4 ms·

I would love something like that. Any pointer?

Ericson2314 10y ago
A large part of it hasn't been researched very mathematically, to my knowledge. If you google music+grammar you can get some stuff with a linguistic approach, which may be less empirically grounded but certainly a richer theory than the alternatives. And don't get me wrong, science is good but as musician mathematician a richer theory that overreaches reality is much more fun, and besides most of this stuff is cultural not immutable so a wrong theory may become correct if is influential. A few stray ideas that may or not be correct: - Grammar of common-practice harmony is probably largely left-branching (see https://en.wikipedia.org/wiki/Branching_(linguistics) https://en.wikipedia.org/wiki/Branching_(linguistics)). This is why so such music makes a surprising transition, then resolves it, and it's orthodox overall. Music is about where it's going. - For a first approximation rhythm models the rational numbers, because all durations exist in a ratio to other duration. - Now the rational numbers are infinitely dense and clearly humans can't do that. So there is a minimum resolution which has been wonderfully termed the tatum. Whoever did this however may or may not have realized that there may be a few minima whose join (as in lattices, I'm sure it's a lattice but I never leaned which one) isn't realized. E.g. you might have 8th notes and triplet 8ths but never triplet 16ths (the join). - Form has all these stupid names when clearly it's a tree and similar structure repeated on every level. - People sometimes try do do harmony wit a markov model. This sucks because how the chords transition depends on the form, which I believe must largely (needed to be orthodox/fluent) have a fair regular rhythm (avoid those 5-bar phrases). I think something like a ruler function (https://en.wikipedia.org/wiki/Thomae%27s_function https://en.wikipedia.org/wiki/Thomae%27s_function) based on time + transitions would be a much better and relatively cheap model. If all the fancy grammar stuff is legit, then this too would be woefully inadequate. - That said, the "meaning" is definitely in the transitions not the states (production rules in grammar case). A chord with no context has very little meaning (in equal temperament everything can be transposed with 0 informational change except for timbre). Given a key, a chord still has relatively little meaning (also 1 and only 1 key is a reduction, look up "tonicization", there is probably a stack of broad-specific key-like things forming a context). now given a trace of chords, the meaning comes out---tension and release as they say. - For form and rhythm, 2 branching factor is the default. Everything else is extra work. Probably even in West Africa and other places where the polyrhythms are mad good. - Emotional relationship definitely changes over time within a culture. Up to the 18th century major=happy minor=happy was far from universal. This is probably why even in popular culture old music is stereotypically all dark and serious. - The big 5 components of (at least Western) music are (in no particular order) Melody, Harmony, Rhythm, Form, Timbre. Timbre has become more important over time, even before recorded music. Call me a cranky old cultural conservative, but you could say that Western Society is loosing it's collective understanding-of/ear-for Western music, and Timbre is the easiest to appreciate due to its lack of rich structure (as far as I can tell). And of course recorded and synthesized music means we can timbregasm all day.
- Ericson2314 10y ago
  To reveal my biases (if they aren't already clear) I most enjoy Baroque and Renaissance music; and Jazz, its Cuban and Brazilian equivalents, and their direct descendants (e.g. R&B).
- zhemao 10y ago
  > Melody, Harmony, Rhythm, Form, Timbre I think dynamics (or at least dynamic contrast) is also an important element. > Timbre is the easiest to appreciate due to its lack of rich structure It does have a rich structure, we just don't really understand it yet. Timbre is essentially the linear combination of harmonics of a single pitch. You could express it as a Fourier series. But we don't have a good model of how to play with specific timbres, since acoustic instruments don't really allow fine-grained control of timbre.
  - Ericson2314 10y ago
    Fourier analysis indicates there is a huge space of timbre, but not necessarily a rich one. In my experience while timbres can be annoying, they aren't wrong like a an arbitrary harmonic progression is. Harmony being such a minefield is what makes its space so rich.
    - zhemao 10y ago
      Ah, I see what you mean. I guess you can think of timbre as a mixture of dynamics and a very simplified version of harmony in which you can only have intervals of an octave.
      - anentropic 10y ago
        you can have fifths and thirds too I think... you can pluck those harmonics on a single guitar string. I don't know if any other intervals are possible as harmonics... perhaps the ratios for other intervals are too big to make it practical, they are too weak to sound
cturner 10y ago
Book: _How Music Works_ by John Powell. Youtube series: "How Music Works with Howard Goodall". Start with rhythm, then melody, harmony, bass.

