Saturation

Saturation#

Saturation means a smooth transition towards hard-defined limits. Take a hyperbolic tangent. Think of any number, a really big one, a quadrillion: tanh will not output anything bigger than 1 or smaller than minus 1. An amplifier is the same, because its hard limit is its maximum output.

Saturation can be reversed#

If you distort a song with tanh, bounce it, drag the bounce back in, then run it through arctanh, which is just the inverse function, it comes back clean, and it nulls against the original. Saturation maps the values one way, so you can map them back. Clipping can't be mapped back, because it is just information loss.

I built Saturation Reverser to demonstrate this. Tanh on one side, atanh on the other. The saturation side is perfectly useful on its own, but the reverse side is really just a fun trick. It only works when the two sides are exactly level-matched, and it is not intended as a restoration tool. It does not magically reverse all distortion. Some people have been using it as a restoration tool anyway, which is fine if it actually works, but it was never the point.

In the video I said that with at least 24-bit there is zero data loss. Technically, that was a lie. Squeezing values together causes quantisation error. At any fixed bit depth only infinite precision would make it lossless. I wanted a simple dichotomy that casual viewers would understand, and it still holds:

clipping is information loss

saturation preserves the detail

A basic saturator is one line of code#

tanh

It can sound like a valve overloading gracefully, and it is one age-old formula, which is why everyone and his dog sells a saturation plugin. You might even say the market is somewhat saturated.

Tractatus is the opposite of that. It is a modular tone factory with tape, amp, waveshaping and stompbox-style modules you can chain in series, in parallel or in feedback loops.

It does the job of clipping and sounds better#

Saturation controls peaks much like clipping does, without the literal information loss, and it usually sounds better. To my ears the nicest version is a transformer core saturating magnetically, which gives a soft, smooth compression. A transistor or op-amp stage running out of voltage just hard-clips, and that can sound much the same as digital clipping. Why they behave so differently is under preamps.

Saturation on purpose#

I'd rather saturation was a process I choose, control and can switch off. What I reject is unspecified mystery distortion baked into an emulation, or whatever colour comes with a particular compressor's topology.

I don't think you need the hardware. Class A transformer-style saturation can all be done in plugins.