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I've saved all the related postings and concatenated them into one file here in case others are interested in the results. If anyone knows of anything I've left out, please let me know.
- Tom Arneberg tom@arneberg.com
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From nfinn@cisco.com Thu Jul 28 18:22:11 1994
To: Probemoter@aol.com
Subject: Re: Needed: Barbershop Physicist
Cc: bbshop@cray.com
> From Probemoter@aol.com Thu Jul 28 14:13:40 1994
> Subject: Needed: Barbershop Physicist
>
> I'm fed to the teeth with jangly, dissonant wind chimes. I want to construct
> a set which puts out a barbershop seventh.
>
> My high school physics class is nearly a half-century behind me, but as I
> best recall there is a precise mathmatical relationship between length and/or
> diameter of metal tubes (assuming wall thickness remains uniform) and musical
> tones. It's the relationship used to tune organ pipes. I seem to recall a
> formula to calculate tonal relationships.
If cut from one length of uniform tubing, the lengths will be inversely
proportional to the frequencies. Since you want the frequencies in the
ratios proper for a barbershop 7th, the lengths come out as:
frequency length
root 1 1
third 5/4 4/5
fifth 3/2 (6/4) 2/3 (4/6)
seventh 7/4 4/7
Since octaves (doubling or halving the length) don't count, you can
mix and match any of the following ratios. Just pick any one ratio from
row "root", one from row "third", etc. You will probably want the
longest (lowest-pitched) pipe to come from the root or fifth row.
root 1
third 2/5 4/5 8/5
fifth 1/3 2/3 4/3 8/3
seventh 2/7 4/7 8/7
Here are three good barbershop 7th chords and the lengths of the
pipes, expressed as whole numbers. (These could be measurements in
millimeters, for example.) Try them out on a piano to see which one
you like. The third one is spread out a ways from the lowest to the
highest note.
Piano notes, low to high: G-B-D-F D-F-G-B D-B-F-G
Pipe lengths (Root, 105 (R) 140 (5) 280 (7)
3rd, 5th, 7th) 84 (3) 120 (7) 168 (3)
70 (5) 105 (R) 120 (5)
60 (7) 84 (3) 105 (R)
For example, you might make your pipes:
1 2 3 4
G-B-D-F G-B-D-F D-F-G-B D-B-F-G
root 12.000" 210mm 12.000" 6.000"
third 9.600" 168mm 9.600" 9.600"
fifth 8.000" 140mm 16.000" 16.000"
seventh 6.857" 120mm 13.714" 6.857"
Of course, you'll have to experiment with the lengths to get the
overall pitch you want. You can multiply every number in a column
by the same number and get the same relationships between the notes.
Column 1 is the GBDF chord with the root (105) = 12 inches. Column
2 is that same chord, with all the numbers doubled in millimeters,
and so on. I gave you the millimeter column because you may find
it easier than measuring 13.714".
Let us know how the project comes out!!
-- Norm Finn,
San Jose, CA, Garden City Chorus
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From dmb@sdiv.cray.com Mon Aug 1 15:31:49 1994
To: panter@micor.ocunix.on.ca
Subject: Re: Needed: Barbershop Physicist
Cc: bbshop@cray.com
Don't forget when building the BB7 chimes that we're dealing with
bells, not organs. We don't care whether we're dealing with tubes
or rods. We can predict the pitch of a tube when we're setting the
enclosed air into resonant motion. We can't predict the pitch of
a pipe used as a chime without knowing its mass and distribution.
I'd point out that it will take some experimentation (and some
artistry) to come up with a proper clapper for the chimes. A tube
chime will ring with different degrees of loudness and brilliance
depending on exactly where you hit it, and exactly how and where
you support it. Support it and/or hit it at the wrong place, and
it will sound dead or dull, or bright and pretty, or even ring an
octave above its normal tone. I gave some mechanical formulas.
It takes an artist to make it into a beautiful chime!
-- Norm
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From owner-bbshop@cray.com Fri Aug 19 13:47:08 1994
To: bbshop@cray.com
Subject: Wind chime update
Some time ago I posted here a request for technical advice regarding
construction of a wind chime producing a barbershop seventh chord. A number
of Harmo-netters responded with precise information, for which I am *very*
grateful. Here's how the project went.
