In 1893, the august Grove Dictionary of Music and Musicians stated that Johann Sebastian Bach wrote The Well-Tempered Clavier to demonstrate equal temperament. That was a misconception. And it has filtered down into hundred of music history texts, a lie so pervasively believed that it will take generations to correct.
Bach, after all, did not write The Equal-Tempered Clavier. But in his day, they did refer to a temperament in which all keys were usable as an “equal” temperament. But the truth was (and all this material comes from a wonderful book, Tuning: Containing the Perfection of Eighteenth-Century Temperament, the Lost Art of Nineteenth-Century Temperament, and the Science of Equal Temperament, East Lansing: Michigan State University Press, 1991, by piano technician Owen Jorgensen) that, back then, they had no way to truly divide the octave equally on a piano or harpsichord. They didn’t have oscillators or electronic tuners. And while, by Bach’s day, composers wanted to have all keys available, no one was interested in making them all the same. Each key had its own interval pattern and its own different color, so that one kind of music sounded better in E flat minor, while another came off much better in F major. There were reasons for choosing a specific key, and Bach wrote his preludes and fugues to illustrate those differences, not to suggest that they didn’t exist.
I do an experiment with my students: in a blindfold situation, I play the Bach preludes each in several different keys, and let them guess which key the prelude was written for. They usually get it right. The E flat minor Prelude, for example, sounds really flabby in E minor, and the C major prelude takes on a weird, too-bright quality in C#.
The tunings that dominated the 18th and most of the 19th centuries are now referred to as well temperaments. There were many different varieties. Tuning, for most of musical history, was an art, not a science, and each piano tuner has leeway to use his own taste. Some of these temperaments have reasonably familiar names: Werckmeister III, Kirnberger III, Vallotti-Young. (That’s Thomas Young, not La Monte – he wasn’t quite in the picture yet, or Beethoven’s sonatas might have sounded very different.) Some of these tunings you can find more information about on my Historical Tuning web page, but to save space I’ll only describe one here: Thomas Young’s well temperament of 1799.
The principle of well temperament is this: Imagine the circle of fifths. Now imagine that you squeeze the fifths nearest C slightly to make the thirds (C-E, G-B, F-A) a little flatter and more in tune. That means that you’ll have larger fifths and thirds on the opposite side of the circle of fifths, around F#. In most well temperament, and especially this one, the keys most closely related to C major/A minor have the flattest fifths and the most consonant thirds. Black-note keys like F# major and Eb minor have purely in-tune fifths, but their thirds are a little harsh and bitter. Therefore, when you want to write something like a Funeral March in an especially bitter, tragic key, you write it in B flat Minor – which is what Chopin did with his Funeral March Sonata. When you want a kind of majestic spookiness, as Beethoven did in the adagio of the Hammerklavier, you write it in F# minor, where the thirds aren’t bad and the fifths are especially stately and in tune.
A 0 cents
Bb 102 cents
B 196 cents
C 306 cents
C# 396 cents
D 502 cents
Eb 600 cents
E 698 cents
F 804 cents
F# 894 cents
G 1004 cents
G# 1098 cents
As you can see, no pitch here is more than 6 cents away from equal temperament, but the differences, if subtle, are still striking. The major third C-E is 392 cents, the major third F#-A# 408 cents, much harsher. All the black-key perfect fifths are perfectly 702 cents, while C-G is only 698 cents; the black-key fifths sound much purer. C# major and F# major are really active keys, bristling with overtones. C and F major are sweet, mild keys, and E flat minor is pungent. This is the tuning in which Beethoven heard his music (before he went deaf), and it clearly influenced his choices of keys, as it did for every other composer before the mid-19th century.
The first recording of Beethoven’s music in the original temperament appeared a couple of years ago: Beethoven in the Temperaments, with pianist Enid Katahn and piano tuner Edward Foote (Gasparo). The disc includes the Moonlight Sonata, the Waldstein, and the Pathetique in a late-18th-century well temperament that brings out subtle color differences among the keys.
Well temperament is hardly a dead issue even for composers today. The Californian composer Lou Harrison loves to use well temperament, and in fact wrote his entire Piano Concerto, recorded by New World Records, in Kirnberger III, which is fairly similar to Young’s tuning above. (Check out the Lou Harrison Web Page.) The mystic New York composer Elodie Lauten often writes music in well temperament, often combining it with equal temperament at the same time for a scintillating, slightly out-of-tune effect.
I have both my pianos tuned to Young’s 1799 temperament, my Steinway grand at home and the Disklavier in my Bard College office. I basically write for keyboard in well temperament, and I see no reason to go back to bland equal temperament. I know of no keyboard music that doesn’t sound better and more interesting in well temperament. The only music that equal temperament supports, as Lou has often put it, is 12-tone music; in 12-tone music, all the major thirds are theoretically equal, all the major 7ths, and so on, so I suppose one might want equal temperament to play 12-tone music authentically. But I see no other advantages. And how many of us play a repertoire dominated by 12-tone music?
Chronologically, this brings us back to 12-tone equal temperament – and if you can’t say anything good about a tuning, you shouldn’t say anything at all, I suppose, which is why I’ll direct you to the just intonation page or back to the tuning page.