Use PUCT MCTS to find harmony according to a cantus firmus.
Rules and environment based on the book "The Study of Counterpoint", from Johann Joseph Fux's "Gradus Ad Parnassum", translated by Alfred Mann.
Repo with latest code can be found in: https://github.com/kastnerkyle/exploring_species_counterpoint
To hear the midi examples without installing packages or running locally, see http://kastnerkyle.github.io/posts/miditests/#example
This repo only shows 3 voice results, but the analysis code covers cases for 2 voice species counterpoint as well.
Three and four voice species counterpoint will be continued in exploring species counterpoint repo above.
See trace_0.wav for an example rendering, using Timidity. All .mid and .ly files are included in saved_*
For viewing .ly files, in Linux lilypond is usually used, the pdf output can be created using lilypond file.ly. .mid files require a midi player, in Linux timidity is a common choice. After installing timidity, the audio can be heard using timidity file.mid.
To run the code (tested in Python 2.7), do python three_voice_pucts_mcts.py. This will begin running the planning algorithm against each cantus firmus from the set of three voice, species 1 examples from the book. After completing all of these traces, it will write out lilypond (.ly) files and midi files (.mid) showing the results
Note that the midi renderings choose standard keys and offsets, but the format we use for a cantus firmus is based against the diff to the last note (generally the tonic note). Some of the renderings which go very low cause issues with midi players like timidity - particularly cantus firmus 4 and 5.
The effect of pitch on perception of harmony is complex, but the pitches for rendering were chosen to be near the center of the scale. Adapting based on the chosen pitches is something we plan to do in the future (so it can sound a bit better).
For the exceptionally willing, changing the Timidity soundfonts to fluidsynth can sound a lot better than the standard timidity piano sound. I have some loose instructions in this link http://kkjkok.blogspot.ca/2018/04/reconfiguring-timidity-for-different.html.
Kyle Kastner | email: kastnerkyle@gmail.com | @kastnerkyle