Music theory for nerds

> 1. Why do we like pieces when played forward but not backward or inverted?

Why do we like text when read forward, but not backward or inverted?

There are, of course, works that are palindromic or otherwise written to be read/heard backwards, but most of the time that kind of global transformation tends to ruin the "spelling"/"narrative".

> 2. Why do certain sounds evoke certain emotions?

Just like text, evoking emotions needs some sort of narrative. A story isn't a single fact or statement (or a single sound); it's about how those facts (or sounds) flow or change.

In music you might hear a brief bit of new melody that foreshadows something big later in the song. A clear rhythm or melody might be repeated to get the listener to follow along only to have it cut short at a key moment to deny the obvious resolution (similar to a melodrama that suddenly reveals a new twist in the plot as a cliffhanger).

It's the story you tell that matters, and it takes a skilled composer to put sounds together to make a song emotionally evocative. The song that is mostly a 16 bar loop probably sounds boring (but not always!), while the song that introduces the same 16 bars and then plays with variations of it to create an initial conflict, rising action, and a climax is probably a lot more interesting. An obvious example might be Mozart playing Salieri's march in Amadeus[1]. It's not just that he embellished the simple march; Mozart adds a lot of variations that culminate at a comic ending.

[1] https://www.youtube.com/watch?v=P5n0pkNpDWY

Those qualities aren't universal in people and as such what you are describing is more of a study of culture than musical theory. You would probably enjoy a music appreciation course, and possibly one taught by a philosophical professor.

You can't read ahead easily with it. Totally useless.

Sounds like... And is it? ;)

In terminal run vimtutor. The sound will change.

Does anyone know of a similar tutor for sheet music?

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)). 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) 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.