In a question at Mathoverflow, I asked about how to measure the similarity of two musical notes:


The method is described here, and I will link to it, since I can not write math formulas here: https://drive.google.com/file/d/1EhXpiG1XremKbdS5AENZT3TvBV8JAwM8/view?usp=sharing

Looking at the second matrix from a musician perspective: Is the ordering ok as it is there or not?

Edit: For those interested in algorithmic generation of music, here is a csv-dataset I released using the similarity functions for consonance (pitch) and volume, durations, is-rest:


Related answer: https://music.stackexchange.com/a/4441/74955


The second reference lost me at "We see in the matrix above that a perfect 7-th"

Also, the writer didn't do much diligence (or show a basic knowledge of music theory), because there have been robust theories of harmonic density and consonance for decades.

That being said, the order seems approximately correct to me. But the word "similar" is a misnomer. All pitches are similar in that they represent similar wave shapes but stretched over a different period. Better might be "consonant."

  • thank you very much for your answer. The word "similar" refers to a mathematical function / term, but you are right, I mean consonant in musical terms, and yes, I have no previous training in music. Sep 19 '21 at 19:25
  • I think by "perfect 7th" @stackExchangeUser means "perfect 5th" which has 7 semitones. Sep 19 '21 at 20:03
  • @user1079505: Yes sorry for being unclear or using the wrong words. Sep 19 '21 at 20:06
  • 3
    Oh, I see this isn't a link to a supporting source, this is YOUR paper. Well, I have to say, if you aren't trained in music, and you came up with that list on your own, then that's a pretty good achievement. But you need to watch a YouTube video about the naming of intervals or something. Sep 19 '21 at 22:01

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