I understand your reasoning, but it is based on incorrect assumptions.

The first assumption you make is that we actually know how pre-18th century music sounded like. We have guesses, some better than others, but we know that we are likely wrong.

The second assumption is based on the idea that music somehow improves in complexity and quality. We have many scores that have survived the test of time, but these provide a huge selection bias. Only scores that were popular, widely copied and preserved due to timelessness are currently available. Musical ideas that could not be expressed using the scoring techniques didn't survive. Nor did musical ideas that didn't mesh with following eras. Therefor, what we see is a pattern of scores that are popular (of low complexity), easy to write (of low complexity) and similar to following eras (of lower or equal complexity). See the selection bias?

Lastly, and more concretely: 18th century musicians didn't suddenly start caring about bending time. They started caring about sharing musical ideas outside of their direct sphere of influence (printing press), so they understood the need to add extra markings on sheet music, such as rubato and accelerando.

And saying you try to understand jazz is akin to saying you try to understand philosophy. It cannot be done, too much has been written and one cannot understand all standpoints simultaneously. Try to understand a specific era, like Bebop, or a specific musician, like Chick Corea.

Good point about loss of information from historical, technological and cultural restriction. My reasonning is based on what people today call music theory in most schools and below a certain level. Surely Berklee talks about all kind of stuff.

I don't think all was lost, things that weren't writeable could be passed orally as virtuoso techniques that weren't deemed useful to be written for the average player anyway. See how Spanish guitar technique has survived time.

My attempt at understanding jazz is that it revolves rhytmically around swing. And that core swing can be described through a tinier and principled abstraction rather than a crude ternary feel mark left for the student to figure out. Also from trying to make sense of jazz music without the traditional formalisms (I barely know two modes, and never learned that many progressions). There are some tiny tiny notes in Herbie Hancock playing that shifts the whole world. I'm sure "the" truth lies in there. see the finale solo https://www.youpak.com/watch?v=95TAfOWJKwg

This is a thread around drumming, but there is also the mathematics of intervals, harmonies, dissonance, resolution...

Music is not _like_ mathematics, music _is_ mathematics, it’s just a different way of expressing it.

Could you elaborate please? To me, music is entirely a subjective aesthetic experience which leverages our shared history to elicit certain emotional responses. I view mathematics as the opposite of that, being objective, where everything is derived from explicitly stated axioms.

I can understand if you say that music (in general, or at least in the west) conforms to a system of patterns and relationships, but I question whether those patterns and relationships are integral to the experience of music. I suspect that they are more a result of our expectations than a fundamental property of music.

It's missing the inertia part I was trying to convey. This is rarely taught. Except for a crescendo flag on the score. But to me it is essential to what music is. Intervals, harmonies seem like side effects (I'm exagerating).

I don’t know if this is wha you mean, but when listening to music, the human brain is constantly making predictions about what will happen next. Jerry Coker explains that the quality of the experience lies in the balance between the familiarity of being right and the surprise of being wrong.

Thus, when listening to syncopation, you constantly comparing what your brain hears to a steady 4/4 it ‘expects' to hear. And when listening to a soloist improvise, you are comparing the notes your brain hears to the melody it ‘expects’ to hear.

This is obviously not the only effect, not by a long shot, but is that what you mean by “inertia?"

I've heard this idea too. The inertia is the physical incarnation of the predicted motion. I'm talking about playing the music, not only listening, it makes a difference. Talking about syncopation in terms of overall time signature is only partially valid. You can syncopate by altering an accent place while still on the same time. Think a dead note on drum or bass. It totally alters the feeling. My understanding is that A B C D isn't interpreted the same as A b c D, because there's a variation of energy between these for notes. It's implied in most music. For instance Rock is 4/4, Funk is 4/4 but it's not rock.. where's the difference ? implied change in energy (Rock is almost linear, a smooth wave; funk is superficially linear, close inspection reveals very weak and short changes). Same for jazz, to swing a beat you can't just play at the right time; it has to be the right momentum. Otherwise it will be flat aka no swing. It's hard to describe, the best I could find was in physics, momentum and internal system energy. The inertia is in your wrist and stick, it's always flowing back and forth between cymbals and your fingers. The change of perception of the listener comes from the player understanding of this.

There's a lot of "feels" that you cannot represent without that. But these aren't studied formally, funk, latin, caribean music. Jazz is but I think the people studying jazz don't explain everything because they're talking among themselves and already have internalized all this. So they just write "swing this" above a measure and the cats will deal with it.

oh: and I just thought of something else. The idea of prediction; since I relate everything to physics, often feels similar to a sense of internal balance. I mean your body position, as in not tripping. Syncopated music often feels like falling. Maybe it's synesthesia but considering that all these music were linked to parties and dance I think it's not far fetched that our musical prediction is the same as the one that tries to predict how to balance movements and body.

All this stuff can be precisely measured and explained (and has been - there are a million drum instructional videos that get academic about how to play various styles).

Swing feel isn't a closely guarded secret among jazz musicians - it just isn't quick to explain. There's a sliding scale of the ratio between the first and second eighth note, where at slow tempos it's 2:1, and at fast tempos it's 1:1. The exact ratio at a given tempo is something that's passed down aurally. There's also a harder articulation on the second eighth note. There are other nuances too, but those are the most important ones.

Ha well, I didn't see them all, I did see quite a few and it was never explained at all. At best a few slowed down classical swing patterns. But it was all imitation and no deeper meaning.

The 1,2 ratio is nice, but I use to see response curves... a bit like interpolated splines...