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Generative Adversarial Networks can generate realistic photos of people, such as thispersondoesnotexist.com. I wonder whether one can train an artificial intelligence on a batch of plain solo melodies (no instruments) and ask it to produce a new and similar one.

This article suggests the techniques require a lot of work and are still young:

We have explored and evaluated the generation of music using a Generative Adversarial Network as well as with an alternative method in the form of an N-gram model. Our GAN is able to capture some of the structure of single track music. We have accomplished our goal of identifying structural similarities shared across music compositions. However, the music we created lacks coherent melodies and needs improvement.

What is the state of the art in melody generation?

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you do not need ai for that, just a little bit of math / statistics:

audio: https://m.soundcloud.com/user-919775337/sets/algorithmic-reinterpretation

method: https://stats.stackexchange.com/questions/541044/a-new-method-for-processing-music-scores

source code: https://github.com/githubuser1983/algorithmic_python_music/blob/main/12RootOf2.py

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