Questions tagged [music-theory]

For questions on mathematical problems arising from music theory, e.g. scales, harmonies, rhythms, and compositional techniques (such as dodecaphony or minimalism).

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Using lower note ratios to create a reward function for music reinforcement learning algorithm

I am creating a music learning reinforcement algorithm. Would a good reward function reward highly movements that result in ratios with the lowest integer numbers used within a chord and between the ...
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18 votes
4 answers
2k views

Kolmogorov complexity of classical music

I have an impression that classical music pieces are more "structured" than white noise and more "complicated" than the soundtracks of the Billboard Hot 100 songs. So assuming we ...
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How to measure perceived note similarity in music / simplicity of ratios?

I have discovered a method to measure the similarity of two successive musical notes which I wanted to share with a question: It is known in music theory that two successive pitches $a,b$ which sound “...
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205 views

A new method for processing music scores?

I have developed a method and python script: https://github.com/githubuser1983/algorithmic_python_music which allows the user to input a midi file and then chose a few numbers as parameters, and the ...
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8 votes
7 answers
823 views

Techniques from number theory used in algorithmic compositions?

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 ...
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3 votes
1 answer
130 views

How to identify the two copies of $D_{24}$ in the homomorphisms of the 2 musical actions? [closed]

Let $S$ be the set of minor and major triads. Two sets of actions are defined on the set: 1) Musical transposition and inversion; 2) P, L, R actions $$P(C-major) = c-minor,$$ $$L(C-major) = e-minor,$...
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85 votes
8 answers
10k views

Books on music theory intended for mathematicians

Some time ago I attended a colloquium given by Princeton music theorist Dmitri Tymoczko, where he gave a fascinating talk on the connection between music composition and certain geometric objects (as ...
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4 answers
536 views

Survey papers of results (relevant to mathematics) produced during research on the relationship between mathematics and music theory

It is well-known that there is a relationship between music and mathematics, and there are many references that explore this topic (for example, Benson's book). However, I would like to ask if there ...
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17 votes
1 answer
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Relation between math and piano music

What, if any, is the relation between Cantor's function and Ligeti studio: Devil's Staircase?
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36 votes
2 answers
3k views

A weaker version of the ABC conjecture

I posted this question over at Stackexchange, where a user informed me that it was probably more appropriate for Mathoverflow. Here's to hoping that the answer is out there: The ABC conjecture states ...
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4 votes
0 answers
273 views

What is known about orbifolding ordered groups and sets? Who has been involved? Links to Lee metrics?

In mathematical music theory several ordered groups are considered. Some examples contain the frequency space or Tonnetzes. Other groups (commutative and non-commutative ones) are discussed by Dawid ...
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5 votes
2 answers
464 views

Computer platforms for combinatorial search problems/mathematical music theory?

I'm finding programming various combinatorial searches (connected to mathematical music theory) in a general purpose computer language tedious, so I'd like pointers to computer platforms/environment ...
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8 votes
2 answers
628 views

What does the space induced by this unusual metric(?) on R/Z look like?

The motivation for this question comes from music theory. Dmitri Tymoczko models "good" voice leading as minimizing distance between pitches in successive chords. While this theory works well for ...
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