  We detail the mathematical formulation of the line of "functional quantizer"
modules developed by the Mathematics and Music Lab (MML) at Michigan
Technological University, for the VCV Rack software modular synthesizer
platform, which allow synthesizer players to tune oscillators to new musical
scales based on mathematical functions. For example, we describe the
recently-released MML Logarithmic Quantizer (LOG QNT) module that tunes
synthesizer oscillators to the non-Pythagorean musical scale introduced by
indie band The Apples in Stereo.
