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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