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
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 50 years longer
than we have.
I'm John Lienhard, at the University of Houston, where we're interested
in the way inventive minds work.
Temple, R., The Genius of China. New York: Touchstone Books,
Simon and Schuster, 1989, pp. 209-213.
The Engines of Our Ingenuity is Copyright © 1988-1997
by John H. Lienhard.