Eight short mathematical compositions constructed by similarity

Similar sounds are a formal feature of many musical compositions, for example in pairs of consonant notes, in translated passages, and in continuous musical lines. The aim of this article is to introduce techniques derived from those of existing tonal music via the notion of similarity, and demonstrate interactions with existing techniques, also derived from the notion of similarity.

We describe eight short musical compositions that have been constructed mathematically using these techniques. The building blocks of our compositions are entities we call quasi-notes, which correspond to points on the stave, and are certain composites of pure tones. We explore various ways to combine these quasi-notes, pursuing the principle that similar sounds should combine and follow each other.