wind chimes

Hi all,

Following a link from Pat Missin's site, I found a page of Tom
Arneberg's, titled -
Harmonet postings about building wind chimes with barbershop 7th chords.

I started reading it and found that Herb Bayles, having
measured the following lengths and notes on a small set of
wind chimes, was puzzled by the fact that they didn't follow
the same laws as notes on a stretched string -
C 352mm
E 315mm
G 286mm
A 217mm
C 248mm (the octave above).

So I constructed a spreadsheet in Excel to find the actual
relationship between frequency (or interval from the root)
and length. Mindful of our recent discussions about John
Harrison using logs to determine frequency-size relations
for bells, I took logs of both variables and plotted them.

With the assumption that the measurement for A is wrongly
transcribed, and should instead have been 277 mm, all the
frequencies are very nearly proportional to the inverse
square of the length. The fit of the data is extremely good,
as can be seen by the coefficient of determination being
almost 1.

Interestingly, the last post in Tom's page has Dave Chapman
mentioning this exact law, which is useful confirmation.

If you'd like to make yourself a set of wind chimes, note that
each chime should be suspended at about two-ninths the way
from the end. (More exactly, so the length is 4.55 times the
distance of the suspension point from the end.) There are
recipes on the page for constructing two sets of chimes, one
an octave higher, from (US) standard 10-foot lengths of
3/4-inch copper pipe. As we've been all-metric in Oz for
decades, I'm not sure what the standard lengths are, tho we
do use 19mm copper pipe, very nearly 3/4".

Spreadsheet attached, in Excel 2000 format.

Regards,
Yahya
------------------------------------------------
Yahya Abdal-Aziz
Yahya@MelbPC.Org.Au
Melbourne PC User Group
Member 1075
Convener, Graphics Interest Group
Convener, Music Interest Group
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