Kirnberger's keyboard temperament, 1771, playing Bach

But when I finished auditioning them. I found that the equal temperament setting sounded painfully out of tune! After only 15 minutes or so of hearing pure intervals, my ear was already confused.

The pure c -e third is interesting ... when in passing it sounds comically flat ... but when imbedded in the triad at the end, it's lovely. I have equal temperament soaked ears (I'm a piano tech), of course. Recently I had an interesting experience. I play a Rogers electronic organ which has various temperament settings. I found most of them WAY too crazy for the congregation.

what is the relation between the clavier temperament and its tuning. im really got in but i have difficulties to understand most of you tell. could someone pls tell it in an easier way?

Ok. Temperament means an instrument's capacity to play in all keys but still sound like it's in tune. Why is this so wonderful? well, take an intrument like the guitar for example. If you tune it to sound perfectly in tune in C major, it will sound out of tune in other keys like E major. This is because the human ear doesn't hear harmonies mathematically, yet mathematic ratios and values are how we describe musical scales and chords.

If you tuned an instrument according to the mathematical ratios we use to describe sound frequencies, it would sound horribly out of tune to the human error, despite being perfect on paper. And, if, as in the guitar example I used earlier, you tune the instrument to sound perfectly in tune in a given, it will sound horribly out of tune in other keys. The solution? COMPROMISE. You tune the instrument so that it's not quite tuned according to the human ear, not quite consistent with maths.

Final part of the answer :) so now I hope you see why temperament is so important for an instrument like the harpsichord which is expected to be able to play in all keys. This is why I love listening to early music with lutes and other strings - they know how to tune their instrument to fit the key they play in. So they're not tempered, but as long as they stick to a given key you hear what to be really in tune means. There's no such thing as a tuned piano - it can only be tempered.

"Temperament" does not refer to an instrument's capacity to play in all keys but still sound in tune.

A "temperament" is simply one of many TUNING SYSTEMS which compromise the pure intervals of just intonation to satisfy certain aesthetic requirements.

ALL temperaments are compromises.
For example, you can tune a piano, organ or harpsichord to have pure 5ths or just major 3rds or be able play in all keys. But you can't have it all !

Harpsichords and organs were not always expected to be able to play in all keys. Mean tone tuning persisted past 1700.

New temperaments arose to meet the needs of changing harmonic aesthetics.

E.g, before the Renaissance, they like pure 5ths and 4ths.

Later, they wanted pure triads.

Later, they wanted to be able to modulate to more remote keys.

Pianos, organs and harpsichords all have the same problem: Once you tune the instrument, you can't adjust the intonation on the fly like you can with the human voice or a violin.

Lutes and gambas, because they're fretted, have somewhat the same problems as keyboards, but to a lesser degree, since you can adjust the intonation by rolling your finger. Some gambists split frets to make it easier to play the right enharmonic.

On a piano that's tuned to equal temperament, Ab and G# are the same note.

But on a viols, violins or voices, they are not the same note. This is especially noticeable when a consort of, say, viols, plays an chord, like an E-major or Ab-major.