Well, sort of... The output of the microphone is required to drive both the mic cable (which may be capacitive, and is probably reactive) and the input impedance of the next device. If you know a little about Ohm's law, you know that, the smaller the impedance is, the more current it will require from the output of the previous device's stage, and of course, the reverse is true as well.
So, imagine that we have an output stage that is designed to put out a signal at a given voltage level, say , .001 volts (~-60dB) at a given current level, say 60 microamps. Let's say that we can drive a 1500 ohm load with that much current, although truthfully that's a bit on the lean side, since the load won't always look exactly like 1500 ohms depending upon the frequency of the waveform.
But then, lets say that we change the load from 1500 ohms to 1000 ohms. Suddenly, we don't have nearly enough current to drive that load, and we start seeing a rise in load-based distortions at certain frequencies. These load based distortions are mostly 3rd harmonic (some people claim a 7th and 9th harmonic distortion), and they are at such low-levels that they would be perceived more as a "coloration" than anything else. If we were to drop the load to something egregiously low, my instinct tells me that we'd see a lot of the 7th and 9th as the microphone's active output struggles to push that load.
For transformers, something a little different happens. Instead of load based distortions, you get something more akin to filtration. Because a transformer is an inductor, and inductors alter phase response, most transformers will have resonant peaks. The way that we tame these resonant peaks is to use a Zobel network, which is just a simple resistor/capacitor combination. This will, in a sense, fool the transformer into behaving a particular way within that (previously) resonant band, causing its response to flatten out. Altering the load will alter the behavior of the Zobel network, causing a change in the transformer's frequency response.
If we go the opposite direction and increase the input impedance, we get different effect, at least in theory. Because our load is demanding less current from the microphone's output stage, more current is available to the output stage to actually conduct the AC signal, so you get the opposite effect, at least to a degree. With a transformer, I'm not certain. I suspect you would see an increase in resonant behavior, but truthfully I've never seen that addressed, and I've never actually witnessed it, so I can only guess.
Anyway, that's just a tip on an enormous iceberg.
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