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Everything You Always Wanted to Know About Windchimes (But Were Afraid to
Ask)

INTRO
I am writing up some notes after constructing a set of JI-tuned windchimes.
(Actually at this writing I don't yet have them in their final windchime
mounting, but the chimes themselves are all tuned up and I figure that's
the most interesting part.) This is to record and crystallize some of my
thoughts and to share with others in the hope of inspiring others' projects
and also to learn some things myself as the result of feedback. I started
just writing some basic notes and items to keep in mind next time to avoid
pitfalls, but it gradually mutated into a fairly detailed report. So here
it is!

For a long time I'd been wanting to make an instrument from metal, and
finally got around to starting something in fall 2000. I thought
windchimes would be a fun project, and a good way to get my feet wet
without embarking on something too involved yet. In themselves the
windchimes should be fun to have, but in the back of my mind building these
has been practice for some future microtonal tubulong instrument. (With so
many time commitments in my real life these days, this may be quite a way
off?)

MATERIALS
The basic chime materials are 3/4" steel EMT ? electrical conduit. This is
easily available at the local hardware store, and is cheap!

THE TUNING
I thought about a few different possible scales and chords (Just and
otherwise) for these chimes. To my mind, all had merit and I won't go into
describing my (almost arbitrary) thought processes to make a final
decision. The final result consists of 9 chimes in a harmonic series chord
with the ratios:
4-5-6-7-9-11-13-15-16

CUTTING AND TUNING
After looking at some other windchimes, I took a wild stab at desired tube
lengths and decided the shortest tube should be around 30 cm. Since my
total range is 2 octaves (4/1 ratio), the longest tube would be 60 cm
(length ratio = square root of freq ratio). Based on 60cm for lowest
pitch, I calculated on a spreadsheet the nominal lengths of each tube. The
equation for cutting the tube lengths is:

length / Lo = sqrt( fo/f)

where length = new tube length
Lo = known base tube length
f = new tube frequency
fo = known frequency of base tube

You don't need to know any absolute frequencies to calculate lengths for a
given set of ratios, as long as you don't care about tuning to some
absolute frequency reference. I had no specific frequency reference in
mind (e.g. A=440, etc.), since I really didn't have any idea what
frequencies would result when I cut the tubes to length. I figured
absolute reference didn't really matter anyway, since these will probably
not be used in an ensemble setting and have nothing to tonally clash with
(except perhaps the neighbors' windchimes). By sheer coincidence it turns
out my "9th harmonic" chime is pretty close to standard A.

Over Labor Day weekend I cut the tubes out of long pieces of conduit using
a hacksaw. (This actually takes some exertion. Next time I won't try to
do this while recovering from minor surgery!) I also drilled holes at the
node locations for stringing them up. The nodes are located at
approximately 0.22 of the total length. I strung up the tubes in my
basement and kept them around for several months while trying to decide how
to mount them and how to go about fine tuning them. They already sounded
great, and I often got distracted playing with them whenever going
downstairs for some unrelated purpose. The rough tuning got across the
general chord ok, but I was well aware of some significant mistuning.
Finally in February 2001 I borrowed some equipment ? a microphone, preamp,
and a basic Fluke multimeter with a frequency counter feature. (A
co-worker once suggested a great sales slogan "If you got a good
measurement it must be a Fluke!") This simple setup worked far better than
I had imagined possible. I was able to get clear, stable frequency
readings in Hertz, lasting for at least a few seconds after striking the
tube. This particular counter gives frequency to nearest 0.1 Hz. For my
purposes this should be fine.

I measured the frequency of all the tubes, and calculated a spreadsheet
showing what corrections needed to be made for each tube. (Obviously the
corrections are made by filing tubes to raise pitch, since it's pretty
difficult to lengthen the tubes once they are cut down.) These first
measurements were done in the lab at work. The next day I brought the
setup home to continue tuning over the weekend. Much to my dismay, my
frequency measurements had all increased by anywhere from 0.5 Hz (low end)
to around 2 Hz (high end). The first measurements had been done at room
temperature of probably 72 degrees F, and the later measurement was after
the tubes had sat in my basement for several hours?approximately 60 F. I
set all the tubes next to a small electric heater for a couple of minutes
and confirmed that the measurements lowered again. This surprised me,
since I had read that metal tubes are very stable with regard to frequency
vs temperature and other atmospheric conditions. Apparently not so, or at
least maybe it depends on the specific materials and quality. Since the
measurements seemed stable enough without changing temperature, I decided
to proceed at the colder temperature reference. (Generally the more
prudent choice when living in Minnesota.) Based on what I have seen, the
frequency drift with temperature seems to happen proportionally with base
frequency of each tube. So when the 4th harmonic chime drifted 0.5 Hz the
16th harmonic chime drifted 2 Hz. This is good?at least the chimes should
remain in tune with each other even if they drift together as a whole.

