theory, but not only.