I purchased a "stick" (ten foot length) of common 3/4 inch rigid copper pipe.
Using a metric tape measure, an ordinary tubing cutter tool and the "measure
twice, cut once" philosophy, I proceded to reduce the stick to short tubes.
These, I drilled near one end, strung them on monofilament line and tapped
them with a small mallet. The result? Alas, it sure as heck wasn't a
barbershop seventh! Far from it, in fact.
I'm not sure what went wrong. Finished lengths were not quite precise; it's
tough to be completely accurate with the tubing cutter I used. Still, the
finished tubes are within a milimeter or so of the lengths prescribed. Also,
the tubing cutter crimped the ends of the tubes to a small degree. Perhaps
that had some effect on their tone. One day soon I shall get a reamer and
remove the crimp.
Anyway, folks, that's the present status of the barbershop wind chime.
Bowed, but unbeaten, I shall try it again some time in the near future.
Thanks for all the assistance.
Herb Bayles
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From owner-bbshop@cray.com Mon Sep 5 13:09:30 1994
To: bbshop@cray.com
Subject: Wind Chimes
To: Don Bray
Hello, Don,
I think you have hit on something significant. I'm the guy who originally
raised the wind chime issue, and I received a lot of E-mails citing the
mathmatical relation of length to tone.
However, my attempt, using the ratios cited, were a total flop. I didn't get
the notes I expected. Also, the common rigid copper pipe I used didn't
produce a very pleasing tone.
The reason, I think, is explained by your observations that the metallurgical
property of the metal and its resonance, rather than the length of the air
column determines the musical tone and its quality.
So, I guess it's back to square one for my project.
My neighbor has a wind chime with nice musical notes, but sadly, it's a
C-sixth chord; very unpleasant for a barbershopper. I note that the tubes in
his wind chime are chrome plated and seem to be a very hard metal. I offered
to try and tune (shorten) the sixth note (A) tube to a B-flat, but he wisely
refused me.
Herb Bayles
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From owner-bbshop@cray.com Mon Sep 5 18:08:31 1994
To: bbshop@cray.com
Subject: Wind chimes redux
I have been stymied in my efforts to build a wind chime which sounds a nice
barbershop seventh chord. A number of you Harmonet-ers came up with specific
suggestions, but they simply didn't work. Then Don Bray, College Station,
Texas, <73250.2107@compuserve.com came up with clues which may explain my
failure.
Don suggests that wind chimes are *not* resonating columns of air like a pipe
organ, but are *bells.*, and their tones are products of their metallurgical
quality, mass *and* size.
Makes sense, Don.
Consider the pipes in a pipe organ. They are essentially *whistles,* closed
at one end and excited by introduction of a flow of air. Then, there's the
old toy slide whistle. It has one basic tone which may be infinitely altered
by moving the slide. (Effectively, changing the length of the column of air
resonating within it.)
Now consider bells, be they the ones in carillon towers or the ones used by
bell choirs. No resonating air there; they aren't even tubes.
The notes they sound are certainly determined by their size, but I suspect
they also vary from one another in their thickness and possiblilty the
material from which they're cast.
Consider, now, marimbas and xylophones. No chance of columns of air there.
Simply wooden or metal bars resonating when struck.
My neighbor has a wind chime which sounds a solid sixth chord (ugh!) almost
in the key of C. I carefully measured the tubes from which it is made (they
are 3/4 inches in diameter and seem to be made from a non-ferrous
metal--possibly tempered aluminium) and came up with the following
dimensions:
C 352mm
E 315mm
G 286mm
A 217mm
C 248mm (the octave above)
Calculated ratios among these lengths bear absolutely no resemblance to the
ratios for wind-blown tubes.
Back to the drawing board! Any ideas?
Herb Bayles
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From owner-bbshop@cray.com Thu Sep 8 18:11:37 1994
To: bbshop@cray.com, owner-bbshop@cray.com
Subject: Re: Wind chimes redux
This is pretty long, so if you're bored to death with the wind-chime
blow right past this now... :-)
Herb Bayles wrote (heavily editted):
>I have been stymied in my efforts to build a wind chime which sounds a nice
>barbershop seventh chord. ... Then Don Bray, College Station,
>Texas, <73250.2107@compuserve.com came up with clues ...
