This page describes ongoing experiments to improve the algorithm that automatically assigns pitches to notes. When you have listened to the results, your feedback would be much appreciated.
In 5 limit just intonation, there are two versions of the minor third. In the matrix introduced here, one version is the combination of the lefthand E and the G below:
| E | ||||
| G | E |
That version has a pitch ratio 6/5. The other version is the combination of the righthand E above and the G. That version has pitch ratio 32/27. The notes below represent various inversions of this minor third. The pitch ratio is given for each chord.
They sound as follows:
You may wonder why we would ever use the 32/27 minor third if in almost all cases the version with pitch ratio 6/5 sounds better. The simple answer is: if we suppress 32/27 minor thirds, syntonic commas pop up. So we better be reluctant to suppress 32/27 minor thirds. The goal of this experiment is to strike a balance between 32/27 minor thirds and syntonic commas.
The first step of automatically assigning pitches to notes is preparing the input: for each chord in the score determine the allowed shapes in the matrix. In this experiment we shall avoid some shapes of triads, namely those that have minor thirds but none with pitch ratio 6/5. For instance, for the chord E-G-A, the following shape will be considered, because it has a minor third with pitch ratio 6/5:
| A | E | |
| G |
But the following shape will be ruled out:
| G | A | E |
The reason is that E-G is the only minor third in this chord and in this latter shape has pitch ratio 32/27.
We apply this restriction to triads, but not to tetrads and beyond, under the assumption that those would be dissonant enough to mask the beating of minor thirds with pitch ratio 32/27. (This assumption is not generally true though. Check Sleep.)
Results for this experiment are available for the following pieces: