Chinese bells

Dear Martin,
I located an article "Acoustics of Ancient Chinese Bells" in Scientific
American, April 1987 but as I reread it, it's pretty scant on actual
pitches. I'll send you the article. An excerpt from pages 107 reads as
follows:

The interval between the two pitches on a zhong bell is selected by
casting and tuning. The choice of the interval is arbitrary, but it
should suit the melodic progression of the compositions it will
perform. In addition the interval should not be a discord since, in
spite of the efforts of the designers, traces of the secondary tone may
persist after the primary tone has died down. Zhou engineers tuned
their bells so that the intervals of the overtones, as well as those of
the fundamentals, were harmonics. The second partial of the gu tone,
for example, is always an octave plus a major or minor third above the
sui tone; the partials of a zhong bell with a minor third separating its
two pitches are in the ratio 1:1.2:2.4:2.81:3 and those of a bell with
an interval of a major third are 1:1.25:2.5:2.81:3.

When bell-chime intervals from several periods are compared, a
historical trend toward the major- and minor-third intervals represented
in Marquis Yi's bell collection becomes apparent. . . .
RT

Subject: Re: [tuning] Digest Number 375
Date: Mon, 1 Nov 1999 10:24:03 -0500
From: martin hatch <mfh2@cornell.edu>
Reply-To: tuning@onelist.com
To: tuning@onelist.com

From: martin hatch <mfh2@cornell.edu>

"Tuning" people,
Can anyone tell me the location of an article on the tuning (including
partials) of the original Hubei Marquis Yi bells? I specify "original"
because the bells that toured the U.S. (and are recorded on the Fontana
CD
called "The Imperial Bells of China") are facsimiles made in the 20th
century. In my quick spectral analysis of the tuning of a couple of the

bells from the facsimiles, I think that the partials have been tuned as
1:1, 2:1, 3:1, 4:1, and 5:1 (the lowest bell is 172.3, 344.7, 516.5,
689.4,
and 861.2). Were the originals that way?

Marty Hatch

Marty Hatch
Department of Music
Lincoln Hall (now in White Hall 316)
Cornell University
Ithaca, New York 14850, U.S.A.
607-2555049
fax: 607-2542877