>
>Don suggests that wind chimes are *not* resonating columns of air like a pipe
>organ, but are *bells.*, and their tones are products of their metallurgical
>quality, mass *and* size.
>
>Makes sense, Don. ....
>
>My neighbor has a wind chime which sounds a solid sixth chord (ugh!) almost
>in the key of C. I carefully measured the tubes ...
>and came up with the following dimensions:
>C 352mm
>E 315mm
>G 286mm
>A 217mm
>C 248mm (the octave above)
>
>Calculated ratios among these lengths bear absolutely no resemblance to the
>ratios for wind-blown tubes.
>
>Back to the drawing board! Any ideas?
So, I decided to see what I could lend to this.
I dug up some information on bells and their harmonics. All of this is
from _The Science of Musical Sound_, by John R. Pierce (Scientific
American Books/W.H.Freeman and Co.). (I had to cheat on a couple things,
re-phrased in [brackets], to keep this in ASCII.)
"The sounds of orchestral bells and of tuned bells are not
periodic, and these sounds do not have all the properties of
periodic musical sounds. One can play tunes with bells,
and the pitches that are assigned to bells can be explained
largely in terms of the frequencies of prominent, almost-
harmonic partials." (p. 37)
..."Furthermore, we can have a sense of pitch and unity of
sound even when the frequency intervals between successive
higher partials are not exactly equal. This is how we
ascribe a pitch to bells. This pitch is not the frequency
of the lowest partial (the _hum_tone_), but an average of
the frequency separations between some higher partials of
the sound of the bell." (p. 89)
..."Bells and gongs differ from strings in that, as we have
seen, their partials are not harmonically related. Their
tones do not give conventional effects of cosonance and
dissonance when we use them to play conventional harmony;
yet we can play recognizable melodies on bells and gongs,
which do give a sense of pitch.
"A great deal of study has been devoted to bells, gongs, and
related instruments. Among these are orchestral chimes,
which are long, uniform metal tubes hanging from one end so
that they can flex and vibrate freely. The frequencies of
the first few partials of a typical chime are shown [below].
Here the fourth, fifth, sixth, and seventh partials are
approximate harmonics of a frequency equal to 4.5 [times the
fundamental], which is therefore heard as the perceived
pitch of the chime." (p. 183)
The following is a close copy of a table on p.183 labeled
"Partials of a chime" :
1st 2nd 3rd 4th 5th 6th 7th
1 2.76 5.40 8.93 13.34 18.64 31.87 x fundamental
4.5 2x4.47 3x4.45 4x4.66 7x4.55 x fundamental
^
+------ percieved pitch is 4.5 x fundamental frequency
The author goes on from this last quote to mention that the tuning of
bells was figured out largely by experimentation with lots of castings; and
that such tuned bells sound more like chords than the musical tones produced
by other (string, wind) instruments. (Hmmm... a BBS7 bell, anyone?)
I don't have access to chimes (anymore- I did play them in High
School!) but I'll bet a 7th chord played on them doesn't "ring". Or
at least, not much.
Also, note that the table gives you the harmonics for an expensive
instrument. I'll bet that it would take a lot of work to get
wind-chime tubes to conform to this progression! The "tinkly" sound
of wind chimes is due to even less orderly harmonics, I'll bet.
I conclude from this two things:
The wind chime tubes' lengths should be cut not to the fundamental
frequency, as was tried, but to a length 4.5 times that, to give a
*percieved* pitch equal to the note you want each to produce;
and
Even if you do this, it won't "ring" well because the harmonics
aren't quite right. (Odd to talk about bells not ringing!)
(Sanity check - if my first conclusion is correct, the longest of the
chimes (.352 m) measured by Herb should produce a percieved pitch of
f = 4.5*(v/2L) = 4.5*(344/((2*.352) ) = 2199 Hz
The closest C to this is 2093 Hz (C''). Pretty close, but not C!. The
315mm chime would be percieved as 2457 Hz, closer to D-sharp at 2489 Hz
than E at 2637 Hz.... How sure are you of those notes, Don?)
(Sanity check 2 - Don, did your chimes sound a lot higher than you thought
they would? )
Finally, in an appendix on synthesized sound, the author notes that
synthesized bells and gongs have different envelopes for each partial.
