Interpolation, the means of getting smoothly from one point to another, is an important topic in computer audio and music. We’ll start by studying linear interpolation.

For simple discussion and explanation, study MSP Tutorial 2: Adjustable Oscillator, and my articles on Linear change and Fading by means of interpolation. (Don’t worry if you don’t understand the visual part of the example Max patch in that latter article.)

Miller Puckette’s text discusses the same topic, in the sections on Smoothed amplitude control with an envelope generator and his more technical discussion of Interpolation. In that latter article, he’s comparing different methods of interpolation for calculating an intermediate point between two known points. (We’ll leave discussion of cubic interpolation for later.)