Generating waveforms is simple enough. What I needed was a way to get my raw data from my own data structure to the OSes sound system. That's the sort thing a framework like Allegro 5 was designed to hide, not give easy access to. I also found the documentation on the audio system tends to gloss over the advanced features.
There is a callback function for Allegro's mixer data structure, which is designed for post-processing but can be used to set the values directly. And it works - mostly. The problem I found is that there is no way to manually set the update rate that the callback function is called. For my system and the audio settings I was trying (mono 16bit int sound) the function was fixed at 2048 samples per call. At a playback rate of 44100Hz, that's roughly a twentieth of a second per call which is a noticeable amount of lag. As far as I can tell from sifting through Allegro's source code there isn't any function calls or config settings to alter that short of putting them in the library myself. Which seems more trouble than it's worth given I'll probably break everything trying to make Allegro do more than it's supposed to do.
The better answer to me is to look for an audio library that is designed for this kind of thing. I'm trying out PortAudio. I haven't had much time with it yet, but so far I've got it running and outputing square wave beeps with a callback function running on my own set number of samples per call. 256 samples and the beeps sound instantaneous.
Given that's all I need PortAudio to do, I'm happy. The downside with a low-level library like PortAudio is that is all it does, so if I want to extend this to working on wave files I'll need to write my own loaders. Right now, I'd like to see how far I can go with old-style tone generation.
Additional: I've noticed these journals have tag functionality, which I'm currently not using. Is there a standard for how tags are used on GameDev.net?