The higher-frequency ones decay faster. This is clearly not the case
with the human voice. So even if you *can* get a wind chime tuned to
a BBS 7th, it wouldn't ring very long, as the higher frequencies would
die out more quickly. Maybe the repeated striking of each tube would
compensate for that, but somehow I doubt it- imagine a quartet, each
member fading out and re-entering on one note, all with different
timing...
This doesn't say that it wouldn't be worth trying to do a good 7th chord
in wind-chimes; they would still probably please a barbershopper more
than Herb's neighbor's do.
By the way, Herb, do you *like* this neighbor? :-) Have you thought about
how the two set of wind chimes will sound *together*? :-) :-) Or does
the same wind not blow in both your yards? :-) :-) :-)
--Andy
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From owner-bbshop@cray.com Fri Sep 9 12:08:36 1994
To: bbshop@cray.com
Subject: Re: Wind chimes redux
>Andy Hogan wrote:
>
> "A great deal of study has been devoted to bells, gongs, and
> related instruments. Among these are orchestral chimes,
> which are long, uniform metal tubes hanging from one end so
> that they can flex and vibrate freely. The frequencies of
> the first few partials of a typical chime are shown [below].
> Here the fourth, fifth, sixth, and seventh partials are
> approximate harmonics of a frequency equal to 4.5 [times the
> fundamental], which is therefore heard as the perceived
> pitch of the chime." (p. 183)
>
>The following is a close copy of a table on p.183 labeled
>"Partials of a chime" :
>
> 1st 2nd 3rd 4th 5th 6th 7th
>
> 1 2.76 5.40 8.93 13.34 18.64 31.87 x fundamental
> 4.5 2x4.47 3x4.45 4x4.66 7x4.55 x fundamental
>
> ^
> +------ percieved pitch is 4.5 x fundamental frequency
>
My own wind chime seems to support the above theory.
I have a wind chime that I bought 3 years ago at a county fair. I had been
looking for months but none had the right purity of tone, "ringing" harmonic
structure or long decay that I was trying to find.
The chimes I found at this fair were by a guy in California, and had the most
beautiful tone and longest decay of any I had ever come across, as well as the
most varied selection of chords imaginable (he did custom chords as well). I
asked him why his sounded so pure, and he said he used oversized stainless
steel tube stock which he then milled himself, used pins inside the tube in
which to hang the tube from, and tuned each tube individually, since the art in
a pure, long decaying sound was finding the correct point at which to "hang"
the tube. He wouldn't tell me how he determined the correct point though.
I purchased a B min b5 b6 b9 (B minor flat 5 flat 6 flat 9) set of chimes from
him. You music theory buffs will see right away why I like the sound of these
the best, as when you take away the top and bottom notes you have a G7 bbs
chord in second inversion!
Anyway, this discussion prompted me to take some (somewhat coarse)
measurements.
Length of tube Hang point from top of tube Ratio
-----------------------------------------------------------------------------
B - 23.25" 5.125" 4.54:1
D - 21.25" 4.75" 4.47:1
F - 19.5" 4.375" 4.46:1
G - 18.375" 4.125" 4.48:1
B - 16.25" 3.625" 4.48:1
C - 15.75" 3.5" 4.50:1
As you can see, even with crude measurements, the ratio of the length of tube
to the hang point for all of the tubes is extemely close to the 4.5, which
seems to impy that the correct hang point will reinforce the perceived pitch of
the tube!
So for those trying to make their own, 4.5 is the "magic" number!!
Chris Hebert
San Jose Garden City Chorus - Director
chebert@sanramon.sgi.com
--
Chris Hebert
Silicon Graphics, Inc.
Northern California Office
chebert@sgi.com
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From owner-bbshop@cray.com Fri Sep 9 13:22:56 1994
To: andyh@rosevax.rosemount.com, probemoter@aol.com
Subject: Re: Wind chimes redux
Cc: bbshop@cray.com
Thanks, Andy! Looks like you're on the track to solving the great
wind chime mystery. Bells are a lot more complicated than strings!!
I gotta hunch that it's not as simple as a straight 4.5 ratio, though.
If it were that easy, Herb would have gotten a BBS 7th, but displaced to
a higher pitch. He says the intervals are all wrong, though.