What I still had not taken into account was the fact that grinding two
pieces of metal together generates heat. Every time I made a tuning
adjustment by grinding the tube end with a file, the tube heated up. After
I had fine-tuned every tube (or so I thought) I measured later and found
that every tube had drifted again! I was very frustrated to discover that
I was shooting at a moving target. Since some of the tubes were now higher
than their original target frequencies, I recalculated new target
frequencies on a new higher base. This time I proceeded more carefully,
making smaller adjustments and then leaving the tubes for a long period of
time before measuring frequency. (Note to self: next time get hold of an
electric grinder?filing by hand is very tedious!) Finally I got all tubes
within approximately 0.4 Hz (worst case) of target frequency and decided to
"quit while I was ahead", although I would have preferred to tune all tubes
to within 0.1 Hz if I had the patience and time to keep repeating these
fine tunings over and over! It appears that all tubes are within 0.6 cents
of target, so I'm content with these results.

THE WELD
One problematic issue involving musical electrical conduit is the fact that
there is a weld along the length. You can clearly see the weld when you
look inside the tube. The weld disrupts the symmetry of the tube and
causes different tone qualities depending on where it is struck. Some
trial and error is needed to determine the right point(s) around the
circumference to strike the tube to get a clean sound. At some points you
will get a clear tone, and at other points you will get a slightly wobbly
beating tone. Ultimately it's a matter of taste, and the beating may be
inconspicuous or even desirable in some contexts, but my preference for now
is to get the cleanest tone possible. I generally found the cleanest tone
striking the tube about 60 degrees around circumference from the weld. I
marked the best striking point with a marker so I would know exactly where
to strike to get the best frequency measurements, and to try to best orient
the chimes when mounting. Unfortunately I didn't think this through when I
drilled holes for the hanging strings, so the hole locations are somewhat
haphazard.

IMPRESSIONS
The chimes have a beautiful sound. The harmonic series chord works
incredibly well, and creates a very vivid sonic impression. The longest,
lowest chimes have a wonderful deep tone with good volume and long sustain.
The highest chimes have much shorter sustain and weaker fundamentals.
Generally I would recommend keeping to the longer lengths. One could go
too far and make the tube so long that the fundamental tone is weaker than
other higher inharmonic partials, but my 60cm tube doesn't seem to be
pushing at that boundary.

After fine tuning the tubes the difference tone effects became more vivid.
Since a harmonic series will give combination tones in the same series, one
would expect that the more out of tune the individual members are the more
murky the complex of difference tones would become. (Even a 1 Hz error
down in the 100 Hz range of periodicity translates to about 20 cents!)
Indeed, the "rough cut" chimes before fine tuning played a reasonably
pleasant chord but did not give a strong unified feeling. Individual
chimes were off by as much as 20 Hz in the high end (most errors landed
between 10 and 20 cents from target). As it is now, the differences from
target are at least within 0.4 Hz. There is certainly a little bit of
error but it's close enough to clearly bring out the harmonic unity in the
tuning. When playing the chimes I hear a shimmering droning sound from
"somewhere behind" the chimes. The composite sound of all the chimes
together seems to fuse into one solid timbre.

COMMENTS ON TUNING VS. TIMBRE
On the tuning list and in other microtonal writings, one often encounters
discussion of the dreaded "tuning vs. timbre" issue. Obviously chimes are
struck tubes and have inharmonic partials. Does a harmonic series tuning
war against the inharmonic timbre? From reading some people's theories,
one might expect wretched results. I admit I was slightly nervous about
how these chimes would sound, and whether the effect of the JI tuning could
really come through with this timbre. In fact the final results are very
beautiful and striking (no pun intended), and vividly just.

Even though inharmonic spectra with a JI scale cannot produce the
coinciding partials found when using harmonic series timbres, there are
other effects unique to JI which still come into play. Mainly these are
combination tones and periodicity. These are very much in evidence when I
listen to my chimes, particularly up close (i.e. at high volume). That the
scale of my chimes is one harmonic series chord further reinforces the
sense of periodicity of the whole.

