In the hi fi world we were measuring very low amounts of harmonic and transient intermodulation distortion using distortion analysers and they are interesting and helpful. In your case you are looking at much larger amounts of distortion being introduced on purpose. It is easier to see and hear as a result.
I would be interested in
when the preamp was being very clean and at what point any distortion was being introduced. There are some signal level things to consider. Our signal is at various levels at each point in the signal chain. The first level is the level just outside the preamp being fed in. A continuous sine wave at that point of various frequencies and levels would be desirable.
(hardware oscillator and true rms voltmeter very handy at this point) (It is important to know how any balanced and line inputs are configured. The block diagram of the pre will tell you this. Some lnputs actually bypass certain input stages in some pres, others do not. They just attenuate the signal and run it in through the Mic pre anyway.) Inside the pre amp the first input gain stage may be overloaded by the input signal itself. The first stage can often feed a second gain stage and then various amounts of distortion can be added in by pushing the second stage from the first stage.
(or an output transformer being driven hard by the input gain pre, Neve likes coupling one stage to the next with transformers, he uses them a lot) The second level is from any first stages inside the pre into its output stage. The third point in the signal chain is the signal and it's level leaving the preamp itself.
(Hardware oscilloscope true rms voltmeter and hardware spectrum analyser good bits of kit to have hanging on the output) I would start with the input gain set down low and having any output controls set high. And then looking at the waveform to see how clean it is in real time. You can record of course and playback. You can also use oscilloscope software and there are free ones that will show you quickly. A spectrum analyser would be good to have on hand to see if any other harmonics start rising up.
I would be increasing the level of the input signal slowly while monitoring its level as well
(true rms voltmeter) while observing what is happening to the waveform at the output of the pre amp. Time domain waveforms
(such as normal DAW wafveforms) will start to distort their shape too as distortion sets in. The spectrum analyser
(frequency domain waveforms) will start popping up other harmonics and you will be amazed by how much!
Square waves are excellent test signals too. They show up all sorts of ringing and oscillation issues that may be inside the Mic pre. But be aware of what the harmonic structure is like for a square wave when looking at it on the spectrum analyser. Sine waves are excellent because there is only one fundamental and it is very easy to see harmonics popping up. The square wave on the output will tell you a lot from its shape change while in time domain mode even.
I would keep the output high but set the input gain now much higher eg for a microphone perhaps recording a softish instrument. I would do the level shift input thing again to see at what point the output wave form changes its shape too much and when the harmonics start to appear. Then you will have a range of input voltages that you know the pre is clean and from what point it starts distorting. You also need to see what happens when you drive that input gain stage hard and into the output stage that is turned down lower. Waveforms are going to change shape sooner and harmonics will start to rise up as well. You need to note where the controls have to be set in this mode and for ultra clean modes on your pre too.
It is well worth finding all this out. You may be introducing distortion in small amounts without knowing it simply because you are not fully sure how your pre is behaving and what it is doing to your input signal on various control settings.
(And the range of input levels hitting the preamp) All of this stuff applies to expensive mic pres too.
I have got one of those Behringer valve mic pres and I did the same with that. A series of tests which now allow me to set those input and output controls for either very clean operation or quite dirty if need be on top adding in some interesting colour.
Here is a link to a virtual oscilloscope that was recommended by Sound on Sound. It is only very small and free. It has a very stable trigger mode which allows you to come in very close while still maintaining a perfectly still waveform for more detailed observation.
http://www.jaggedplanet.com/VST/jscope.html