Real-time physical modelling for analog tape machines

For decades, analog magnetic tape recording was the most popular method for recording music, but has been replaced over the past 30 years first by DAT tape, then by DAWs and audio interfaces [1]. Despite being replaced by higher quality technology, many have sought to recreate a "tape" sound through digital effects, despite the distortion, tape “hiss”, and other oddities analog tape produced. The following paper describes the general process of creating a physical model of an analog tape machine starting from basic physical principles, then discusses in-depth a real-time implementation of a physical model of a Sony TC-260 tape machine. "Whatever you now find weird, ugly, uncomfortable, and nasty about a new medium will surely become its signature. CD distortion, the jitteriness of digital video, the crap sound of 8-bit all of these will be cherished and emulated as soon as they can be avoided." -Brian Eno [2].