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.

翻译：我们详细阐述了密歇根理工大学数学与音乐实验室（MML）为VCV Rack软件模块化合成器平台开发的“功能量化器”模块系列的数学公式化描述。这类模块使合成器演奏者能够基于数学函数将振荡器调谐至新型音乐音阶。例如，我们描述了最新发布的MML对数量化器（LOG QNT）模块，该模块可将合成器振荡器调谐至独立乐队The Apples in Stereo所引入的非毕达哥拉斯音乐音阶。