AlgoMusic's M51galaxy VSTi, like the original Casio CZ synths, offers 8 basic waveforms:

1. Waveforms.

The choice is not arbitrary. While the first two waveforms are very identical to those offered by almost any analog synth, the others are not.
For example, waveform 3 (Pulse) and 4 (DoubleSine) were designed with E-piano and Organ type of sounds in mind. Waveform 5 (Saw-Pulse) offers a more vintage type of sawtooth sound, and the 3 resonant waveforms were to emulate a resonant lowpass filter.

But, there is more.
PD also offers a second set of (identical) waveforms that can be added to the first, but the way of adding is quite unusual. For example, what happens when you add a Square (2) to a Sawtooth (1) waveform, or a Reso1 (6) to a Saw-Pulse (5) waveform?

A short introduction to PD synthesis.

Hmmm, not at all what you expected, right?
Instead of simply adding the two waveforms, the second wave is pasted at the end of the first. This gives a typical 'octave' type of sound.

2. Block Structure of a typical Analog Synthesizer, and that of a Phase Distortion Synthesizer.

As you can see there's not that much difference.
OK, a PD synth is a digital synth, so you have digital sound, and digital control signals, but apart from that it's all pretty much the same. The only real difference is the label in the timbre block called 'PDM', which is short for 'Phase Distortion Modulation'.
The next chapter tries to explain what Phase Distortion Modulation (and Synthesis) really is.

3. Phase Distortion Synthesis.

PD, like FM employs only sine (or cosine) waves stored in ROM (or in a lookup table in RAM) to create new, harmonicly more interesting waves. So, how for example do we get the waves shown in chapter 1?

Let's for now concentrate on waveform 1, a sawtooth, and have a look at the 3 pictures below.
The first picture shows what happens if the phase angle of a cosine wave is read from 0 to 2pi in a linear way and at a fixed speed: the output is still a cosine wave. Nice, but not what we're looking for.
But, what would happen if we were to speed up the read back angle from 0 to pi, and then slow it down from pi to 2pi? Then the phase angle would be no longer linear, but distorted, and the output waveform no longer a cosine. In fact, it already begins to look a bit like a sawtooth wave (pic. 2).
Now, the more the phase angle is distorted, the more the resultant wave resembles a sawtooth wave (pic. 3).
Finally, all we have to do is make the distortion of the phase angle a digital control signal, and voila, we have what we were after: Phase Distortion Synthesis!

Ok - fine, but how does it sound? Well, pretty much like opening the filter of a analog syntheszer, a bit more clean perhaps, but still very warm, and certainly more versatile, because of the many waveforms at hand.
And, there's more to PD, of course: very typical are the 8-stage Envelope Generators, as opposed to the fixed ADSR envelopes of more traditional synthesizers. 8-stage EG's can shape the sound in much more detail.
But that's for the next chapter.

5. Phase Distortion and the M51 VSTi.

4. The 8-stage Envelope Generators.

Back to the eighties?

While doubtless one of the greatest features of the CZ synths, the 8-stage envelopes were also a real nightmare to program.
Can you imagine setting up to 18 parameters for each of the 6 available EG's with only a set of up/down buttons, peering at a dim lit 32 character LCD? That's where the first MIDI equiped computers like the Atari ST came in rather handy.

While the picture certainly looks impressive - if not intimidating, the way it works is actually pretty simple.
Each stage is called a segment and has two parameters: rate, and level, which are selfexplanatory.
Furthermore, there are 2 segments that are a little different from the others: one is the end segment, the other is the sustain segment. Any segment can be the sustain segment, the choice which one (if any) is up to you.
The same goes for the end segment, but there are some differences. The first is that the end segment is used to set the number of stages, and the second is that the end segment cannot be ommitted.
There are, of course, a few more exceptions to these rules, but that's really beyond the scope of this tutorial.

The 'timbre' envelope (see chapter 2) is of special importance since with PD there's no 'frequency cutoff' knob like on a analog synth. This may, at first glance, look like a serious oversight, but really, it is not.
Once you've learned to focus on the envelope instead you'll soon forget about the knob!
Another (and practical) reason for the ommission is that the digital domain is not as tolerant for overflows as its analog counterpart. It's quite hard to 'window' the modulation range, without all kinds of nasty and unwanted sideeffects.

The M51galaxy VSTi of course, with it's many modulators modelled after the much acclaimed M42 Nebula VSTi, really takes Phase Distortion to a another level.
But, let's first have a look at the (simplified) block diagram below, then discuss the various possibilities.
Note that you see only half of the M51.

(to be continued)

You can see that each half of the M51 has in fact two synths aboard, a PD one, and a VA one (also called SUB), making three types of synthesis available: PD, VA and FM.
The modulators, however, are applied to both synths alike.