The Cantor Set as a Tool for Composition

Here, I apply the structure of the Cantor ternary set to act as the main building block for the composition I call: Atonal fractal template!  This piece is composed for solo violin.  I chose a particular set class, 3-12 [048], essentially an augmented triad, which has an interval class vector of <000300>, which states that the major third is the only interval this symmetric set contains.  A 12-tone-matrix is built up by using the general serial techniques for constructing the prime, retrograde, inversion, and retrograde inversion.  This piece has build into it a soft dissonance due to the major third.  However, the way in which the prime form is constructed, there are minor seconds, such as G-G# and F-F#, which I use to create tension and from the tonal structure of the major thirds.  Groups of rows are chosen to construct the Cantor set, I chose rows Po, Ro, RIo, and RI9.  I can build up major chords, such as B-D-F when constructing the Cantor set, then I can use the sharper dissonant intervals, such as G-G# and F-# to create a tense environment.  I hope this doesn’t make you too up tight.

When listening to this piece, you will hear an overall atonal character, eventually resolving in a quasi-tonal manner.  The following diagram represents the 12-tone matrix:


The following rows, except for RI2, were used to construct the Cantor set for Atonal Fractal Template:


The next diagram shoes how I use each row from the 12-tone matrix to construct the details of this piece:


Please enjoy listening to Atonal Fractal Template:


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