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A perfect ,-.%ample of a Pi Disk, probably dating Jro,,, i/- sixth
century B. C., beautifully carted from a piece f .v unrous jade.
fixing of the handle or other provision for suspension.
Small wonder that the proper pitch was rarely hit in the
casting process itself. A separate tuning procedure had to
follow, and it is here that we find the first evidence of
the amazing scientific skills and techniques of ancient
China. Wings and tongue -shaped protrusions are added
to the shape of the original casting mould, and then these
protrusions are ground or filed down to raise too -low
pitches until the desired intonation is reached. A much
more complex problem is the flattening of too -high
pitches, because any decrease of sonorous matter tends to
raise the pitch. The Chinese solved this problem by
grinding away matter from the bells' large surfaces at certain
critical points where the acoustical vibration nodes
are located, or by punching holes into the bell body at
these points. As a consequence, the bell's elasticity was
raised, thus yielding a lower pitch (provided the loss of matter
in this process did not outweigh the flattening effect!).
If the hole were just a tiny bit too big, the pitch would
get too low and the bell would he spoiled for good.
It did not take the Chinese scientists and sound -engineers
very long to find out that though bronze bells
were a lot better than the unreliable bamboo pipes, they
were still very far from being ideal standards for invariable
pitch. All bronze bells produce a number of harmonic
overtones and non- harmonic partials which add certain
"impurities" to the ideally "pure" tone. Also, bronze
bells develop patination and finally corrosion as time goes
by, affecting the surfaces and interior molecular structure
of the bells, thus gradually destroying their true pitches
and sonorous qualities. In their search for the ideal sonorous
material they finally found the last and definite answer
-which is still good in 1955 A.D.- stone.
Probably as early as the sixteenth century B.C. the
ancient physicists and mathematicians experimented with
various substances, mainly limestone, marble, nephrite,
and jade. The earliest specimens of sonorous stones known
so far may go hack as far as 1600 B.C. They already show
an approximation to a pentagonal form which was to hecome
tradition in later centuries, and an incised ornamentation
of cultic symbolism. The next find, chronologically,
is from the Shang dynasty period and may be dated
as early as the fourteenth century B.C. Here the traditional
pentagon is fully developed and the stylized tiger furnishes
proof of a major acoustical and artistic achievement:
the scientist -lapidaries knew already how to calculate in advance
the effect of the carved ornamentation on the pitch.
And now comes the great surprise for our research.
The Royal Ontario Museum of Archæology in Toronto
possesses 18 sonorous stones which were found in
the Princes of Han tombs near Lo -Yang in North
Honan Province. The circumstances of the find make it
clear that the 18 stones belonged to probably six different
sets of 16 stones each; accordingly, 78 stones were missing
- lost or left behind undiscovered. I tested the 14 best
specimens, which were in perfect or near -perfect condition,
with high- precision frequency measuring equipment that
permits accuracy within one cent (r /too of a semitone).
The results were sensational: all stones were in perfect
Pythagorean intonation, i. e., derived from a circle of pure
fifths of 702 cents each, and the intonation of all
of them was precise within 2 -4 cents of mathematically
correct pitch. (The best -trained professional musicians of
our century cannot distinguish pitch differences below 3
or 4 cents in the frequency range represented by these
stones. And until about ten years ago we did not possess
electronic instruments precise enough to measure pitch
differences smaller than 4 -5 cents).
As the stones are odd pieces from various (up to six
or more) sets and still true to the same Pythagorean intonation,
it follows that they were all intoned to the
same sacred standard pitches and hence at will interchangeable
within various sets. This is a condition not
frequently met by the instruments of our modern symphony
orchestras, where most of the units have to be
re -tuned before and during every performance. Some of
the Toronto stones show circular marks from a grinding
process which was applied for precise and definite tuning.
The tombs of the Princes of Han were closed between
45o and 230 B.C. according to the latest archeological
opinions. This gives us a dating for the stones of 230 B.C.
or earlier. My own investigations have convinced me that
these lithophones were made between Continued on page 8i
Earliest perfect sonorous stone known. It was tuned and decorated
(with a tiger) during the Shang dynasty, at least 3000 years ago.
With the exception of the picture opposite this box, all photographs
for this article were taken by the author. The photographs
on pages 32 and 33 are used by courtesy of the Royal
Ontario Museum of Archaeology in Toronto; the photograph
at the top of this page is used by courtesy of the Metropolitan
Museum of Art, New York; the photograph across the page is
from China Reconstructs, No. 4 Peking, 1952.
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