Also, after the initial attack (a fraction of a second after striking) the
timbre is predominantly a sine tone at the fundamental. (Of course
depending on where and with what it is struck?) I looked at the waveform
of individual chimes on an oscilloscope and confirmed that the overall
waveform is a clear sinusoid with "a bit of other small stuff riding on
it". So the inharmonic partials may be a bit of a red herring here (at
least in this particular case). This may also be true for idiophones with
resonators for the fundamental, as others have mentioned before.

CURRENT STATUS
Currently I still have the chimes strung up on a wire in my basement, and
I'm still playing with them whenever I happen to walk by. I've got some
wood and plexiglass pieces which I plan to cut up for final mounting of the
windchimes. I'll arrange them in a circular pattern in such a way that the
weight will distribute more or less evenly, and hang them so that the
striker will line up with the center of each chime. Hopefully this will be
done before spring has fully sprung. (As I write this, we've still got
about two feet of snow in our yard.)

FINAL LENGTH AND FREQUENCY TABLE
The following lengths were calculated for the 60 cm base. The final actual
lengths are probably within a couple of millimeters of these values.
Frequencies are the final measured values.

pitch cm calc hz meas hz calc cts meas cts
1 1/1 60.00 393.2 393.2 0.0 0.0
2 5/4 53.67 491.5 491.5 386.3 386.3
3 3/2 48.99 589.8 589.9 702.0 702.2
4 7/4 45.36 688.1 688.1 968.8 968.8
5 9/4 40.00 884.7 884.8 1403.9 1404.1
6 11/4 36.18 1081.3 1081.7 1751.3 1752.0
7 13/4 33.28 1277.9 1278.0 2040.5 2040.7
8 15/4 30.98 1474.5 1474.6 2288.3 2288.4
9 4/1 30.00 1572.8 1572.9 2400.0 2400.1

Comments and questions welcome...
regards,
kris peck

"...destruction is, after all, a form of creation."
--Graham Greene

Hi Kraig-

" As a last resort one can file in the middle of the tube all the way
around if need be to lower
the pitch. This though can be visually unappealing. "

-I thought of this, but in addition to being ugly I think it would also
compromise the evenness of striking surface if you want to strike in the
middle.

" I have noticed that the woodstock chimes will start the scale in
places that are sometimes
surprising and then i realized it is to keep it from "resolving". like
starting on the fifth of a
scale or where a tritone or semitone hits against the lowest bar. They are
great random note generators and can involve quite a bit of ingenuity."

-I'm not sure what you mean. Do you mean the order of the tubes in their
physical arrangement? Or the range of pitches (highest and lowest) in a
given scale? I suppose I could get a similar effect if I removed the 4 and
16 chimes so the "tonic" is never actually voiced. No place to "come home"
to.

" Have you noticed difference tones with your tubes?"

Yes- I mentioned this briefly in my original post. An interesting thing to
try is picking out a particular pair of chimes and play them together,
listening for the difference tone. Then play the chime corresponding to
that tone to confirm the perception. For example, I can play the 11 and 16
together and then play the 5. Or the 13 and 7 together and then play the
6, etc. This makes a very vivid demo of the difference tone effect!

I was fascinated by the difference tone effects on your metal instruments
when I visited last fall! The effect on my chimes is much simpler, but
also pretty clear. I think I do agree with others on the list who have
mentioned that combination tones are ultimately the result of nonlinear
distortion in the ear because of high SPL levels. I haven't carefully
checked this, but I'm guessing you wouldn't notice difference tones when
playing the chimes (or other) quietly.

Question to you Kraig and any other metal-workers... I mentioned my
experience of the frequency drifting with temperature. Does that ring a
bell (sorry...) with your experience? I know a couple of cents drift is
not necessarily a lot, but I would think it would drive some people nuts
and I'm surprised I haven't seen this effect mentioned before. Again,
maybe it affects some materials more than others. I wonder if nice
aluminum alloy no-weld tubes would be more temperature stable than steel
welded EMT?

windchimes

🔗kris.peck@telex.com

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗kris.peck@telex.com

🔗Alison Monteith <alison.monteith3@which.net>

🔗Kraig Grady <kraiggrady@anaphoria.com>