I don't know of a defined syllabus but here is what I did:
1. Write some basic synthesis code(naive oscillator and volume envelope) and some way of sequencing it. Write little toy trackers and some procedural audio with this technique.
2. Try and fail a few times to write dataflow engine for audio like Pure Data. (this is kind of a big project and it turns out, you really don't need it to experiment.)
3. Write Standard MIDI Format playback system for a one-voice PC beeper emulation. This turns out to be a gateway drug for me learning more in depth because all you have to do is add "just one more" feature and every MIDI file you play sounds a little better.
4. Expand MIDI playback and synthesizer in tandem. End up with polyphonic .WAV sampler, then Soundfont playback. Learn everything about DSP badly, and gradually correct misconceptions. (DSP material can be tricky since the math concepts map to illegible code, and a lot of the resources are for general engineering applications instead of audio.)
5. Rewrite things and work on custom subtractive synthesizer, after getting everything wrong a few times over in the first synthesis engine. Still do not know to write nice sounding IIR filters; steal a good free implementation instead.
And that is where I stand today. I know enough to engineer complex signal chains, how some of the common formats are structured, and some tricks for improving sound quality and optimizing CPU time; what I miss is the background for writing original signal processing algorithms, which gets really specialized(there are some people who devote themselves entirely to reverbs, for example). These algorithms and their sound characteristics are effectively trade secrets, so the opaqueness of the field is not just a matter of the problems being hard - DSP just hasn't become as commodified as other software.
With due respect to yourself (and jfb) the first paragraph is what I am talking about. I can just about guess you mean produce a sinewave, chop it into time slices and output those in some audio format.
I think I will give it a go shortly - close your ears :-)
1. Write some basic synthesis code(naive oscillator and volume envelope) and some way of sequencing it. Write little toy trackers and some procedural audio with this technique.
2. Try and fail a few times to write dataflow engine for audio like Pure Data. (this is kind of a big project and it turns out, you really don't need it to experiment.)
3. Write Standard MIDI Format playback system for a one-voice PC beeper emulation. This turns out to be a gateway drug for me learning more in depth because all you have to do is add "just one more" feature and every MIDI file you play sounds a little better.
4. Expand MIDI playback and synthesizer in tandem. End up with polyphonic .WAV sampler, then Soundfont playback. Learn everything about DSP badly, and gradually correct misconceptions. (DSP material can be tricky since the math concepts map to illegible code, and a lot of the resources are for general engineering applications instead of audio.)
5. Rewrite things and work on custom subtractive synthesizer, after getting everything wrong a few times over in the first synthesis engine. Still do not know to write nice sounding IIR filters; steal a good free implementation instead.
And that is where I stand today. I know enough to engineer complex signal chains, how some of the common formats are structured, and some tricks for improving sound quality and optimizing CPU time; what I miss is the background for writing original signal processing algorithms, which gets really specialized(there are some people who devote themselves entirely to reverbs, for example). These algorithms and their sound characteristics are effectively trade secrets, so the opaqueness of the field is not just a matter of the problems being hard - DSP just hasn't become as commodified as other software.