Fb1_ODE – an Interface for Synthesis and Sound Processing with Ordinary Differential Equations in SuperCollider

The class Fb1_ODE, included in the miSCellaneous_lib quark extension library [1] of SuperCollider (SC, [2, 3]), enables the audible integration of ordinary (systems of) differential equations (ODEs) with initial values in realtime. The prefix 'Fb1' refers to the class Fb1 for single sample feedback and feedforward, on which it depends [4]. Consequently, the numerical integration of ODE systems with a step width of one sample is possible with arbitrary block sizes of SC's audio engine. Fb1_ODE opens the possibility for immediate audio experiments with models from physics, electrical engineering, population dynamics, chemistry, etc., preferably those with oscillatory respectively quasi-oscillatory solutions or chaotic features. Designing new ODEs from scratch or altering respectively disturbing systems can also be interesting regarding the sounding results. Wrappers of Fb1_ODE include wellknown systems like Van der Pol, Duffing, Hopf, Mass- Spring-Damper, and Lorenz; users can interactively add other systems with the class Fb1_ODEdef. The modulation of ODE parameters, system time, and the feeding of additional audio signals into ODE systems are, amongst others, further options for unorthodox synthesis with differential equations.