"I don't think the speaker or the primitive sound circuitry could genuinely produce multiple tones at the same time."
It is possible to generate multiple tones at the same time, but it requires MOD PLAYER type pre-calculations on the fly, outputting audio to the 1-bit speaker, as if it was a 5-bit DAC, the same method as blitting the PC internal speaker.
You CAN mix down multiple channels of audio, on the fly, but only in carefully timed ASM, 6502 ASM, for the Apple, you see, but you gotta be a whiz.
People have done it, it's just marvelous to see & hear.
The Music Construction Set for Apple ][e COULD play 3 note polyphonic sound on the internal Apple speaker, cause it did something along those lines, and it was a native Apple program.
It's possible, to do it 'proper' and to do it in the 'cheat' way of arpeggio.
Banana phone! We need more lemon pledge. * exploding fist of iced tea! * I see your psycho cat and counter with a duck that has a broken leg, in a cast.