> I don't know calculus, yet, so if anyone offer advice in layman's terms I
would greatly
> appreciate it.

I'll give it a try:

The tone produced is a function of a variable in time. As time progresses the
voltage swings back and forth between a positive and a negative value. We
hear this as a note.

When you affect the time variable we hear a change in pitch. If the time
variable progresses faster we hear a higher pitch, if it progresses slower a
lower pitch.

The difference between PM and FM has to do with what we do to the time
variable. Suppose you add another sinewave to the time variable. Then you
alternately fastens and slows down the time variable. This is the sound of a
vibrato. The other sinewave could be an LFO, but also a true audio frequency.

If you add a constant value to the time variable you will get a phase shift
and not a pitch shift, because the added constant means that you are
constantly "ahead of time".

If you add the integral of a function to the time variable, you really add
the area below the funtion to the time variable, which is another function.
So you add a function to the time variable.

If the function before making an integral happens to be a sine wave balanced
around 0, then the integral funtion will swing equally on boths sides of 0
and the net effect is that the original tone has the same frequency.
Furthermore the integral of a sine wave is another sine wave, pitch shifted.

However, suppose the sine wave to be integrated is not perfectly balanced
around 0. This is what a DC-offset is all about. Then the integral of that
function will be a function that accumulates the area, instead of swingin
back and forth between 0. So in time the value will increase and increase.
Since we add this value to the original time variable, the net effect is that
the total time variable for the outer sine wave moves ahead through time too
fast. This we hear as a permanent change in pitch!

This does not happen in PM where you just add a sine directly to the time
variable, because if the inner sine is not balanced the net result is like
adding a constant - and this only produces a phase shift, but still has the
same pitch.

In fact you can't really change the pitch in PM, unless you add a non-
harmonic function instead of the sine. In FM you can change the pitch.

In analog systems it is really difficult to make a perfectly balanced
harmonic function. If the second funtion isn't even a sine wave, the areas
above and below zero are likely not to be the same. Just think of a 90% PW
square. Most of the wave will be above 0, if the DC-offset is not adjusted.

On a MiniMoog, try to modulate OSC1 with OSC3 and bring OSC3 into the audio
range. Then you can clearly hear how the different OSC 3 waveforms change the
pitch of OSC1.

This is at least an attempt to explain in common words. Somebody (preferably
an engineer) correct me if this is totally wrong.