Shaku
Design
Lookin' for the Buzz?

Updated 4/24/08

Getting the body of a flute to vibrate is a fairly simple matter--if you like that kind of thing. John Singer, in a fine article, calls this phenomena "chikuin". To some, these vibrations are seen as evidence of a superior flute and perhaps it's true, but they arise from purely geometric circumstances.

Now for a little geometry. A circle is an ideal shape in that it contains the greatest area for its perimeter. Thus of any shape, a circle is optimal in it's area to perimeter ratio--a factor of 1/2. The ratio for a square is 1/4 and all shapes fall in the range 1/2 to 0. A line, which can be thought of as a completely squashed and flattened circle, has a 'perimeter' but no area--a factor of 0.

Now think of a soap bubble. Blow them up and they want to form spheres (three dimensional circles). Why? Because any other shape has a smaller area (in this case, volume) so the gas pressure is higher. By altering it's shape to spherical, a bubble reduces it's gas pressure. Water flows downhill and bubbles seek the lowest pressure possible.

A circle is already optimized and can't improve it's shape--it's already maxed out. So to get a flute to vibrate we have to seek a bore shape with a ratio lower than 1/2. We want a shape which can trade up to being a cirlce. And that's where the oval comes in.

For the purposes of this discussion, an oval is an unhappy circle. It wants to be a circle and given the change it'll change it's shape toward that of circle. You haven't been blowing many ovaloid soap bubbles lately, because given a choice they all instantly assume the spherical shape. In the case of a flute, when an ovular bore comes under pressure it seeks a circular shape but is restrained by the rigidity of the bore walls. So it moves just a little. When the pressure is released the bore snaps back to it original oval shape. But when a flute sounds, air pressure is applied and released a few hundred times a second. That's what sound is. So hundreds of times a second an ovular bore strains toward a circle and then falls back--that's flute body vibration. It's a matter of shapeshifting.

What your shak to buzz? Here's how.

The task of creating a vibrating flute is two fold: 1) Pick a shape which wants to be a circle and 2) Make it easier for it to get closer to being a circle. Do that and you've have a fine vibrating flute. We've got to make it easier for the oval to deform toward a circle. And to do so we will reduce the strength and rigidity of the bore wall in both planes--horizontal and vertical.

Creating an oval bore will thin the bore walls in the horizontal plane in the process. Now take a hacksaw blade (or some such) and make cuts in the vertical plane, cutting inside the bore. The thinner the walls are in both planes the easier it is for the oval to shapeshift--thus the greater the vibrations. Vibration robs energy from sound volume so it's hard to have a LOUD and vibrating flute at the same time.

Anyway, for greatest vibratory effect: 1) make the bore ovular, 2) add relieving cuts which extend as far down the bore as possible. These two things reduce the thickness of the bore wall in both planes.

From a purely engineering standpoint there is a further consideration called mass-loading. When the mass of the bore walls is just right for the frequency; body vibrations will be greatest. Any smaller or greater mass will dampen the effect. Since flutes sound at different frequencies during play, mass considerations are difficult. There are other factors which effect vibration, rigidity of the bore walls and so on, but without the basic geometry nothing is going to happen in the first place.

Now here's the problem with all this 'flute body vibration' stuff. Play Ro, Tsu, Re--those three notes. Did the vibrations also change notes? Play Ro, Tsu, Re on a marimba. Did you play it all on the same bar? Of course not. A flute who's body will vibrate does so at a single pitch, so the sound arising from this vibration would be heard as a drone note as it's pitch would be unvarying.

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