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I'm currently working on a probabilistic, procedural music engine and although I could choose relatively decent arbitrary distributions, I'm curious as to whether or not there have been any formal/academic studies that have looked into this?

More specifically, I'm hoping for links, references or statistics directly from Musical academics/researchers that give a breakdown of data gathered from popular music. I'm primarily interested in Western popular music, but would also be interested in other forms of popular music.

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    The most common (popular?) is 4/4, but that's in the Western world.That's why it's called common time, although the 'C' at the beginning isn't shorthand for common. And that is often sub-divided into different 'feels'. The term 'popular music' is possibly too wide reaching, making the question too vague ? – Tim Nov 2 '14 at 9:26
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    Musicians are altogether not interested is accumulating statistics of how many times things happen. We are interested in sounds, why they happen, and how they make us feel. This question is impossible to answer as it is impossible to certifiably quantify every piece of music written. It is akin to asking "what is the most popular number of tree rings" and asking for evidence from every tree in the Americas. – jjmusicnotes Nov 2 '14 at 15:02
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    @jjmusicnotes the header of this stack exchange states "Musical Practice". The musical practice I am involved in is procedural composition, to which probability and statistics can play a huge role. > "...it is impossible to certifiably quantify every piece of music written" You seem to have misinterpreted my question - I would never expect to see stats for "all music". However like any strong research, I'd hope that a lot of data was collected (i.e. every song to enter the top 100 for the past X years). – mindTree Nov 2 '14 at 15:58
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    @jjmusicnotes as an example of similar research, the folks who run this site have analysed and documented popular chord progressions (from thousands of songs) in order to learn about composition and generate chord progressions using Markov Chains. – mindTree Nov 2 '14 at 16:02
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    @jjmusicnotes Actually, countless musicians I know (me included) are interested in this type of information. It can have a significant answer with a big enough sample size, and the information can be categorized. The scenarios you are painting are too rigid. I understand that some musicians might not be interested, but saying that "musicians are altogether not interested" is just wrong. – Jamm Nov 3 '14 at 16:11
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You might want to check out David Temperly's work:

http://theory.esm.rochester.edu/rock_corpus/

He's been doing corpus studies on reasonably large samples of pop-rock music, and has published on it as well.

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