A large part of it hasn't been researched very mathematically, to my knowledge. If you google music+grammar you can get some stuff with a linguistic approach, which may be less empirically grounded but certainly a richer theory than the alternatives. And don't get me wrong, science is good but as musician mathematician a richer theory that overreaches reality is much more fun, and besides most of this stuff is cultural not immutable so a wrong theory may become correct if is influential. A few stray ideas that may or not be correct: - Grammar of common-practice harmony is probably largely left-branching (see https://en.wikipedia.org/wiki/Branching_(linguistics) https://en.wikipedia.org/wiki/Branching_(linguistics)). This is why so such music makes a surprising transition, then resolves it, and it's orthodox overall. Music is about where it's going. - For a first approximation rhythm models the rational numbers, because all durations exist in a ratio to other duration. - Now the rational numbers are infinitely dense and clearly humans can't do that. So there is a minimum resolution which has been wonderfully termed the tatum. Whoever did this however may or may not have realized that there may be a few minima whose join (as in lattices, I'm sure it's a lattice but I never leaned which one) isn't realized. E.g. you might have 8th notes and triplet 8ths but never triplet 16ths (the join). - Form has all these stupid names when clearly it's a tree and similar structure repeated on every level. - People sometimes try do do harmony wit a markov model. This sucks because how the chords transition depends on the form, which I believe must largely (needed to be orthodox/fluent) have a fair regular rhythm (avoid those 5-bar phrases). I think something like a ruler function (https://en.wikipedia.org/wiki/Thomae%27s_function https://en.wikipedia.org/wiki/Thomae%27s_function) based on time + transitions would be a much better and relatively cheap model. If all the fancy grammar stuff is legit, then this too would be woefully inadequate. - That said, the "meaning" is definitely in the transitions not the states (production rules in grammar case). A chord with no context has very little meaning (in equal temperament everything can be transposed with 0 informational change except for timbre). Given a key, a chord still has relatively little meaning (also 1 and only 1 key is a reduction, look up "tonicization", there is probably a stack of broad-specific key-like things forming a context). now given a trace of chords, the meaning comes out---tension and release as they say. - For form and rhythm, 2 branching factor is the default. Everything else is extra work. Probably even in West Africa and other places where the polyrhythms are mad good. - Emotional relationship definitely changes over time within a culture. Up to the 18th century major=happy minor=happy was far from universal. This is probably why even in popular culture old music is stereotypically all dark and serious. - The big 5 components of (at least Western) music are (in no particular order) Melody, Harmony, Rhythm, Form, Timbre. Timbre has become more important over time, even before recorded music. Call me a cranky old cultural conservative, but you could say that Western Society is loosing it's collective understanding-of/ear-for Western music, and Timbre is the easiest to appreciate due to its lack of rich structure (as far as I can tell). And of course recorded and synthesized music means we can timbregasm all day.

Ericson2314 10y ago
To reveal my biases (if they aren't already clear) I most enjoy Baroque and Renaissance music; and Jazz, its Cuban and Brazilian equivalents, and their direct descendants (e.g. R&B).
zhemao 10y ago
> Melody, Harmony, Rhythm, Form, Timbre I think dynamics (or at least dynamic contrast) is also an important element. > Timbre is the easiest to appreciate due to its lack of rich structure It does have a rich structure, we just don't really understand it yet. Timbre is essentially the linear combination of harmonics of a single pitch. You could express it as a Fourier series. But we don't have a good model of how to play with specific timbres, since acoustic instruments don't really allow fine-grained control of timbre.
- Ericson2314 10y ago
  Fourier analysis indicates there is a huge space of timbre, but not necessarily a rich one. In my experience while timbres can be annoying, they aren't wrong like a an arbitrary harmonic progression is. Harmony being such a minefield is what makes its space so rich.
  - zhemao 10y ago
    Ah, I see what you mean. I guess you can think of timbre as a mixture of dynamics and a very simplified version of harmony in which you can only have intervals of an octave.
    - anentropic 10y ago
      you can have fifths and thirds too I think... you can pluck those harmonics on a single guitar string. I don't know if any other intervals are possible as harmonics... perhaps the ratios for other intervals are too big to make it practical, they are too weak to sound

cturner 10y ago

Book: _How Music Works_ by John Powell. Youtube series: "How Music Works with Howard Goodall". Start with rhythm, then melody, harmony, bass.