I'm a jazz musician--it's interesting stuff, there is a whole area of research dedicated to this type of work.
Jazz chord progressions are pretty simple ultimately when expressed in compressed form, but tend to have actual semantics behind them be pretty communicative so I doubt this will cover absolutely everything except the popular works.
You can generate something very close using a formal grammar but you get stuck in the same position as the logicians in Chomsky's time. I've had some really great thoughts about ML approaches, however, with some sort of seq-to-seq approach.
Here, too, the development is moving away from RNN and LSTM in the direction of Transformers. One of the most promising algorithmic composition projects I recently came across is https://openai.com/blog/musenet/.
If you're interested in this sort of grammar application, I created a project a while back that uses a generative grammar to connect LEGO bricks into models:
Interesting, My holiday code project happened to be generating chord progressions with graph theory and it worked very well (imo) check it out: http://signalsandsorcery.com
This makes me think of the way that an experienced jazz musician can seemingly know an overwhelming amount of standards (common practice jazz songs). Or how jazz musicians are expected to pick up a tune on the spot even if they don't know it. The key to this seems to be that most jazz progressions are based on circle of fifths, or interlocking cells of CoF progressions. This would imply that there is a grammar of jazz chord sequences that experienced musicians use to play or fake a massive amount of repertoire without having to cram rote learning every day.
Jazz guitarist here, and yes. One of the nice things about the instrument is that a relatively small number of forms for chords and scales are transposable up and down the fretboard, so once you burn the usual patterns into your head (iim7-V7-IM7, etc.) reading a new sheet usually doesn't take too much work.
Most pop music is even simpler, as illustrated by Axis of Awesome.
Have you explored Barry Harris and his diminished sixth approach to jazz? I'm still clawing through it, but it seems to simplify the amount of chords you play to only 2 and then defines what variations will consistently sound good.
Yeah, diminished 6th system basically “fixes” classical music theory IMO. Like, classical music theory has to bend over backwards describing very common and pleasant groupings of chords (think Debussy), but in BH stuff, by adding an extra note to the major scale, now all of that stuff is not only easy to explain it’s in fact very natural. What I like especially about it is how all the very diatonic stuff ends up being slight outliers (ie “borrowing” notes from neighboring diminished chords), while the combination of maj6 + dim is the standard. It creates very pleasing sounds.
I haven't looked into this yet but is the added note you are talking about like the added note of the Major bebop scale between Sol & La? Or is it the sharp Fa of the Lydian sound?
Yeah, you add a sharp between the 5th and 6th scale degrees, making for 8 notes in total. Then if your harmonize that scale by playing every other note, you end up with alternating inversions of the root maj6 and the diminished chord.
This is the theory behind drop 2 voicings is it not? Being that as you alternate b/w Maj & dim voicings you copy the top note of the RH in the LH, I like to add a chromatic flourish to the LH note and it gives you a very George Shearing sound.
But wait there's more! Not only does this function harmonically, it also functions melodically. The added scale tone makes it so that a chord tone ends up on every down beat when playing in eighth notes. I've actually found that it doesn't matter where you add that extra scale note, you can do it all the way up and down the piano anywhere you like as long as you get chord tones where you want them.
Never done a deep dive on BH but I'm very aware of him. It's funny how theory can seek to reduce down so much, the positive and the negative. Kinda like Shankerian, except I would be much more interested in what BH has to say since Shanker was such an terrible person.
I haven't been able to find much of him teaching directly outside of this series from the Lincoln Jazz Institute [0].
However, this person has compiled a thorough overview of the underpinnings [1], provided you can ignore the diminished quality of the first few videos.
This foray into jazz actually chewed up a ton of my quarantine free time, for better or worse :)
There is an entire chapter, about 20 pages, on Harris's theories in Berkman's The Jazz Harmony Book. It's probably the best harmony book I've ever read because it's extremely down to earth and focuses on worked examples.
This is why I love HN, thank you for these links! As someone who grew up listening to crappy compressed CDs of early jazz recordings I can easily look past the poor video quality.
Trombone also works in a similar way with the slide positions and overtone series. In fact, experienced trombonists will refer to transposing licks up or down the slide or overtone series as fretting.
What's the relation in chord progressions between Jazz and Blues? I only read the article quickly so it might be mentioned, but it's odd that the title says "Jazz" and mostly deals with the progressions known as "12 bar blues". A straight 12-bar blues progression would be recognized as "blues" by any listener, so presumably there is something that makes such a progression sound more like jazz than blues. But what is it? Is it through the number of tweaks added, such as more "jazzy" chords like 9/11/13 chords? Is there something else that distinguishes jazz from blues in a 12 bar progression?
Blues is both a style of music as well as the name of a chord progression (that’s used in that style of music). You could play that chord progression in a Latin or bebop style and you’d be playing a 12-bar blues, but you wouldn’t be playing the Blues.
A fun example: NRBQ has a (classic) song called "12-Bar Blues" with lyrics about playing a "12-bar blues" and demonstrates a 12-bar blues progression inside it but whose tone/style is much farther toward R&B/Rock than the Blues.
The chords don’t need to be different. A jazz blues would also (usually) be characterized by a walking bass and lack of a backbeat on the drums. Thelonious Monk’s “Blue Monk” is an example with pretty standard blues changes.
That being said, there are infinite variations of blues chord progressions in the jazz canon. Some great examples are Charles Mingus’s “Goodbye Pork Pie Hat,” and “Nostalgia in Times Square.”
Then you have examples that are closer to standard blues but with a few substitutions, like Joe Henderson’s “Isotope.”
I think the article focuses on the 12 chord blues progression to show how the rules can turn I-IV-I-V into something which could be considered jazz, by introducing sevenths and substitutions.
And since it's a generative grammar, it also needs a starting point...
All rules have exceptions, but the top two that come to mind is that blues usually start with a dominant 7th chord (for the I) while jazz standards don't, and blues usually has a 12-bar progression while jazz has a 32-bar AABA structure.
I wonder if anyone’s written a parser for this and applied it to a large number of songs. I would be curious to see how often each rule is used. On a related note, I would be interested to know whether the grammar is ambiguous.
Many have. This is more or less how I learn every new programming language. Generative music is really fun and immediate. Anyway, I think the first time I ever saw anyone introduce recursion into music generation was Giles Bowkett's Archaeopteryx. That was way back in the days when Ruby was still young and cool. He did some interesting stuff for keeping a stable clock in ruby using recursion without blowing up the stack, but also managed to use the same technique for generating variations on probabilistic sequences. Pick your language and you will find people doing small projects like this all over the place.
Jazz chord progressions are pretty simple ultimately when expressed in compressed form, but tend to have actual semantics behind them be pretty communicative so I doubt this will cover absolutely everything except the popular works.
You can generate something very close using a formal grammar but you get stuck in the same position as the logicians in Chomsky's time. I've had some really great thoughts about ML approaches, however, with some sort of seq-to-seq approach.