"Bach was the first composer to use equal temperament. This is illustrated by his 48 preludes and fugues, in all keys." This statement is often bandied about by pianists, and it's rubbish. It also requires some explanation. Sorry if the following preamble is lengthy, but if you're going to have a blazing argument with a pianist, you need the info.
Let's imagine you own a clavichord (if you actually do, then you can skip this bit). You don't get in a clavichord tuner every six months like you do with a piano, because clavichords have light, wooden frames, and they don't hold their tuning that long. No, you tune the thing yourself at least every week, and you'll generally do some fine adjustments every time you play it. Here's a tuning method. No real clavichord player actually does it this way, but it will serve to illustrate the principle.
First, get middle C in tune with a tuning fork. OK, an electronic tuner if you must. Now play middle C and the G above it, and tune the G until you can hear that it's exactly in tune with the C. You'll need good ears, but you do it by listening for "beats" - a sort of "wowowowow" sound that occurs when notes are very slightly out. When the beats disappear, the notes are precisely in tune. You can now tune the F to the C in a similar way, and if your ears are good enough, you can go right through the middle octave, tuning each note to the C. Finally, tune the notes in the other octaves to the corresponding notes in the middle octave.
What this gives you is "Just Intonation" The frequency of each note is in exact proportion to the frequency of the C, and therefore exactly in tune, and it's not just theoretical. You can hear it. What's more, the clavichord has the sort of tone that makes the most of slight tuning differences, so you have to be really accurate and train your ears.
This is fine if you want to play in the key of C. Everything sounds wonderful. Now play a piece in F sharp. It sounds utterly horrible. That's because all the intervals are related to C. Use F sharp as your key note without re-tuning all the intervals, and they're all wrong. There is no way round this, it's a fundamental property of music and harmony. You can only get everything precisely in tune in one key.
Well, maybe we can dispense with the key of F sharp, but we can't play everything in C. Bagpipers may stick to one key and use perfect drone tunings, but we want a bit more sophistication. Actually, we can get away with playing in the closest related keys of G or F. They're slightly out, but not horribly so. Let's move further away, and try pieces in D and B flat. Now the tuning is getting a trifle offensive.
The solution? Temperament. We drop the perfection of just intonation and tweak a few of the notes so that a respectable number of keys sound acceptable. Nothing is precisely in tune, but as long as we restrict ourselves to, say, six or seven of the common keys and their relative minors, we can get away with it. Actually, we might start to like it, because every key has its own character, due to an individual pattern of intervals which are slightly out of tune and "edgy".
There are, of course, various schemes for tweaking those intervals, and they all produce slightly different effects. If you want to stay pretty close to perfection, you can use Pythagorean tuning (following the principles of Pythagoras). If you want a bit more versatility, there's quarter-comma mean tone, Werkmeister 1, 2 and 3, and several others, all of which have been used at various times. The ultimate, though, is equal temperament. Here, we do a comprehensive tweaking job on all the notes, so that they are all equally out of tune. This means that all keys sound the same, apart from the difference in pitch. This allows you to move from the key of C to the key of F sharp in the same piece if you want, and it won't sound any worse. Enter Wagner. All modern keyboard instruments use equal temperament, and so all modern music is equally out of tune.
Equal temperament sounds OK on a modern piano, because it has a very thick sound which masks slight tuning errors. But you don't use it on harpsichords or clavichords, because it sounds slightly "off", but at the same time bland and boring. Bach knew all about equal temperament, and probably experimented with it, but he didn't regard it as a serious proposition for tuning keyboards. There is still some argument about exactly what tuning he used on his "Well tempered clavichord". It was no doubt his own home-brew method that he taught to his students, and it was probably similar to Werkmeister 2. It certainly wasn't equal temperament. The whole point of the 48 preludes and fugues was to exploit the differences in character between different keys. And in equal temperament, there are none.
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