Perhaps you have tried the Society for Mathematics and Computation in Music (SMCM) http://www.smcm-net.info/

Thank you for the recommendation. Unfortunately, I do not see that the SMCM addresses the question of topography of music.

There is a paper in the proceedings of the Third International SMCM Conference that refers to the topography of music.

Could you link the paper or give its name?

Try https://books.google.co.uk/books?id=P1YOBwAAQBAJ

Thank you so much for the link. Very interesting.

The most difficult problem of creating music topology is incorporation of psychophysics of tonal relationships into a robust mathematical model. The tonal relationships are the foundation of the music that we can sing and dance with (Bach, Schubert, Ravel) as compared to aleatoric methods (Berg, Stockhausen, Xenakis). Neither of the papers touches on this very difficult subject of integrating the acousmatics and mathematics.

Perhaps, if you have not already done so, you could attend a SMCM conference and present on that problem of incorporation of psychophysics of tonal relationships into a robust mathematical model. That way, you might find some people who might have ideas on ways to approach the problem.

The problem needs a cooperation of top-noch topologists, musicologists, and music psychologists. Tonal space is fundamentally unlinear. While notes in a scale are arranged lineary frequency-wise, the tonal relationships among the notes is a different story.

Dear M.N. Korsakova-Kreyn,

I just want to present my material as a mapping of musical notes into geometric images Appassionata.pdf using Beethoven's "Appassionata" as an example.

Is this mapping relevant to your topic?

Dear Dr. Fedulov, thank you for the response.

My question was about visualization of time-tonal relationships, which is true to the psychophysics of music perception.

Obtaining mathematical representation of a complex structures or processes when using top-down approach can be challenging. Take the planetary motion fro example; if you try to derive the mathematical representation of it, without knowing/considering the Newtonian gravitational equation can be tricky; knowing the gravitation equation helps to take a down-top approach, where you can model not just the planetary motion, but the motions of even the bigger and more complex structures in the space.

Now, I would speculate that the same pattern applies to the musical structures. Until recently we did not have any theory that explains (at least partially) music at the lowest detailed level, so we were not able to apply down-top modeling.

Luckily, recently in 2017, we have published a paper that attempts to explain consonance, where by using computational neuroscientific model, we were able to reproduce precisely and completely the consonance pattern (Helmholtz’s order of intervals by consonance) for the first time ever. More precisely, we show that ANY system featuring Hebbian neuroplasticity will be able to reproduce some form of a consonance pattern. We go even further, by citing evidence provided by other authors, offering a hypothesis that suggest how the consonance pattern translates to pleasantness (or non-pleasantness for the dissonant sounds).

Therefore, (if) the consonance pattern is produced as a result of a very simple neural network calculations, when feeding with simple input stream, that should be enough for a math expert to derive a purely mathematical model (assuming such is possible).

Here is a link of the paper, and feel free to contact me for more details: https://doi.org/10.1016/j.bica.2017.09.001 ( or the free preprint: https://auditory.solutions/publications/Consonance1preprint.pdf ).