Home > Mathematics, Statistics > Vol 11 No 2 December 2023 Abstract 3
VARIATIONS ON A TUNING ALGORITHM
WILL TURNER

Abstract
In previous work we have presented a tuning algorithm for music written on a stave. The main idea is that tuning the music written on a stave in this way preserves a body of the consonances of the piece. This body of consonances does not consist of all the consonances of the piece, but rather a subset of the set of all consonances determined by a specific algorithm. The consonances form the arrows of a certain quiver whose vertices are the notes of the piece and whose underlying graph is a tree. In this paper we follow up on some of the possibilities of this algorithm, by presenting variations on it. The variations each have a musical purpose. For example, when we select certain tunings, applying our algorithm gives music which in part lies outside the human audible range; a variation corrects for this. To give another example, for certain tunings, the resulting music has big leaps between notes; a variation moderates this.

Full Text: PDF     DOI: 10.15640/arms.v11n2a3