This is my own limited experience, so I hope an expert also answers. In the Handmade Hero video series/project, he codes a game engine from scratch. I didn't get very far into it, but I followed along coding it myself, using what I learned watching him. He writes it in a way that all the platform-specific code is in its own file, and he does it in DirectX, although other people have ported it to other platforms. Early in the series, he gets it to where you can create a sound buffer of samples and play it out to the speakers. So I played around with simply adding sine waves to generate things such as dial tones, busy signals, and DTMF dialing sounds. I would consider that "ground up" for the Windows platform. It should be pretty simple from there to load audio samples from files, adjust their volume, play them back faster/slower, and mix them together. And/or generate more complicated sythensized music. There is a book about building modular synthesizers, and I was thinking about using that but doing it in software.
The best motivator for me was to start building a Standard MIDI Format sequencer and test its output on MIDI files. The underlying MIDI standard is a well-understood protocol with many resources, while SMF adds some room for creative interpretation since it's meant to work across sample-based synths, FM, etc. I started with a simple square-wave beeper, added polyphony and volume envelopes, and built it up from there. By the end, the architecture I had initially built was melting down, but it was playing Soundfonts to some degree, and I could confidently claim to understand audio coding.
There's a lot of room to do things incorrectly and not notice in audio, which makes it forgiving to learn: e.g. playing a sample at a different pitch can be done badly by adding or removing arbitrary samples, but resampling it with minimal distortion is actually a fairly intensive DSP problem. Or when computing a volume, the linear amplitude usually isn't the parameter you want to work with(see every UI where volume changes imperceptibly until you reach the bottom 10% of the slider), and while there are computations to convert between linear and dB values, you still have to qualify it with one of these various references and suffixes[0]. There's a lot of crossover between audio and electrical signal terminology that can make it hard to follow this material.
So you can spend a lot of time doing simple things well!
