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 , 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: