Is there a reference for math for analog Machines

Hi, I’m new to sound but have a computation physics PhD.

When I look at the manual’s appendix, I see terms like sweep time, snap amount. Google and Wikipedia are not very helpful.
the best things i found are in this forum What's the pitch sweep time? and are not enough.

is there a book that breaks down each of the controls into a mathematical formula that helps me understand what happens with the wave?

or at lease a technical explanation

Thank you!

Unless I’ve miss understood the term sweep time can be applied to various things. If for instance you use an envelope to open a filter the sweep time would be describe the time it takes for the filter to go from open to closed or vice versa?

Welcome to the forum btw!

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I’d say Sweep Time corresponds to an exponential envelope time, assigned to pitch.
No maths !

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It is easier to test it with BD CLASSIC imho as there is Sweep Depth. Max decay.
Default BD HARD has a fixed depth.

Welcome to the forum! My guess is that the actual relationship of each macro encoder (sweep, etc.) to parameters in the underlying model is a proprietary secret. Perhaps you have the background necessary to discover more through experimentation?

from the manual

STIM (Sweep Time) sets the pitch sweep time. The depth of the sweep is fixed.

I guess it makes sense that it’s the time of exponential decay. and because the manual mentions “pitch”, this is an exponential decay related to pitch but still unclear to what level.

seems like the best option is to give up on math and play it by ear. your insights did help to have a better intuitive understanding.

looks like to understand how the sounds are constructed, I should start with supercolider or something similar

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Found a few resources for books in case someone else is looking. Going to look through them How to learn synthesis and sound design (books/resources/etc) - YouTube
https://www.reddit.com/r/synthesizers/comments/ad8cbw/besides_the_fantastic_welshs_synthesizer_cookbook/
Creating Sounds from Scratch: A Practical Guide to Music Synthesis for Producers and Composers 2017
Welsh’s Synthesizer Cookbook: Synthesizer Programming, Sound Analysis, and Universal Patch Book Paperback – January 1, 2006
David Friend, Alan R. Pearlman, Thomas D. Piggott - Learning Music with Synthesizers-H. Leonard Pub. Corp (1974)
he Synthesizer: A Comprehensive Guide to Understanding, Programming, Playing, and Recording the Ultimate Electronic Music Instrument 2014