Herb -- I'd suggest that if you want good chimes, make a big tube with
a nice, pleasing bass note. For the second tube, you cut/test/cut/test/
grind/test/grind ... until you get it tuned to the first one, and so on.
And always remember when grinding and tuning: it's a lot easier to remove
length than to add it back on! :) :)
-- (a considerably humbler) Norm Finn
San Jose CA Garden City Chorus
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From owner-bbshop@cray.com Mon Sep 12 13:01:23 1994
To: bbshop@cray.com
Subject: wind chime redux, redux
I could yet get a barbershop seventh wind chime built!!
Chris Hebert's "magic number" (4.5) may be the answer.
I re-measured my now well-known C-sixth chimes and found that their
suspension points were very close to Chris' "magic" 4.5. Individually,
their ratios of tube length vs. suspension point are 4.46, 4.5, 4.54, 4,59
and (oops!) 4.35.
In my original attempt, using common rigid copper pipe, I simply (appropriate
word for the situation) drilled suspension holes a convenient half-inch from
the end of each tube.
Hokay, folks, I'm off to the work bench for another try.
Herb Bayles
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From owner-bbshop@cray.com Mon Sep 12 18:46:06 1994
To: Probemoter@aol.com, bbshop@cray.com
Subject: Re: wind chime redux, redux
Herb Bayles got excited and wrote:
>From uunet!cray.com!owner-bbshop Mon Sep 12 16:08:35 1994
>
>I could yet get a barbershop seventh wind chime built!!
>
>Chris Hebert's "magic number" (4.5) may be the answer.
I could "harrumph" but I won't. Chris did confirm it nicely. ;-)
>I re-measured my now well-known C-sixth chimes and found that their
>suspension points were very close to Chris' "magic" 4.5. Individually,
>their ratios of tube length vs. suspension point are 4.46, 4.5, 4.54, 4,59
>and (oops!) 4.35.
Another good confirmation! :-)
>In my original attempt, using common rigid copper pipe, I simply (appropriate
>word for the situation) drilled suspension holes a convenient half-inch from
>the end of each tube.
>
>Hokay, folks, I'm off to the work bench for another try.
This prompts a couple other comments:
Orchestra-quality chimes are usually suspended by an "X" of non-metallic
string. (I think a monofilament line is most commonly used these days,
but the ones I played in High School had something that looked like cat
gut.) Anyway, there are two holes drilled through the tubes, and the
hanger is threaded from the upper hole on one side, through the lower
one on the opposite side, and then back again. Or something like that,
I can't quite see how it works right now.... Maybe there are two separate
loops?
In any case, this seems like it would be mechanically similar to the
arrangement Chris described, with a post of some type welded to the
tube and the hanger attached to the post. But it might be used on the
expensive chimes to give a more pleasing tone.
Also, ochestral chimes have caps on the tops of the tubes. Tone, again??
In any case, some experimentation with the hanging arrangement might help
the clarity of the tone. Or just sneaking off to a High School and looking
at their chimes... (why re-invent the wheel???)
--Andy
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From owner-bbshop@cray.com Mon Sep 12 18:48:25 1994
To: bbshop@cray.com
Subject: windchime redux-doo-le doodle do
Success!
Chris Hebert's 4.5 "magic number" (actually, 4.5:1; the ratio of tube length
to its suspension point did the trick.
I re-drilled the tubes I'd cut much earlier and found that with their new
suspension points their persistence (or decay rate) of resonance is greatly
improved, as is their quality of tone.
So with tubing cutter and file I attacked the tubes again, and tuned them to
the prettiest barbershop seventh chord (key of C) you'll find anywhere. And
it's *mellow*, not tinkle-y! Thanks a million, Chris!
Should anyone else care to attempt such a project, here are my findings,
using 3/4 inch rigid copper tubing available at any home improvement store.
C--430mm
E--386mm
G--353mm
B flat--321mm
C--302mm
G (an octave lower)--505mm
C (an octave lower)--630mm
Be advised, I used a fabric measuring tape from my wife's knitting basket, so
my measurements may not be absolute. Also, I may not use the low G and low C
tubes. They "bong" rather than chime.
