[a_lieb]

For this, I would highly recommend the music theorist/composer Dimitri Tymoczko. His career project is to rebuild the basics of harmony from the ground up from (mostly simple) rules, closely based on how people hear. A catchphrase he uses a lot is "why does music sound good?"

He teaches a set of 2 comprehensive introductory music theory classes at Princeton, and he makes the lecture notes public: https://dmitri.mycpanel.princeton.edu/teaching.html. These are a really underrated resource and have now grown to be as complete as a full intro theory textbook.

There is a serious lack of stuff that teaches music theory from the ground up (how a lot of us hackers like to learn). So much of the confusion around music theory just comes from most theorists using using old, incredibly crufty "data structures" to describe music, when the actual material isn't so hard. Tymoczko is one of the few researchers pushing back on that. He is best known for his higher-level, mathy research (he wrote the first music theory article ever published in Science), but those lecture notes are a great way to get started for anyone who gets frustrated with learning theory the traditional way—which is pretty much everyone.

[munificent]

It's important to remember that there is no real "bottom-up" when it comes to music theory. Sure there's a couple of rough audio-acoustic rules like how simple fractions of frequences sound more harmonious because there's less beating, but those rules are few and don't get you far.

They're equivalent to noting that, say, vowel sounds with similar formants are harder to distinguish. That's true, but there's no way to reason up from that all the way to Shakespeare and Dickens.

The way to look at music theory is that it's like linguistics for sound. It doesn't say "here are the rules that are required to generate X". It says "people have already generated X, Y, and Z (using whatever intuitive cultural processes and/or academic learning they had) and here are the patterns we observe about the result."

People creating music are not outputting new provable theorems derived generatively from the axiomatic rules of music theory. Music theory cannot disprove a song.

People just make stuff they and others like (or don't). And then music theorists try to find the common threads that link it to better understand how the world of music fits together. It is descriptive and not prescriptive.

Knowing theory can help you write music because it can take information you already have in your intuitive "ear" and move it to your front cortex or somewhere more accessible to your hands. But many other musicians skip this step entirely and just connect their hands straight to their intuition though tons of practice. Either path is valid for producing beautiful music.

[eslaught]

Expanding on your comment about vowels, I don't think it's fair to say that music is completely arbitrary in the same way as, say, language. Whereas for language we can be pretty confident in saying that it really is truly arbitrary, e.g. see the birth and development of Nicaraguan Sign Language: https://en.wikipedia.org/wiki/Nicaraguan_Sign_Language

To put this another way, two hypothetical languages developed in complete isolation from each other would be completely different. Two musical traditions developed in complete isolation would be different, but not completely different. There is still an underlying theory that unifies them to some extent. This is why music theory exists as a useful topic of study, even if it is not sufficient for writing aesthetically pleasing music. Whereas I know of no equivalent for linguistics: linguistics is truly a descriptive field, it can only describe what exists, not predict what properties a new language can/should have.

[PaulDavisThe1st]

Your claim about linguistics here is subject a great deal controversy in the linguistics world. The question of whether there is, for example, a deep grammar that is shared across all languages, is a matter of long lasting and deep debate (these days it seems to be leaning to "no", but the debate is not over).

So... I agree with your point about music, but I'm not sure you're right to try to contrast it with language in this respect.

[munificent]

> Two musical traditions developed in complete isolation would be different, but not completely different. There is still an underlying theory that unifies them to some extent.

What theory do you have in mind? My (limited) understanding is that across cultures there is wide variance in rhythms, time signatures, how many tones span each octave and what emotions are associated with different intervals and chords.

[zozbot234]

One can argue whether Tymoczko's approach genuinely leads to understanding theory "from the ground up". His research is best understood IMHO as a worthwhile (in itself) "tweak" and generalization of a previous theoretical approach known as "Neo-Riemannian theory", named after Hugo Riemann's descriptions of tonal harmony (i.e. the general working of 'chords', or rather, major and minor triads). Seen from that POV, it's quite helpful. As a general description of what might go on in a piece of music (even "classical" music)? Maybe not so much.

[a_lieb]

All good points. I don't know much about his actual higher-level mathematical stuff (I'm pretty bush-league about theory overall, really!) But I've heard that a lot of people in the music theory world say it's awfully close to regular Neo-Riemannian theory.

That said, in the Princeton lecture notes, he does seem to start a given topic on fundamental/"why" questions and then build out, more than any other intro music material that I've seen. A far as I can tell, his own theories are in there, but more as a framework to help explain things, rather than demanding you think that way.

For example, in the first pages, he describes a bunch of well-known fundamentals in music theory/psychoacoustics, but in a very "Tymoszco-esque" way. He lays out five principles common to a huge range of music styles: some combinations of notes are considered more pleasant than others, you don't want to have melodies that jump around too much, etc. (These all go for the Western musical tradition, but also many others.)

Then he says that our scales are essentially "solutions" to how you can chop up the octave into steps and meet all of the five requirements. It turns out there are a relatively small number of ways to do that, we've found just about all of them, and those are pretty much exactly the list of scales that we're using. But then he quickly builds it out to common scales that you can play on a keyboard written out in normal notation, and goes from there.

This is extremely satisfying to my hacker brain, like picking a handful of criteria and doing a search to find all the possible lists of numbers that meet those criteria.

I wouldn't be surprised at all if you can explain music theory from fundamentals just as well using traditional Neo-Riemannian theory, or even something totally different. I just haven't ran into any intro-level materials like that.

(Also: it could even be that his list of requirements isn't really true, but it's hard to see which ones you would want to deny for Western music.)

[zozbot234]

Thing is, NR theory is almost as far from fundamentals as you can get; loosely speaking, it's a description of how very "far" modulations between triads (and to some extent, scales/keys) can nonetheless be made to work. It's describing a "trick", so to speak. Tymoczko's additions make the approach somewhat more useful, but it's still nowhere near the actual fundamentals of how music is understood in general (which is what one would expect "theory" to be about).

[a_lieb]

Huh, maybe his intro-level materials are far different, then. I'm not going to die on the hill that there's any connection; I don't even know whether he claims there is. But it at least seems that this specific stuff (at least in the early chapters I've read) is both more fundamental and more grounded in math (very basic math in this case) than the other intro theory stuff I've seen.

[creative-coder]

Thanks a lot for pointing to these lectures ! Sometimes even freely available quality material doesn't serve its intended purpose due to lack of awareness among those who want/need it