Towards a bendable circuit model of the Casio SK-1 keyboard

Abstract

The Casio SK-1 keyboard was introduced in 1985 and synthesizes sampled and built-in sounds via pulse-code modulation and additive ("harmonic") synthesis. Initially important as one of the first home keyboards with sampling capabilities, the SK-1 has become one of the most popular instruments for circuit bending, the process of creatively modifying or augmenting sound-producing electronic devices. I create a parameterized component-level software model of the analog circuitry of the Casio SK-1, with applications to archiving and preserving its historic sound, expanding its basic behavior through circuit-bent modifications and extensions, and providing circuit benders with a resource for informed bending. Throughout, special attention is paid to creating models in terms of the circuit's component values. The SK-1's Percussion, Bass, and Chord Filters are modeled and analyzed in continuous-time as transfer functions and discretized via the bilinear transform. The non-linear (including diodes and transistors) Envelope/Pitch Mixing Circuit and Melody Filter are analyzed with linearizing simplifications to elucidate design intent, and modeled as ordinary differential equations to capture their behavior accurately. A review of techniques for the numerical solution of ordinary differential equations follows. A model of the internal speaker's impulse response and estimated static non-linearity rounds out the project.