An ignorant question about impedance

I've read over these many years about the importance of properly matching a preamplifier's output impedance with an amplifier's input impedance. I've always just accepted this as something that has got to be dealt with by folks who understand such things. But now I'm wondering: What happens when there is a mismatch? Is there some threat to the equipment, or does the reproduction of music suffer in some obviously discernable fashion? (Highs or lows or mids are like this or that or some such?) I recognize that this is a boneheaded query, but I've found myself wondering and I've not been able to find the answer through my online searches. If someone could point me in the right direction, my non-technical mind would rest easier. Thanks.
If a preamp has a high output impedance (fairly common in tube designs) and if the amp that is hooked up to it has a low input impedance, the frequency response will be curtailed at both ends but most noticibly in the bass. So you will have a lot less bass and a little less high frequency extension. The extent will depend on the severity of the mismatch. It will still be flat in between the rolloffs and there will be no damage to the equipment.

I would like to point out that a low amplifier input impedance at first looks like a problem but the upshot is a quieter input stage so noise doesn't also get amplified along the line. This advantage shouldn't be overlooked IMO.

If an amplifier has a high output impedance (again, common with tube designs), and the speaker is of typical impedance (NOT resitance), the frequency response will be very unexpected - typically has waves in it all across the audio band. The waves change depending on the speaker impedance because an amplifier's output impedance is much more constant. Again, no damage but you may get a 2 ohm peak at like 70Hz, 1.5kHz and 10kHz for instance, which will change tonal balance of the system.

Your question is very legitimate and I am sure many Agoners have the same one. I have seen these effects first hand due to my career choice but if you read the Stereophile test results for their reviewed equipment, you can learn a whole lot about all aspects and ranges of this kind of behavior, among many others, each month. I think you are ready to take advantage of this valuable information.

Arthurs answer is correct, but FWIW although there are suggested guide lines for calculating the appropriate ratios (10 to 1, for example, i.e. a tube pre-amp with a 600 ohm output should be matched with a power amp with an output higher than 6000 ohms) it really depends on how the units were measured - not all spec's are equal. Interestingly I've run amps/preamps with less than a 10 to 1 ratio with no problem and some with a ratio much in excess of 10 to 1 with roll off. IOW, you've still go to listen to a combo to be sure you've got it right! Ditto with Athurs comments on speakers and tube amps. Listening to a combo is very important. If the speaker/amp impedence issues interest you (and I think they should because they are far mor important IMHO than amp/pre amp issues, especially to tube users, there was a recent thread with much excellent info on this.

Hope that helps a bit.
The ratio of 10 to 1, for amplifier input impedance to preamplifier output impedance is mostly looked at as a minimum acceptable limit. You hear about this mostly being a problem when matching tube preamps to low input impedance SS power amps. Many SS power amps have input impedance in the range of 50K to 100K ohms, and generally have no significant matching problems. However some amps, such as my McCormack DNA500, have a lower input impedance of 10K ohms. The other consideration that compounds the problem Aball already pointed out (low bass roll off) is that the preamp output impedance is often reported at 1K Hz, where it can be relatively low, but then the output impedance (that they don't report) increases significantly in the lower bass frequency range, due to limitations of the coupling capacitor size. I looked at some tube units with output impedance reported in the 200-400 ohm range, that when tested increased to around 4,000 ohm +/-. This could easily cause bass issues when using reasonably full range speakers. However, if you are using monitor speakers with limited output below 40Hz, that may not be a consideration for you. Those type issues are why you cannot simply put together a system of Class A rated components and expect to have good sound (there are other issues with reviews and ratings, but that is for another post!). BTW, impedance matching issues also sometimes arise when matching source output to preamp input.
Linearity is best preserved with low output impedance and high input impedance over the audible frequency range.

The impact of interconnects, speaker cables and speaker impedance variation with frequency should all be minimized in this case.

10 to 1 is a ratio at which effects barely begin to become audible (changing a cable, or interconnect or driving a speaker with a variable impedance load)

There are other factors too, including some very good points made by others already on this thread...but this is the essence.
Thanks so much for your clear and thoughtful responses. Back in college (in the 1970s) when I was spending a bit of time studying English literature and journalism (and a lot of time drinking beer) I used to wonder what those guys over in the engineering building were up to. I'm betting now that some of them were learning about impedance and all that kinda stuff. I've got some reading (and listening) to do. Maybe, just maybe, I'll ask one o' these days about cartridge loading. Thanks, again.
You guys are all right. -- Howard