Im is not sure about the idea between tune and cpu was the case of the stutter really, have newer understand its the reason for the stutter? there is both tune and sfx played same time, which is also the reason for the stutter as well.
howover im can see in the remixes im have done (like the above one), the "beeper" note was trigged each 4 frames in a speed of about 50 frames of second. with that in mind, two notes per 4 times (one for tune, game logic, other for sfx, game logic), then the framerate would been 25fps for game logic (and graphics update). this if the cpu would have wait for the notes to been played finished. But its a slow paced game anyway.
So its actuelly possible wiki has right, but im do have seen much faster games since that with better rutines, but its qutie a very early game to been remembed.
On the Commodore 64, tunes is just tied to the screen rate and often/allways in the interups, so its dont got interupted from the game logic. Some tunes might uses cia timing throught (not tied to screen rate, but cpu based)
