> you built what was basically a raspberry pi with a microcontroller by hand, and you had to use the dumb speaker and controller to make your own music firmware to produce notes

This sounds like they were most likely bit banging square waves into a speaker directly via a GPIO on a microcontroller (or maybe using a PWM output if they were fancy about it). In that case, the audio frequency will be derived directly from the microcontroller's clock speed, and the tolerance of an internal oscillator on a microcontroller can be as bad as 10%.