TuningII

From: "Brent" Date: Sat May 7, 2005  Subject: Re: tuning the 1st chime

We could probably get you close to what range of notes and octave your tube may be producing if we knew what type of metal it's made from, its outside diameter (OD), its wall thickness or inside diameter (ID), and the length of the tube - that would be the first step in giving an educated guess.

There are a number of spreadsheets and charts that would let you/us know about where your particular tube is starting from by it's type of metal and length/OD ratio; but that doesn't even get the can of worms warm enough to open yet. Unlike a harmonic instrument that produces a fundamental frequency and "harmonics" which are exact multiples of that fundamental (same musical notes but at higher octaves), a chime tube is an "overtone" instrument that produces a fundamental frequency (of some particular note and octave) and many higher "overtones" which are each producing a completely different musical note from either the fundamental frequency or any of the other overtones. Translation: it's just a lot of different notes like you'd smash your hands down on a piano keyboard. Since all the components are of different musical notes, the one or ones that happen to be the loudest in amplitude are the one/ones your ears and brain will try to home in on. The bottom
line is that there are dozens of different factors that can affect the individual amplitudes of each frequency (vibration mode) your tube is producing; so as anything changes those amplitudes (respective to each other), the particular musical note you perceive may also change.

If you are not a musician, then cutting and tuning a set of chimes to some particular notes, key, scale, or chord is probably not worth the effort and frustration. Most people are not musicians and simply enjoy the simple aesthetics of hearing different chime sounds at different pitches or tones. So the simplest of methods is to cut the tubes to different lengths, suspend them properly, and enjoy the Aeolian pleasure of different pretty tones.

The simplest method for a nice set of tuned chimes is to first decide on what particular kind of metal you will use, measure its OD, wall thickness, and ID - then go to Chuck's Chimes (in the "links" section here) and click on his "Frequency/Length Calculator". Once there, just plug your metal type and dimensions into the appropriate boxes, select
the tuning range to the "First" natural frequency, make sure you check the "ideal range" box, then look at the musical notes and corresponding frequencies that are perfect for your particular tubing. Once you've selected some set of notes (e.g. scale or chord) you can obtain in that range of listed notes and frequencies, just cut your tubes to the prescribed lengths in Chuck's calculator. As long as you use the same kind of material from the same stock, the tubes will be in tune with each other - regardless if they may be off a little by any "textbook" definition of any particular note. Here's where Charles is right on because the tubes will be in tune with each other, will sound good together, and will be good. Using Chuck's calculator in the "ideal" range at the "First" natural frequency will usually make your tube's fundamental frequency the highest in amplitude (loudest) over the non-harmonic overtones; so, that is the most recommended (by me anyway) way to ensure you'll probably hear what you expect to hear.

The most difficult of tuning methods is to grab any frequency/length spreadsheet or chart, cut any type of tube to the prescribed length (much longer or shorter than Chuck's ideal range), and try to determine some "note" out of a jumble of all the wrong frequencies at unpredictable amplitudes; at that point, the brain's "fuzzy logic" process turns into "hairy confusion". Before trying to tune such a tube (s), be sure to stock up on plenty of beer, mark a soft spot on the wall for your head, and have the local shrink reserve you a room at the Waldorf Hysteria. Brent

From: "Brent" Date: Mon May 9, 2005  Subject: Re: long chimes, short nodes

David;

Chuck would be the resident expert on the actual (and true) physics of various node points other than the standard .2242 node location for the fundamental transverse mode (first natural frequency).

I can only give a logical guess and wait for Chuck to pin my ears back with actual fact. The fundamental frequency and pure harmonic frequencies (that exist in a harmonic device) all find some kind of resonance in the same length (e.g. a given length would be ½ wavelength of the fundamental, one full wavelength of the first harmonic, 2 full wavelengths of the second harmonic, and so on). However, an overtone device (like a chime tube) has no forced nodes and produces non-harmonic overtones as higher frequency components over the fundamental - which are neither exact multiples of the fundamental
frequency nor find any natural resonance in the tube's length.

It's my understanding that an overtone results from a complex trigonometric combination (vector/phase angle addition) of a harmonic frequency (which is trying to exist) with the fundamental and any other lower overtones as the overtone number proceeds upward. That continual vector/phase angle addition with the fundamental and each progressive overtone(s) is why there's a very non-linear looking, non-whole number multiplier of the fundamental frequency that's associated with each
progressive overtone.

Sorry if that's confusing because it is; but the bottom line is that overtones are being constantly generated and sustained by the presence of the fundamental frequency. Even though the fundamental may be at a very low amplitude, it must be there for the rest to continue existing in a non-resonant length of tubing for any particular overtone frequency.

Even though the tube has a non-resonant length for any overtone frequency (by itself), one can still plot any overtone's sinusoidal frequency curve along the tube's length and find a node point for that particular frequency (which would not be common with the node point of the fundamental). So suspending the tube from a particular overtone's plotted node point should make the tube offer less impedance to that particular overtone frequency.

Here comes the wild assumption that I'm sure Chuck will quickly correct to both our benefits. Moving the node point will obviously cause the fundamental frequency to decay faster in amplitude; and when the fundamental frequency finally decays to nothing, there will be no other way for the overtones to exist either. However, as long as the fundamental is in existence to any degree, the "favored" overtone you've selected as a node hang point would probably sound considerably
louder for the duration of tube vibration because the fundamental and other overtones would be decaying pretty rapidly with respect to the favored overtone mode.

Unfortunately, I see all of that as a moot point because killing off the fundamental mode more rapidly means that the tube will not vibrate as long as it would if you made conditions more favorable for the fundamental's sustained existence. So, that's why I stick with the conventional node suspension location for the fundamental mode and use Chuck's calculator (at the first natural frequency) to pick the ideal length/OD ratio for any note or octave I'm trying to produce. Brent

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