Softness of diode knees

[Steben]

These measurements are great. They just might look a bit oriental to me given the zero is at the right. 

The softness on itself is only comparable when the curves are scaled towards an "agreed" forward voltage. As R.G. mentioned.

If you compare the lowest voltage zener to the stacked silicons you see a comparable softness. As Rob mentioned.
I've seen curves of <3V zeners that are softer than that.
Yet... nothing that much different from adding a small resistor in series with the silicon diodes.

Basically, Germanium is the softest followed by silicon / zener and then LEDs.

Not shown here are schottky diodes. They tend to go in between silicon and germanium.
Curves show them as silicon with the first part of the path cut off. Scaled to silicon this makes them a bit softer.
But overall not a special addition soundwise. They are excellent though for trimming forward voltages or designing asymmetrical clipping.
Think of adding a tad of volume to a DS-1 by using 2 schottky's instead of 1 silicon but without change of sound.

One of the typical elements in comparing diodes is the fact diodes all follow the same pattern but different parameters. One of those is internal resistance.
Soft diodes will always have higher resistance.
You cannot have a single diode which has sharper slope (almost no resistance) while having a softer knee.
4 x germanium range is comparable to 3 x  silicon.
They sound the same as 1 x germanium as long as the input signal is 4 x bigger.
The germ combo will clip sooner, softer but given a large enough signal the output will become louder than the silicon combination too! The internal resistance of the germanium is highest.
This means stack of soft diodes might see a sudden opamp clipping in the curve sooner than wanted. It is not a very interesting to do knowing a single diode sounds the same with a lower signal.

Now what we can do with these things is replicate curves of amp stages.
Looking at the non-feedback push pull stage in for example an AC30 we see a curve that starts bending very gently (very very soft clipping) until it softly hits the rails.
This is typical for the absence of feedback which would straighten the curve until breaking point.