Updated 2/21/11

The desire for big bore, deeply pitched, rumbling, wheezy flutes must be hidden in the psyche somewhere and it never seems to go away. We've looked at long flutes, now let's investigate chubby flutes. In the graphic below, the blue section indicates the dimensions of the vast percentage of shakuhachi. In general, these are 'balanced flutes', capable of playing both first and second octave. Most flutes are pitched between D4 and D3 (an octave lower). For the most part, the blue section IS the world of the shakuhachi and the overwhelming majority of shakuhachi lie in the purple section. As EAR drops, a flute's second octave becomes more and more fugitive to the point where the upper register is difficult if not impossible. Balance vanishes and it becomes, essentially, a single octave flute. That's the tradeoff--second octave for the big bore timbre. True big bore flutes are single octave affairs.

Dimensions for single and double octave flutes
with pitch and timbre elements denoted

There's an upper limit to the flute length that can be played. It's probably somewhere around 1000mm (one meter, 3.3 shaku), and beyond that depends on physical size and persistence. The standard 1.8 shakuhachi is pitched to D4 (294hz) and although there are flutes pitched higher, most shakuhachi exist in the range between D4 and D3 (147hz) in the blue part above. To the right (the red section) is the region of big bore flutes. EAR drops from 32 to 22 and then another 10 points to 12. The demarcation between single and double octave flutes is probably somewhere around EAR 22, but is defined by an individual's playing ability. As ability develops, this demarcation number decreases. Shifting a flute in the red direction makes second octave more tenuous and elusive. Moving in the blue direction brings a flute into better balance. The EAR you're satisfied with will be the result of what you like to hear and playing ability. The shift from double to single octave (blue to red) is gradual and can be noticed as the high second octave notes begin to fade and the flute's highest tonal reach slowly drops. In general, a flute's tonal range is a direct function of EAR. As an approximation: EAR / 12 = Range (in octaves).

The EAR of pipe organs is usually down close to 12 and the pipes are prime examples of single octave flutes. One of the reasons is so that a pipe can't overblow into second octave even when air pressure is stiffened to accentuate volume. Since a pipe organ is just a collection of single octave flutes you can have an appreciation of the timbre of flutes with EARs approaching 12.

The five sizes of Schedule 40 PVC pipe noted in the chart below allow for rapid experiments with big bore flutes. Two of the pipe sizes represented in green will play lower than D3 and will do it at a playable length (under one meter). The 1.25" is interesting in that it will play all the way from D4 down to D3 and during the journey shifts from a single octave flute to a double. The 1.5" between 500 and 975mm makes a very suitable big bore flute. The 2" at 650 to 950mm is a similar arrangement. 1" pipe at about 505mm makes an interesting D flute--also E at ~ 450, C at ~565, Bb at ~635, and G at ~755. These One Inch flutes demonstrate the transition from single to double octave.

One way to get a feel for the whole subject is to cut a piece of 1.25" pipe to 1100mm. Fashion a utaguchi and play first and second octave. Then cut 100mm off the end and play again. Repeat until length is down to 400mm. With some couplings you can add/subtract to/from your flute at will. During the exercise the flute's fundamental pitch will change by over an octave and you'll get a clear sense of the single/double octave phenomena. One of the defining features of the big bore sound is diminished harmonics, it's a 'purer', simpler sound. The tonal migration revealed by this exercise moves from a 'musical' timbre (with harmonics amplified) to a windy, more natural sound. The sounds of nature aren't double octave.

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Within the double octave segment there is a thin acoustical sweet spot depicted in the graphic above.
The formulas (metric only) will produce flutes which fall on the yellow line.

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Try SignalScope (Mac) for a look at waveform and harmonics.

Once you've found the length/timbre/EAR you're happiest with, cut a new flute to that length and drill the holes. Ideally, hole-size should be about 50% of bore diameter but normal fingers can't cover much more than 12-13mm. But there are a couple things you can do to 'increase' hole-size: make the holes oblong (along the finger axis) and really undercut the holes to increase venting. Get the hole chimneys down under a millimeter.

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As a point of interest, if you were to take an Optimal D flute (bore 18mm, length 545mm, EAR 30.3) and double the bore size its pitch would drop almost exactly two notes. Then you'd have a C flute (bore 36mm, length 545mm, EAR ~15). Increasing the bore by one and a half times drops the pitch one note to C# (bore 27mm, length 545mm, EAR ~21) . These two ratios hold fairly well for notes in the vicinity of D.

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