A method for composing with interval cycles as applied to an original composition for symphony orchestra

Tonality is a method of composing with interval cycles that partition the octave. For centuries, this partition interval has been privileged for its acoustical properties. This dissertation takes a fresh look at partitions in general, and seeks to determine if there are broader principles capable of organizing interval cycles such as those used in tonality. However, it is deemed arbitrary to limit interval cycles to any one partition such as the octave. In this dissertation, interval cycles are demarcated into new hierarchical equivalence classes that cordon-off specific invariant traits related to how interval cycles interact in voice-leading space. These equivalence classes include prime-number class, partition class, cyclic family, and cyclic class. The multilevel coherence engendered by the method presented here is realized in the original composition Symphony No. 1.