I'm working on a tape echo emulation in Reaktor, and I've based the frequency response, tape speed warble, high-amplitude saturation and tape hiss on a paper I found about the Roland Space Echo. However, I'm now looking for information about the distortion of low-amplitude signals by audio tape. When I let an echo trail die out to just above the tape hiss level, and then turn up the feedback level to make it audible again, the sound is too clean, and a real tape delay would produce a more distorted sound.
Which simple curve or mathematical transformation of a signal would emulate the distortion caused by recording audio on tape at very low levels? And how should I adapt it to emulate different tape speeds?
It doesn't have to be ultra-realistic or high quality, just something that will add some tape-like dirt to low-level signals only, and be mostly transparent at higher levels.