Here are some ideas about Monk on or around his 100th birthday. People talk to me about Monk sometimes, or I read something they've written, and I tend to think I know a tiny bit more about Monk than other people (aside from jazz musicians or musicologists expert in him, of course), having listened to him since around 1975. Someone tried to tell me recently that Monk could not read music. This was uncomfortable for me because I don't like to show up ignorant people in person and I was accused of "pissing on my parade."
I tend to emphasize not his eccentricity but his musical uniqueness, though you could argue his uniqueness as a musician stems from the fact that he is not a conventional thinker.
I don't try to compose like Monk when I write music, because my mind moves in much more conventional directions. I did write a contrafactum to Bemsha Swing once though.
1) Bebop but not bebop. Stylistically, Monk is not very boppish in his playing if we think of Bud Powell as the standard way of playing in this style. Every other bop pianist sounds like Powell more or less. Monk's playing is one of a kind. You can tell that he began as a stride pianist, because he can revert to that. You can tell that Monk felt time differently than many other musicians, and his use of rubato can be extreme. Because he was not a conventional bop pianist (though a founder of bop) his influence is felt in the jazz avant-garde.
2) Humor. A lot of people don't hear musical humor because it can be relatively subtle. Monk can be very funny. There's a version of "Lulu's Back in Town" on a wildly out-of-tune piano that's hilarious. Tunes like "Brilliant Corners," "Friday the Thirteenth," "Ugly Beauty" or "Boo Boo's Birthday" are very witty too. Playing a standard in a Monk style can be inherently funny because of the disparity between
3) Melody. As a player and composer Monk is all about the melody. He has wonderful melodies like "Monk's Mood" or "Crepuscule for Nellie." I like Andrew Hill a lot, a pianist-composer similar to Monk in some ways, but Hill's melodies are not catchy the way Monk's are. As an improviser, Monk likes to embellish the melody rather than play endless scales over the chord changes. Ornette is another great melodist, of course, whose music would be played more if it had standard chord changes.
4) Structure. He liked to work in 12 bar blues and in 32 bar song form. He could do everything he needed to do without modifying these forms. "Bemsha Swing" has a form even simpler than a 12 bar blues. Harmonically, he could be simple or very complex, depending on the circumstances.
5) Ugly Beauty. Monk's all about the beauty of the music. We can hear lyrical tenderness in "Round Midnight," "Crepuscule for Nellie," "Reflections," "Pannonica" or "Monk's Mood." But what about the dissonance and percussiveness? That just deepens the beauty by making it more complex.
6) Emotion and Intellect. Barthes talks about the dichotomy between the head and the heart as a cornerstone of a kind of bourgeois ideology. I don't know if I am responding to Monk with the thinking part of my brain or on an emotional level, because his music transcends that division completely.