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

https://mathoverflow.net/questions/404259/how-to-measure-perceived-note-similarity-in-music-simplicity-of-ratios

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:

https://www.kaggle.com/musescore1983/measuring-note-consonance-with-psd-kernel

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

mathoverflowUser
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  • Are you asking what is a consonance and how to order intervals from the most consonant to the most dissonant? – user1079505 Sep 19 '21 at 17:29
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    Consider e.g. https://music.stackexchange.com/questions/21940 – user1079505 Sep 19 '21 at 17:31
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    Also: https://music.stackexchange.com/questions/4439/is-there-a-way-to-measure-the-consonance-or-dissonance-of-a-chord/115240#115240 – user1079505 Sep 19 '21 at 17:33
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    And also: https://music.stackexchange.com/questions/67061/consonance-dissonance-of-5th-according-to-the-explanation-of-4th What I'm trying to show here that there are various methods to classify intervals, and also it depends on the musical context. Concerning your table, I don't understand the order: major 2nd, major 7th, minor 7th, tritone, minor 2nd... – user1079505 Sep 19 '21 at 17:38
  • Thanks for the detailed references. I will have to look at it in more detail! Thanks for your help. – mathoverflowUser Sep 19 '21 at 17:54
  • @user1079505: Thank you. That is a lot of material to read, which I will do in detail. – mathoverflowUser Sep 19 '21 at 18:00

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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."

Bennyboy1973
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  • 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. – mathoverflowUser Sep 19 '21 at 19:25
  • I think by "perfect 7th" @stackExchangeUser means "perfect 5th" which has 7 semitones. – user1079505 Sep 19 '21 at 20:03
  • @user1079505: Yes sorry for being unclear or using the wrong words. – mathoverflowUser Sep 19 '21 at 20:06
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    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. – Bennyboy1973 Sep 19 '21 at 22:01