Casio VZ-1 algorithms

Following on to my last post, where I found out that the official documentation of the Casio VZ-1 keyboard synthesizer from 1988 contains vague and incomplete information about how the machine works, I want to write down what I wish the manual would have said.

Casio does a very poor job of explaining the synthesis engine of the VZ-1. They never actually say that it does phase modulation but they do not clearly explain that it does wave shaping either. On top of that the user interface causes confusion by things like:

I am not alone in interpreting Casio's information to mean that the VZ-1 uses phase modulation. In an October 1989 Music Technology review of the related Casio VZ-8M, for example, the reviewer calles the synthesis engine a

digital synthesis system which, in conceptual terms, could loosely be considered as a user-configurable version of Yamaha's FM synthesis

The 1988 book "POWER PLAY VZ!" by De Furia and Scacciaferro, which is a kind of third party manual for the VZ series, says on page 57:

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