Shaku
Design
Sharpening the Second Octave

Updated 4/24/08

You can take a straight tube, drill holes of the right size and location and the notes will be in tune--in the first octave. The second octave is another story. For physical/acoustical reasons the second octave will play progressively flatter. If this weren't true we'd all play a straight tube and be done with it. But it's this fact that leads to much of the fiddling with the bore geometry of shakuhachi. In a previous page we talked about tuning by adding material to the bore. In this page we'll investigate tuning by stock removal.

Surprisingly, the location (within reason) of the holes doesn't make a whole lot of difference as far as tuning goes. And when tuning the second octave by stock removal, computer studies have revealed there's really only one location (the green strip in figure 1) which has a profound correcting effect. It makes sense that any effort toward progressively sharpening the second octave should take place above the holes so as to effect all notes--thus octave tuning should take place in the throat of the flute. And by happy coincidence there is a specific place that works.

Both the orange (holes) and green stripes in figure 1 signify stock removal. Holes, even when closed, create a little 'bump' in the bore--an extra space. To some extent, the 'green' is offsetting and reversing the 'orange'--bringing things back into balance. With a straight tube the extra space created at the green strip can be located mathematically, but in an uneven tube (read bamboo) it's a little more difficult. In general, with bamboo it'll always be less than 1/4 of the total flute length. But the sonic nodes (hence the removal spot) in non-regular tubes can be determined precisely with a little extra effort and equipment. Red and blue in figure 1 signify sonic nodes and anti-nodes--see the general tuning page for more clarification if needed.

Here's the deal: When material is removed from inside the tube, enlarging the bore at the green strip, the second octave will come into tune. It's that simple. Stock removal should begin 1/4 of the flute's length down the throat and proceed for another 1/16 of the length. So for a 600mm flute it'd start at 150mm and end at 188mm--a 38mm wide band removed from the inside of the flute. How deep? A depth of 10% of the wall thickness is usually sufficient. The depth is the one variable which isn't fixed and depends on hole size, wall thickness and other factors. Although the placement of the edges of the internal groove (figure 2) is sensitive, the depth is variable depending on the flute. This spot sometimes corresponds with the upper bamboo node in a non-jointed flute--and sometimes it doesn't. Depends on the bamboo. In any event, it's usually near the top bamboo node and there's a tendency to remove material at the node whether it's in exactly the right place or not. The location is sensitive and a few millimeters one way or the other changes things, not gradually, but somewhat catastrophically.

To go by the bamboo's nodes one has to believe a particular piece of bamboo intended to be a flute rather than a piece of furniture or just wanted to live a long life and die peacefully in the forest. Who knows what's in the mind of bamboo? And until we do it's best to measure.

How to remove material from the inside of your bore? That's the trick. With PVC pipe it's simple to cut the pipe at the green strip and use a coupling to leave an internal space. Otherwise? You now know the place to start digging/filing/cutting/sanding/planing--how is limited only by your imagination.

For those who like numbers, measuring, etc., tuning can be improved slightly by adjusting hole locations. Generally, the thumb hole is about 42% of the flute length from the top. Progressing from the thumb hole downward, set holes at 48%, 58%, 68%, 78%. The old prescription of placing holes a tenth flute length apart appears to have merit. To gain even more tuning balance raise the thumb hole to 39%.

For what it's worth, the most theoretically perfect tuning is achieved by enlarging the bore at the green strip and placing holes at 39%, 48%, 58%, 68% and 78% of the flute's length.

See The Synthesis for a final flute design.

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