Quote from speechchips.com: "The Soundgin is an 18-Pin Microchip PIC18F1320 that has been programmed to generate complex sounds by incorporating six oscillators which can interact with each other in various ways."
Given that you have interupts turned off the PIC can produce correct frequencies.
The tempo, choosing the right note, and the duration of the notes are all in the programming.
Using the PICs timers make the process easier but you can do it with integer math.
A few weeks ago I asked about computer musical notation and Torben (thank you) pointed me to a wikipedia article with a table of notes. https://en.wikipedia.org/wiki/Scientific_pitch_notation
Using that it was very easy. It still sounds like a computer making notes (no attack or decay etc) but it does the job.
If PICs could not do this simple timing based task they could not do serial communication.
Still gotta say...
the dsPIC series is WAY better at this. I mean you can easily interface a codec (DAC/ADC combo) capable of 48KHz 16-bit stereo too. The 16-bit math is great, also the memory is NOT paged which is hella nice to work with.
It's addictive. You start to think about guitar effects, voice changers, noise cancellation, voice recognition, all the neat stuff.