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| from Popular Mechanics - hand made Chime plans |
noun 1. to make chimes. 2. to design chimes 3. to be involved in the community of chimers 4. to ring a chime 5. to sell chimes 6. to write about chimes 7. to collect chimes 8. to read this blog-post
Most Wind Chime plans such as this one pictured above in Pop Mechanics will give you a list of tube lengths ( usually generating a Major Chord or Pentatonic Scale). With a little bit of calculation and knowledge of the Frequency Ratios of Intervals ( that you can get on this blog, links below) it is possible to design a chime to play any manner of weird chord, jazz chord, Scriabin's Mystic Chord, Slonimsky's "Grandmother chord", or just experiment with dissonance and unusual configurations. Granted, on a a windy day your neighbors may hate you for it. My first Chime was a Gm (6,9) chord but that is a rather pleasant sounding chord - happily, the math works out beautifully, though my mechanical design needs a little rethinking. I discovered that the weight of the wind-catcher is very important as is the relative weight of the clapper, but this post is not really about the mechanics of chime-building. There are several suppliers of chime parts on the web but virtually all of it can be homemade using common hardware items and wood, on a small scale.
Here is an easy system for Custom-Designing tube lengths for a tubular Wind Chime. No need for trial and error, you just need to be familiar with musical Intervals and be handy with a hacksaw. Copper pipe, steel conduit, aluminum tubing, it's all good, though there is plenty of variation in tone and resonance. Conduit is cheap.
You might think that an organ pipe would behave something like a wind-chime tube - not the case, not even close. An organ pipe contains the vibrating air, while a chime tube ITSELF is what vibrates and the air inside it is irrelevant. Cut an organ pipe in half and you kick the sound up ONE octave. Cut a wind chime tube in half and you kick it up 2 octaves! - obviously something different is going on here.
This post is all about designing tube length for Wind Chimes, not about constructing the Chime iteself - there are plenty of resources for that on the web and people like Gregg Payne ( video below) have turned it into a Fine-Art. I will skip to the finish and show you the method and save the explanation and formula for the end.
DESIGNING THE TUBE-LENGTHS BY MUSICAL INTERVALS ( not frequencies!) Remember that another term for "Musical Interval" is "Frequency-Ratio". That's what an interval IS... (they are all listed below)
1. Choose a starting length for the lowest ( LONGEST) tube. Pick anything.
2. Choose the desired Musical Interval for Tube #2 and make note of its "Divisor".
(for example, if you want a note that is a fifth above the Reference tube ( #1) choose the Divisor 1.222 )
3. Divide the length of the Reference tube by this number to get the length of Tube #2, always using the same tube material. Tube #2 should sound a 5th above the reference tube. It is the interval that matters more than the actual pitch or frequency.
4. Continue until you have all the musical intervals for the chime design.
5. String 'em up and wait for a hurricane or whack them with a piece of wood.
INTERVAL DIVISOR FREQUENCY RATIO
(tempered intervals)
1/2 step 1.029 1.059
1 step 1.059 1.121
min 3rd 1.089 1.188
maj 3rd 1.122 1.258
4th 1.154 1.332
b5th 1.188 1.411
5th 1.222 1.494
m 6th 1.258 1.582
maj 6th 1.295 1.676
min 7th 1.332 1.774
maj 7th 1.371 1.879
octave 1.414 2.0
min 9th 1.455 2.118
maj 9th 1.497 2.243
(pure intervals)
min 3rd 1.095 6/5
maj 3rd 1.118 5/4
min 6th 1.265 8/5
maj 6th 1.291 5/3
7th 1.323 7/4
Pure intervals don't exist on the piano - even octaves are not quite pure.
Notice that the pure intervals are slightly different than the same intervals that are tempered - there would be an audible difference and a difference in tube length of 1/8" or 1/16" or so, sometimes more on large pipes. Pure intervals exist in nature, in choirs, in string orchestras, not on pianos, or in general orchestral music or pop music. I did not include pure 4ths and 5ths because they are nearly identical to tempered intervals. The pure 7th is an ODD egg indeed and doesn't really approximate any of the tempered intervals that we use in Western Music. I would like to try this in a wind-chime one of these days...also want to try 1/4 steps.
To review the meaning of Tempered Intervals AND Understanding Frequency Ratios of Intervals please read my previous blog-posts on the topics:
Temperament and Ratios CLICK
The Two Most Important Numbers CLICK
This shows how to calculate the frequency ratio for any interval.
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THE DIRECT FORMULA FOR COMPUTING WIND CHIME TUBE-LENGTH
using Musical Intervals ( no actual "frequency" numbers are required )
Where F2 is the frequency of the tube to be cut.
FR is the frequency of the reference tube.
L2 is the length of the tube to be cut.
LR is the length of the reference tube.
F2/FR is simply replaced with the ratio of the desired interval in the above chart. Its Square Root is the Divisor that is used to divide into the length of the reference tube.
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Example:
A 24" steel conduit tube might ring at G below middle C on the piano ( G3) depending on diameter and wall thickness. The exact note or pitch doesn't matter - this is our reference low tone.
To create a tube that rings a pure 6th above this ( a bit flat of E above middle C, but creating a pure interval of a Maj 6th with the G) Divide 24" by 1.291. Cut a tube to 18.59" and voila.... harmony.
Experiments to try:
A series of quarter steps.
A series of stacked 5ths ( The Outer Limits chord, from the old TV series)
A complex 5, 6 or 7 note jazz voicing, maybe with a b13 and a #9 and min7 and maj3.
A series of 3 pure thirds resulting in a dissonant narrow octave.
A series of 4 pure minor 3rds resulting in a dissonant wide octave.
Major triads comprised of a pure major third and a pure 5th ( and resultant pure minor third between the upper two notes. .. a very PURE sounding chord.
A series of minor thirds plus a series of minor thirds up a whole step ( a "diminished scale" )
Japanese 4 and 5 note scales.
Persian and MidEastern scales.
Dissonant scales using 1/4 steps.
Open fifths for two octaves: Gregorian Chant--- Fifth, Octave, Octave and a Fifth, Two Octaves
Major triad plus the 5th below it ( the Joni Mitchell chord, V/I )
Major triad plus the major triad a b5 above the first triad.
Whole tone scale 7 notes spanning an octave.
Whole tone scale for 10 notes
Chimes where the tubes are at different distances from the clapper so that when the wind pickup up
speed the chord gets more complex and more dissonant.
A couple of pure 7ths, an interval that is rarely heard.
Recalculate frequency ratios using the 31 note tempered scale or the 43 not tempered scale and construct chords from those pitches. ( why stick to twelve? ... )
A stack of intervals: min6, maj 2nd, major 6 (yielding a 4-part maj 9 chord with the 3rd on bottom)
(choice of reference tube can change as the tubes are cut)
Happy Chiming. Enjoy this video of Gregg Payne and his amazing extra-large chimes:
