If somebody really wanted to demonstrate ET, wouldn't they just compose a single piece to be played in 12 different keys? To compose a different piece for each of the 24 major and minor keys would defeat the whole purpose, since each piece is different anyway. No, it seems clear to me that the only reason someone would compose 24 very different pieces, to be played in different keys, is to highlight differences and perhaps still to show that all keys are useable.

Since Well Temperament is a genre of systems, and not just a single system, many of the comments Earnest made about Kirnberger also apply to Werckmeister.

Mr. Gann, from David's link says:

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Bach did not use equal temperament. In fact, in his day there was no way to tune strings to equal temperament, because there were no devices to measure frequency. They had no scientific method to achieve real equal-ness; they could only approximate.

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Looking over the system for tuning Well Temperament by ear, the need to actually gauge beats is very minimal; and it's done in a way that's mostly relational. No wonder people found it much easier to tune their own keyboard instruments before equal temperament. Earlier systems mostly involved tuning intervals beatless.

Here's a link to a bibliography with more than anybody (except Jim) will ever want to know on the subject of temperaments:

http://www.xs4all.nl/~huygensf/doc/bib.html

From there I found this piece by someone fairly serious, who claims to know what system Bach used,(he also says Werckmeister), and he explains how it differs from Kirnberger. He gives specific instructions for how to tune this temperament by ear. I'm going to try this. It may be a great use for my Fender Rhodes, that I converted to a bookshelf about 15 yeras ago.

http://ha.kellner.bei.t-online.de/

And here's another, with detailed information on many temperaments. I notice that the date given for the particular Kirnberger he lists is after Bach died. He does say Kirnberger was a student of Bach's:

http://www.rollingball.com/TemperamentsFrames.htm

Here's a great general bibliography on Bach:

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Bach did not use equal temperament. In fact, in his day there was no way to tune strings to equal temperament, because there were no devices to measure frequency.

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On the contrary, people certainly knew about equal temperament then, and they could tune that way. After all, piano tuners do it without electronic help.
The reason that (almost) nobody tuned ET in Bach's day was exactly the same reason that (almost) no steel players do it today: other tunings sound better than ET, as long as you only play in a few keys (a few keys at each fret for us).

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Gann does acknowledge that, toward the top of the linked article:

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Equal temperament - the bland, equal spacing of the 12 pitches of the octave - is pretty much a 20th-century phenomenon. It was known about in Europe as early as the early 17th century, and in China much earlier. But it wasn't used, because the consensus was that it sounded awful: out of tune and characterless. During the 19th century (for reasons we'll discuss later), keyboard tuning drifted closer and closer to equal temperament over the protest of many of the more sensitive musicians. Not until 1917 was a method devised for tuning exact equal temperament.

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I'm almost tempted to say "Big Deal." No one who understands the subject wants a piano (or harpsichord)that's tuned exactlyto the mathematical ET numbers -- which are based only on the fundamental frequencies of notes, divorced from the peculiarities of specific instruments -- anyway.

Divorced from his statement at the top of the page, his comment about frequency counters does sound like he's implying that ET didn't even exist in Bach's time.

I'll have to check around some more when I get time. I'd like to see the early method for tuning equal temperament. Maybe, like the methods for other systems of the time, beats were used in more of a relational way that wasn't based on exact numbers.

It's hard to say how "exact" someone could tune ET by ear during Bach's time, as compared to today, without knowing the earlier systems. If I were to go out on a limb, I'd guess that a tuning comparable to today was possible, but more difficult; since approximate numerical guidelines derived from frequency analysis were not then available as aids.

[This message was edited by Jeff A. Smith on 19 September 2003 at 08:41 AM.]