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This is a more mathematical question. Suppose I have a large representative set of Western music in C major. If I count the occurrence of the individual notes, what is distribution of the notes?

I would assume, that since the music is in C major, notes like C, E, G, F, A would have a much higher percentage than notes like C#, F#, or A#.

What is the percentage of individual notes in C major music?

(I am aware that this is a complex question. Taking duration into the consideration would be even more interesting. But I would be happy about any numbers/papers/sources to have a approximation)

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  • Yes, i am aware that I could generalize the question, asking about the distribution of intervals given a key. Such an answer would be great as well. I just thought that C major is a more direct formulation.
    – hr0m
    Sep 12, 2021 at 22:49
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    This question is fundamentally unanswerable without setting limits on all the different variable that can affect the count. As one example: If a piece is in C major, but modulates at various points, do the notes in the modulatory sections get counted? What about a piece in some other key that modulates to C major? Do we count pieces written before 12-TET was invented?
    – Aaron
    Sep 12, 2021 at 22:54
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    If it helps, i would limit it to 12-TET music of pieces in C major without modulation. You know, the more boring stuff. As I said, pretty much any analysis would already help me.
    – hr0m
    Sep 12, 2021 at 22:56
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    You might find this article interesting: it asks your question in reverse. Pitch-Class Distribution and the Identification of Key
    – Aaron
    Sep 12, 2021 at 22:59
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    There also might be some interest in Normality Test for Distributions of the Music Metrics. (Disclaimer: I found this via Google search. I can't vouch for its veracity.)
    – Aaron
    Sep 12, 2021 at 23:02

1 Answer 1

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There's an article, "Pitch-Class Distribution and the Identification of Key", David Temperley and Elizabeth West Marvin, that give some information along this line. I got it on JSTOR but it was published in "Music Perception" which journal you might have access to. enter image description here

The distribution varies depending on the overall style (Baroque, Classical, Romantic, popular, jazz, etc.) There has been lots of work on the subject but much is only available from university libraries or behind paywalls.

There are some ambiguities in the original question. One can ask, "What is the distribution of tones by the number of occurrences? " or ask, " what is the total duration of each note?" These are not identical questions. The figure consisting of a chain of off-beat quarter notes (or half notes as in fourth species counterpoint) may be split into pairs of eighths or quarters respectively. These have the same harmonic and melodic significance but the counting methods may not agree.

Likewise, the existence of enharmonics matters from the point of view of the musical structures. An Ab7 chord is Ab-C-Eb-Gb (and normally resolves to a Db chord of some type) whereas the German Sixth Ab-C-Eb-F# usually resolves to a C64 chord. It's written with an F# to indicate the next note is G. It's a complication that you might wish to look into.

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    A perfect answer. Thank you for your contribution. Yes, you are right, my original question is a little naive, but for my purposes, this is more than enough.
    – hr0m
    Sep 13, 2021 at 6:49
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    if you go to the hooktheory web site, you can find stats for pop songs and the author is very accessible; he gave me a dump of his database one time I wanted to do some analysis.
    – Thomas
    Sep 13, 2021 at 12:41
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    Very interesting that the fifth is more common than the third in major keys, but their prominence is reversed in minor keys.
    – Michael Seifert
    Sep 13, 2021 at 13:10
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    @MichaelSeifert: I don't know how to classify them, but I think there are multiple flavors of minor. Some minor-key pieces would make musical sense if the key signature were changed to the parallel major, but some wouldn't.
    – supercat
    Sep 13, 2021 at 17:03
  • Although the graph for the major scale shows the expected pattern of diatonic notes occuring more often than notes which are foreign to the scale, I'm scratching my head about what the numbers on the y-axis are supposed to mean. In a naive interpretation where 0 means "never occurs", non-diatonic notes seem to be massively overrepresented. The major seventh, for example, seems to be only a bit more common than really strange notes (like b6 or b2) for which I can't name a single example piece of music off the top of my hat.
    – Marc
    Sep 14, 2021 at 12:27

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