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Just as people have analyzed texts to determine letter frequency, what is the most frequent scale degree? (For typical pieces with a key signature). I'm looking for a count that's treats all note-values equally, e.g. one quarter note C and one half note C each count as one note.

The only thing that I found was https://www.hooktheory.com/blog/music-theory-analysis-1300-songs-for-songwriting-part2/ which only lists chords and doesn't have a direct a correspondence to scale degrees' frequency. What have been the results of such calculations in the past, if there have been any?

I don't have any particular genre in mind, though I realize that restricting to a certain body of music is necessary to conduct such an analysis. A possibility that comes to mind is https://abcnotation.com/tunes , as well as various MIDI datasets for e.g. classical music and jazz. Again, I don't really care what genre was chosen.

The reason I ask is because I am devising my own musical shorthand and would like to make the most frequent scale degrees the fastest to write.

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    The question is not well defined to me. What specifically do you ask about and for what purpose? Like which scale degree appears the most often in the melodies? Including passing tones or only those on downbeats? Treating beat 1 and 3 the same or not? What about the first note of the melody? It is often very significant. Finally, if better defined, that would perhaps make a good topic for a Master thesis, rather than SE answer. Dec 14 '20 at 2:00
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    Yet again, another good music theory question, closed. I know of only one corpus study, but it covers scale degrees in common practice and rock music sets, davidtemperley.com/wp-content/uploads/2015/11/…, you may find other studies, but I don't know any - off the top of my head - about scale degrees. Dec 14 '20 at 15:25
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    I thought I voted to close this on the grounds that it was not clear, and commented on this thread. Yet I see my comment deleted and the close vote seems locked.
    – user50691
    Dec 14 '20 at 16:32
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    It is not clear whether you are asking about "degrees" like tonic, dominant, etc or frequencies like 440Hz etc. We have a pretty good short hand (1, 2, 3, 4, 5, 6, 7, 8). You can't get much simpler than these and they are easy to write. Since you want this to be genre agnostic I'd say it's an altogether inappropriate question since the results will necessarily be genre specific. But, since keys are chosen based on abundance of notes I might guess that "1" is the most commonly encountered note in any key.
    – user50691
    Dec 14 '20 at 16:35
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    Since the core idea is a rapid short-hand notation, the note-frequency issue can be obviated by using a notation where all symbols are equally quick to write. I recommend assigning a symbol to every pitch so that there's no question of how to notate modulations or chromatic alterations. If typing: [0 1 2 3 4 5 6 7 8 9 t e] or [a s d f g h j k l ; t n]. If hand written: [(low dot) (high dot) (low circle) (high circle) | - / \ ( ) U ^].
    – Aaron
    Dec 14 '20 at 18:13
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One initial comment: I don't really see the connection between the question "What is the most frequent scale degree?" and the purpose "devising my own musical shorthand and would like to make the most frequent scale degrees the fastest to write"

The standard I have seen for indicating scale degrees is a circumflex over the scale degree number...

enter image description here

...but it's hard to type that so I have seen the circumflex as a prefix, like ^1.

Of course Roman numerals I II III... have the same scale degree meaning but that context is specifically to mean the degree is a chord root. The circumflex is usual for of a melodic context.

I don't think you necessarily need to know about the frequency of scale degree to take advantage of that scale degree notation for a quick short hand system. Maybe something like: ^5|G:^6 ^5 ^1|D7:^7... for a sketch of chords, bars, and melody degrees.

But, if you want to look for objective info about frequency of scale degrees, try looking up corpus studies. That is where a researcher encodes a large corpus (body) of representative music for the researcher's interest and then does quantitative analysis on that data.

This one study came to mind immediately: Temperly, de Clercq. Statistical Analysis of Harmony and Melody in Rock Music. It's a scholarly article so it describes their methods and the body of music used. It includes a few graphs like Scale-degree distributions in common-practice music, rock harmony, and rock melody. Spoiler alert: the authors come to this conclusion: In all three, the most frequent scale-degree is 1, followed by 5.

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  • This literally does not answer the question. It provides a shorthand for notating notes and intervals, which many comments do as well. But where is the answer to the question "what notes are most frequent"?
    – user50691
    Dec 15 '20 at 1:10
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    @ggcg Perhaps you gave up on the answer before getting to the very last sentence: “ In all three, the most frequent scale-degree is 1, followed by 5.” Dec 15 '20 at 8:01
  • Since this is for writing out certain notes that will only translate to pitches in a certain key, using a circumflex seems a waste. What's wrong with pure numbers. And since 1 (root) will most likely be the most common, what could be easier to write than...1?
    – Tim
    Dec 15 '20 at 8:20
  • It does not answer the question. It merely quotes one source and the op wanted a non genre related answer
    – user50691
    Dec 15 '20 at 11:10
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    @ggcg. No. "non-genre" wasn't specified in the question. This "...I realize that restricting to a certain body of music is necessary..." is how the question was worded. And the study provides an answer from two bodies of music. Dec 15 '20 at 14:52

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