I’ve been fascinated by the Rob Hordijk’s description (in the Sines and Squares masterclass video) of how one might think about sound in three dimensions (rather than the two we are used to on our screens) and how sine and cosine waves can be used to describe the phase and amplitude of a resulting wave, defining its waveshape over time.
He describes it as a corkscrew waveform, also occurring in nature, with the phase describing its rotation, and the amplitude, distance. When viewed on an XY oscilloscope with a slow sine modulating the amplitude of the sine and cosine, it looks like a circle approaching from the distance and receding again. With very low frequencies one can view it as rotating points and get an even better idea of the ‘corkscrew’ effect.
This helps fill out some background on Hordijk’s thinking of sound in terms of depth – for example with his fluctuation waveform, in which amplitude and frequency modulation are combined to provide a special kind of vibrato. Based on a rounded triangle ‘parabol’ waveform, the larger the wave is, the lower the frequency – i.e the lower part of the frequency fluctuation corresponds to the higher part of the amplitude modulation. In his 2015 masterclass on Waveshaping & Fluctuation Hordijk describes this waveform (when modulated) as advancing and receding – giving a perspective effect.
I’ve uploaded a little demo patch (used to create the gif above) to the Audulus forum.