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.
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.
| Original language | English |
|---|---|
| Journal | American Review of Mathematics and Statistics |
| Publication status | Accepted/In press - 23 Oct 2023 |