Today, we set the pitch of a concert
A. 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.
The story is told of a
conductor who had problems with an out-of-tune
soprano. Finally he turned to her in frustration
and hissed, "Madam, would you please give the
concertmaster your A?"
Today's A above middle
C has been set at 440 cycles per
second or 440 Hertz. Before the concert, the
concertmaster bids the oboist play an
A for the winds. Then he tunes to
that A and plays it for the strings.
In the end, all ninety players should be agreed on
the same 440 A, but the best human
ear is hard put to tell a 440 A from,
say, a 442 A. The best-tuned
orchestra is close to, but never exactly on, the
So how did we create that particular pitch before
we had electronic measurements? How did we tune a
tuning fork? Agreeing on pitch became a serious
problem as orchestra sizes increased during the
Baroque era. Baroque musicians often used organ
pipes as standards even though pitches varied
greatly from one organ to another.
In 1619 composer Michael Praetorius proposed a
particular A-425 organ pipe as a
standard. He pointed out that higher pitches led to
broken violin strings. That was almost a half-step
below today's A-440. Down through the
Industrial Revolution, A
generally stayed below that 425 Hertz number. The
tuning fork Handel used in the premier of
Messiah is still around. It gives
But 19th-century instruments took on the
mechanization of steam power and music intensified.
People lengthened violin necks. Gut strings gave
way to steel. Valves appeared in French horns. Orchestras became
larger, louder, and more lush. Pitches also rose.
By 1850 A's were crowding 450 Hertz.
Much 18th-century music could no longer be
performed at those pitches. Musicians grew alarmed.
Enter now a physics professor named Jules Antoine
Lissajous. Lissajous had written a thesis on the
mechanics of tuning forks, and in 1855 he wrote a
paper proposing to set A at 435
Hertz. Three years later Napoleon III set up a
commission to set a standard, and he appointed
Lissajous to be its consultant.
Lissajous had developed clever means for
calibrating a new tuning fork against a standard
fork. He fixed small mirrors to one tine on each
fork. Then he shone a beam of light on one
vibrating mirror so it reflected onto the second
vibrating mirror and then upon a screen. The result
was a steady ellipse if the two forks were in
agreement. The figure would swim about if they were
And so we created standard tuning forks. One rides
in my wife's violin case today. But the French
couldn't stop the trend of rising pitches just yet.
Only in this century has the pitch of an
A been held at 440. Today's orchestra
players are likely to walk onstage with instruments
pretuned to a backstage oscilloscope. An electronic
policeman holds the line. Only Baroque ensembles
revert back to an older and gentler standard -- to
an A of 415 Hertz.
I'm John Lienhard, at the University of Houston,
where we're interested in the way inventive minds
Lindley, M., Wachsmann, K., Rhodes, J. J. K., and
Thomas, W. R., Pitch. The New Grove Dictionary of
Music & Musicians, (Stanley Sadie, ed.) Vol.
14, pp. 779-786.
Turner, S., Demonstrating Harmony: Some of the Many
Devices Used to Produce Lissajous Curves Before the
Oscilloscope. Rittenhouse Journal of the
Scientific Instrument Enterprise, Vol. 11, No.
2, 1997, pp. 33-51.
Lissajous, Jules Antoine, The Dictionary of
Scientific Biography, Vol. 8, New York: Charles
Scribner's Sons, 1973, pp. 398-399.
Tyndall, J., Sound: A Course of Eight lectures
Delivered at The Royal Institution of Great
Britain. New York: D. Appleton and Company,
1867, see especially pp. 58-63.
I have taken some liberties here in the name of
simplicity. Baroque pitches varied all the way down
to around A-390. There is also
evidence that some Italian Baroque ensembles may
have used an A as high as 460. It is
common for harpsichords to tune to
A-392 today. The range form 410 to
425 seems to have been typical in the 17th and 18th
centuries, however. Today, many orchestras are once
again pushing pitches up beyond A-440
in an attempt to create a brighter sound.
I am grateful to several musician friends for their
counsel, notably Matthew Dirst and Katherine
Ciesinski of the UH Music School, Bob Stevenson of
Radio Station KUHF, and Mark Powell of both
From a Lissajou article in
Annales de Chimie et de Physique,
representation of Lissajous's tuning fork
Click on the thumbnail
for a full-size image
Each of the eight rows shows five possible
Lissajous patterns for one in-tune pair of tuning
forks. The pairs of forks sound in the following
intervals reading from top to bottom:
(The last three of these intervals have
fairly inaccurate equivalents in our tempered
(6) 3 to 5
(7) 4 to 5
(8) 5 to 6
The Engines of Our Ingenuity is
Copyright © 1988-1998 by John H.
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