I will give a combination math-history-show-and-tell talk in which I explain the theory and background of subtractive synthesis, an approach to making sounds via electronics. Although not technically the first type of synthesis implemented successfully in an electronic instrument, subtractive synthesis is by far the most popular approach to the electronic creation of sounds for music. We will go over the rudiments of subtractive synthesis, briefly cover the history of the original Moog synthesizer, and along the way I will showcase these ideas using the Moog Mavis, a modern, smaller instrument from the same company based on the same principles.