This distortion plays its own melody using Chebyshev harmonic exciters

The input is one static sine wave. Every note on top of it is an overtone excited by a harmonic exciter (aka Chebyshev Polynomial). This is demonstrated using Black Diamond Distortion — free, VST3 and AU, macOS / Windows / Linux: https://aspeninstruments.com/plugins/... We start by looking at the octave fuzz Roger Mayer built for Jimi Hendrix in 1967, the Octavia. It full-wave rectifies the signal, folding the negative half of the waveform onto the positive half. That wavefolding deletes the fundamental and leaves even harmonics, which is why it sounds an octave up. Then further back, to Chebyshev. He wasn't designing a distortion, but his polynomials do exactly this: T(cos x) = cos(nx). One sine in, one harmonic out, for any n. That identity is what generates the harmonic exciters in the plugin. At the end we rebuild a tanh saturation out of them. 0:00 The melody is the distortion 1:36 Why "tanh makes odd harmonics" is only half the story 2:29 1967: the Octavia octave fuzz 4:09 Chebyshev's transfer function, traced with Probe 4:54 Rebuilding tanh from Chebyshev polynomials Credit to 3blue1brown for creating Manim which is the software I use for the visualizations in this project.