Engines of Our Ingenuity

No. 380:
EQUAL TEMPERAMENT

by John H. Lienhard

Click here for audio of Episode 380.

Today, we invent the well-tempered clavier. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

You hear so much wonderful music on this station. Most of it's played in tempered scales. The notes of a tempered scale are just a little off the natural harmonics of vibrating strings. They're slightly out of tune. At least they are when you compare them with natural harmonics. That's the bad news, but it's not very bad. The difference is so small that most of us can barely hear it.

The good news is that equal temperament lets you transpose freely on a fixed-pitch instrument. If you didn't have it, you'd be able to play a piano accurately in only one key. That's a tradeoff most modern musicians are willing to make.

At first, equal temperament threw two groups into passionate opposition. Purists like the composer Giuseppe Tartini were violently opposed to it. The practical Johann Sebastian Bach was equally intense in promoting it. His great polemic for equal temperament was, of course, his book of keyboard pieces with varied key signatures. It was The Well-Tempered Clavier.

The Well-Tempered Clavier came out in 1722. Eighty-six years before, Père Mersenne set down the modern mathematical basis of equal temperament in his Harmonie Universelle. Only after that did equal temperament start gaining acceptance.

The startling thing about all this is that the modern scheme of equal temperament isn't a Western one at all. Mersenne's book came out in 1636. But a very different author published the same theory a half-century earlier. It was published in 1584 by Chu Tsai-Yu, a prince of the Ming dynasty. The first Western reference to Chu was made by a European mathematician in 1620. That was 16 years before Mersenne; and Mersenne didn't mention Chu at all.

Many European inventions were made independently after the Chinese had thought of them first. Not this one. A Jesuit student of China, Matteo Ricci, attended a Chinese trade fair in Canton the same year Chu published his work. Ricci almost certainly brought Chu's work out of China and back to the West.

Today our ears are so trained to equal temperament that we think natural temperament is slightly out of tune when we first hear it. Equal temperament is as Western as apple pie. We're willing to concede gunpowder and compasses to the Chinese, but surely not this! Yet, even today, the Chinese use the same tuning to play their unfamiliar scales as we do to play ours. The only difference is that they've been using it at least fifty years longer than we have.

I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.

(Theme music)


Temple, R., The Genius of China. New York: Touchstone Books, Simon and Schuster, 1989, pp. 209-213.

Listener Ed Mikkola writes (in 2004) to point out that this episode (written in 1990) is out of date on an important point. Bach wrote for the well-tempered clavier, not for an instrument of equal-temperament -- that the wide use of equal temperament came in with the large orchestras of the nineteenth century. He also points out that most of us, who might have trouble discerning scales tuned in different schemes of temperament, will actually react more negatively to music played in equal-temperament, on a less-than-conscious level.



The Engines of Our Ingenuity is Copyright © 1988-1997 by John H. Lienhard.

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