How would you model a simple musical score for a single instrument written in regular standard notation? Certainly there are plenty of libraries out there that do exactly this. I'm mostly curious about different ways to represent music in a data structure. What works well and what doesn't?
Ignoring some of the trickier aspects like dynamics, the obvious way would be a literal translation of everything into Objects - a Scores is made of Measures is made of Notes. Synthesis, I suppose, would mean figuring out the start/end time of each note and blending sine waves.
Is the obvious way a good way? What are other ways to do this?
MIDI files would be the usual way to do this. MIDI is a standard format for storing data about musical notes, including start and end times, note volume, which instrument it's played on, and various special characteristics; you can find plenty of prewritten libraries (including some open source) for reading and writing the files and representing the data in them in terms of arrays or objects, though they don't usually do it by having an object for each note, which would add up to a lot of memory overhead.
The instruments defined in MIDI are just numbers from 1 to 128 which have symbolic names, like violin or trumpet, but MIDI itself doesn't say anything about what the instruments should actually sound like. That is the job of a synthesizer, which takes the high-level MIDI data an converts it into sound. In principle, yes, you can create any sound by superposing sine waves, but that doesn't work that well in practice because it becomes computationally intensive once you get to playing a few tracks in parallel; also, a simple Fourier spectrum (the relative intensities of the sine waves) is just not adequate when you're trying to reproduce the real sound of an instrument and the expressiveness of a human playing it. (I've written a simple synthesizer to do just that so I know hard it can be produce a decent sound) There's a lot of research being done in the science of synthesis, and more generally DSP (digital signal processing), so you should certainly be able to find plenty of books and web pages to read about it if you'd like.
Also, this may only be tangentially related to what the question, but you might be interested in an audio programming language called ChucK. It was designed by people at the crossroads of programming and music, and you can probably get a good idea of the current state of sound synthesis by playing around with it.