All that's left is to devise methods for suspending the tubes and for a
striker and sail to activate them. Should be duck soup after all I've been
through. I'll probably give the tubes an alkali wash to impart a weathered,
verdigris finish to them, then a coat of flat lacquer to preserve it.
Thanks, all you Harmonet-ers, for your interest, support and advice. You
*are* a great bunch.
Herb Bayles
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From owner-bbshop@ADMIN.HUMBERC.ON.CA Sun Apr 23 21:42:54 1995
To: bbshop@admin.humberc.on.ca
Subject: Wind Chime Modifications
-- [ From: David Wagner * EMC.Ver #2.10P ] --
I just completed my first set of wind chimes according to Herb Bayless
directions and I found out a couple of things that you all might find
interesting.
1) If you cut the 10' stick of copper tubing into 2' sections and
use these sections to make your individual chimes, then the remaining
pieces are precisely an octive up from the original pieces cut. So you
actually have two sets of chimes from the origianl pieces.
2) If you change the pipe diameter from 3/4 inch to 1 inch the tones
change from a C chord to a E chord or approx a major 3rd interval. The
only problem with going to a 1 inch diameter is that the top end pipe
of the second set of chimes is really too short to resonate well in the
1 inch diameter, but its not bad. Its just a little more difficult to
tune because you cant really hear it that well.
3) If you intend to make two sets, be sure and cut the tubing very
precisely otherwise the third tone from the bottom of the second set
(the upper octave) will be somewhat sharp and that is pretty tough to
change because it means that your pipe is already too short. I was able
to make them fit the chord with a little filing on some of the others,
but the easiest way is to first tune your lower octave set and then
tune the upper octave set to the lower octave set. You will have better
resonance with the lower octave and consequently you can hear the match
better that way. But the dimensions that Herb sent me are right on
the money as far as real world dimensions go. The actual dimensions he
sent me are as follows for 3/4 inch pipe and the notes for the 1inch
diameter are to the right. These dimensions are for the lower octave
chord.
3/4 inch dimensions 1 inch dimensions
C = 428mm (low) E = 428mm (low)
E = 388mm Ab= 388mm
G = 354mm Bb= 354mm
Bb= 322mm C= 322mm
C = 304mm (high) E= 304mm (high)
These dimensions are for the upper octave chord using 1inch pipe.
E= 304mm (low)
Ab= 271mm
Bb= 243mm (actuall this is just a little short probably should be
245mm)
C= 211mm
E= 172mm (high) (this one is hard to tune due to the short lenght for
1inch pipe)
Also the suspension point really is critical. I found that a suspension
point of 1:4.55 actually works better. Seems I got a better resonance
with a more precise suspension point. Be sure and mark it as close as
you can (at least to the closest 1/2 millimeter). I used a 1/8 inch
hole at the suspension point and it worked really well.
So for about $15 in tubing and about 3hrs of time, I now have a very
good sounding two octave set of wind chimes based on a E major chord
with a flated 7th making it a very good sounding barbershop chord..
Thanks Herb for the initial info, will try a longer set in the near
future, the longer the tubes are the better they seem to resonate.
David Wagner
Bari...and proud of it.! Dallas Town North "Men of Note" Chorus
##########################################################################
To: toma@mcs.com
X-URL: http://www.mcs.net/~toma/
Sender: "David M.F. Chapman"
From: dave.chapman@ns.sympatico.ca
Subject: Wind Chimes
Date: Sun, 9 Nov 1997 10:51:06 -0400
Tom: I just read your summary of newsgroup postings on wind chimes. I
didn't digest the whole thing, but I wondered if anyone finally figured
out that the resonant frequencies of chimes (bars, tubes, etc.) scales as
the inverse SQUARE of the length? It seems there were a lot of frustrated
builders out there!
I recently held a workshop for high school physics teachers on musical
acoustics, and one of the examples I gave was the wind chime. By
comparing the pitch of the chime with the piano, one can determine the
percieved frequency. Then one simply measures the length of the rod.
These are easily plotted on a spreadsheet to show the above relation.
By the way, very few people---even acousticians---are aware of the
"illusion" of pitch in a vibrating bar, where the ear/brain supplies the
"missing" fundamental to the approximate harmonic sequence supplied by
overtones 4,5, and 6.
cheers
Dave
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