>>55137508
It can't just be adding sample by sample, right? That would just be additive synthesis and sound like a single thing. (I ask because I'm working on an audio application)

I don't understand the question. Everything you hear can be expressed as waveforms of varying complexity.
You should read up about harmonics and auditory perception.

>>55137625
Same poster here. I think I understand what you're getting at.
Perhaps a more accurate question would be "why is polyphony not interpreted by the human ear as a single note?", and the answer to that is "harmonics". Harmonics are created by all basic waveforms besides the sine wave, and are also pretty much unavoidable in the physical world (try creating an acoustic instrument that creates a perfect sine wave). Harmonics also aren't random, they occur at very specific multiples of the principle frequency.
I don't know all the specifics of the human perception side, but our ears can use harmonic information to tell different tones apart.

>>55137745
Thank you for taking additional time to try to understand my poorly phrased question. This sort of touches on what I'm getting at, but isn't quite it.

This whole question came about when I was trying to make basic chords by generating wave tables and sending them to an output stream in portaudio. I listened to the output, and it appeared to be a messed up wave that I didn't recognize. So I did some research and found the phenomenon you mention. I then remembered that I had made proper chords a while back using fmod's oscillator (supposedly playing just sine waves), and became confused. How can fmod play these tones and have them sound distinct if they're just sine waves?

>>55137972
I don't really know anything about fmod so I can't really answer your questions about the wavetable generation and stuff.
However, the question about chords with sine waves is quite easily answered: the fundamental frequency can still create consonance and dissonance (to use music terminology) with other sine waves.
Also keep in mind that volume plays a large part in our perception; harmonics of a more complex tone are fairly quiet compared to the fundamental. If you reconstructed say, a saw wave, by layering sine waves (which is completely possible) it would sound ridiculous if the fundamental and all the harmonics were the same volume.
Also keep in mind that the volume relationship of a fundamental can be manipulated for interesting effects. Playing harmonics on a guitar is a good example. By positioning your finger on the string in a certain way you can amplify certain frequencies in the string's harmonic series and also diminish the volume of the fundamental. Tuvan throat singing is also based on manipulating the amplitude of harmonics.