TITLE: Techniques from number theory used in algorithmic compositions?
QUESTION [8 upvotes]: I have been experimenting with number theoretic techniques to get some algorithmic compositions. I use python (mingus) to create the midi, import it on musescore 2 and have the corresponing score.
The method is based on a few ingredients:

I use C-major or C-minor and use a symmetric function $f(a,b,c,\cdots)$ and plug in numbers $a,b,c,$ from $1 \le x \le 31$ or some other intervall and compute $f(a,b,c,..) \mod 8$ or $\mod 5$ to generate the pitches.

To generate the rhythms / bars, I use a technique to map natural numbers to binary trees (divisorTree, sumTree). This way I have some control over the rhythm fast / slow by plugging in different numbers.

In a mixed ensemble I use binary digits to determine at which bar the instrument plays. This creates attention to the listener, so that he/she asks himself/herself, what comes next.


Which other algortihmic techniques from number theory do you know which are used for algorithmic compositions?
Thanks for your help.
The scores can be found at:
https://musescore.com/user/37663311
Edit:
I use e new technique to create a piece of 48 min with 8 instruments and 650 pages scores: (I hope you enjoy:)
https://musescore.com/user/37663311/scores/6651858
Another edit:
Voronoi diagram / Delaunay triangulation of pitch consonance similarity, as measured with the kernel $k(a,b) = \frac{\gcd(a,b)^2}{ab}$:
https://www.reddit.com/r/musictheory/comments/tcamot/an_image_of_pitches_for_pitch_consonance/

REPLY [3 votes]: You may add this recently published paper to your reading list.

P. Špaček and P. Sobota, Musipher: Hiding information in music composition, Rad HAZU, Matematičke znanosti, Vol. 25 (2021), p. 161-179, full text online.

Abstract. In this paper, we present a new way of hiding information. We store the information directly in the process of composing music,
based on musical theory. We created an algorithm to produce music based
on binary string, where each bit is transformed into a music composition
decision. We follow simple rules to make music, which sounds good. We
conducted survey to find whether our solution works, and found promising
results of our approach.