Shaku
Design

End Blown Flutes

Updated 4/24/08

The beauty of PVC is good instruments from a trip to Home Depot and five bucks. I think the trick is to keep the concept within the ability of the determined hacker. --Peter Riley

Hack the Shak. --N. Zink


An end-blown flute is a variety of flute in which the airstream is directed against the sharp rim of the open upper end of a pipe by the player’s lips. Despite its unsophisticated appearance it is very difficult to play. The pipe is often fairly long and the number of finger holes is frequently only two or three. The main materials are bone, horn, wood, bamboo, or occasionally metal, and the bore is usually cylindrical. The angle at which the instrument is held varies according to the style of the upper rim. End-blown flutes are found in every continent but especially in South America and Asia, and examples exist dating from the Stone Age. In examples of modern end-blown folk instruments wood or bamboo are the most usual materials, though in some countries a length of metal tubing is used. Made from bamboo, the Japanese shakuhachi has an uncharacteristic wide bore that is internally lacquered. –Musical Instruments of the World


Note: As we're a little hazy on nomenclature, on this page we'll use the term 'utaguchi' to mean mouthpiece--including, but not restricted to the actual blowing edge.


Generally, end-blown flutes have an aspect ratio somewhere in the range of 40, thus the shakuhachi is unusual in that its aspect ratio usually centers around 30. Why 30? One conjecture is that at or near the aspect ratio of 30 the amplitudes of the even and odd harmonics are roughly equal. The shakuhachi has staked out the sonic ground right between first and second octave. Through playing techniques the shakuhachi can emphasis either even or odd harmonics (timbre bending) and thus it is an instrument of great psychoacoustic range.

The ratio of the amplitudes of even and odd harmonics can be varied in two general two ways: By changing the basic aspect ratio of the bore and/or by varying the ratio of the area of the blow hole (utaguchi) to the area of the bore. The first is fixed, being set by the instrument maker, the second is constantly manipulated during play. The ratio of blow hole to bore area which best explores the border between first and second octave is usually between 20% and 30%. Painting with a broad brush, let’s call it 1/4 or 25%.

Any end-blown flute with a blow hole ratio of 25% and an aspect ratio of about 30 will sound pretty much like a shakuhachi. If a shakuhachi is defined by its acoustic properties rather than particular construction techniques and materials, then any end-blown flute with the proper ratios IS a shakuhachi.

The design of the shakuhachi blow hole (utaguchi) provides for and encourages the considerable effects of pitch bending. In end-blown flutes pitch and timbre bending are inseparably bound together and, in a way, two different aspect of the same thing. So, a flute with considerable pitch bending capabilities makes precise hole tuning somewhat irrelevant and perhaps impossible. In such flutes, the question of whether they are “in tune” is somewhat meaningless.


In traditional shakuhachi the utaguchi is ill-designed as far as accommodating the player's lips and mouth. The design conforms much more to the parameters of the bamboo and the general criterion is aesthetic rather than practical. In short, the utaguchi is built more for looks than play.

Problems with the traditional utaguchi:

1) It's not designed to facilitate a good air seal as Peter points out:

The bane of the woodwind instruments is air leaks. Fingering, joints and keys all conspire. The saxophone with its big keys that must seat squarely is a prime offender. The simple elegance of the shakuhachi does not escape leak problems. In small bore instruments the soft, pliable, fleshy lower lip (provided it is hairless) works well as a gasket to close the area below the utaguchi. As the bores become bigger i.e. 1”-2” and the radius starts to reach down into the chin area. Closing off to be airtight becomes virtually impossible. Very small leaks in the mouthpiece area will quickly stop resonance. In experiments with large bores I made a gasket for this lower area from modeling clay. This was simply a worm of clay pressed onto the edge of the tube. When pressed against my chin it formed a tight seal. I was startled to find many of my "playing failures" dying out. I found that if I made a small leak with a toothpick in the clay resonance stopped completely. The problem is that a clay gasket is short lived and needs to be repeatedly pinched up and reseated. Now, the soft wax seal of the didgeridu makes a lot of sense. It seems to me that the shape of this lower area needs to be an oval such that the lower lip makes the seal not the chin or chin/lip transition. In PVC instruments, I found that the coupler concept tended to leak. If the assembly will not hold a vacuum it leaks! When I gave up the PVC coupler and simply joined the short mouthpiece/utaguchi section to the barrel of the rest of the instrument with tape a great deal of the mystery disappeared. Cosmetics can come later with a Turks Head knot or a glued, leak proof version of the PVC coupler covering the seam.

2) It's not designed for good control. The distance from the lower edge of the mouthpiece (where it rests on your chin) to the blowing edge is usually about an inch. To institute finer control this distance needs to be shorter.

3) In a previous page we explored the role of the lower lip in forming a hole with the blowing edge and with standard utaguchi the lower lip is wedged into the uppermost part of a circle. A more sensible utaguchi would accommodate the entire lower lip and allow it a wider range of mobility.

Reducing the utaguchi to its fundamentals, we need a structure which positions the lower lip in respect to the edge--this is the first thing that needs to be achieved. Without proper lip placement the rest is irrelevant. The utaguchi need not be larger than the lower lip in its relaxed and uncramped state--say 1/2" x 1".

The blow holes in Figure 1 all conform to the shape of the material from which the flute is constructed. With PVC a new generation of flutes can be constructed as, with a little heat, PVC is malleable. Thus, all manner of utaguchi can be designed and constructed.


The Oval Utaguchi

See below for a drawing of a stick to form a suitable mouthpiece in 3/4" schedule 40 PVC using the principles we've set forth. Simply heat the end of a PVC pipe with a heat gun and insert the tool until the tube conforms to the tool. Let cool and withdraw the tool. Put a slight curve in the bottom edge to fit just below the lower lip. The blowing edge will have to be cut deeper than usual because the lip is now comfortably within the end of the tube. Make the blowing edge about 5/8" wide and 1/4" deep. Depending on your lip thickness file the blowing edge with an overcut or an undercut. Or somewhere in between with a little of both.


Yesterday my wife spirited me off to Wally World (Walmart) and there, can you believe it, a heat gun fairly sprang out at me! The first try at an oval mouthpiece, a 1 1/2" worked better than anything so far! When I first looked at it I thought the oval was too big and would reach around to my ears but not so. My only caveat is that this technique requires knowledgeable carving. I had to chase the sound with my knife. Also there is no way I can describe the multiple curves that are required. --P.R.



Oval Utaguchi

This design is easier and more interesting to play than the traditional utaguchi as it addresses the three problems outlined above. It provides a good air seal, gives the player about twice the control of a standard shakuhachi, and allows the lower lip greater latitude during play.


4) The fourth problem with the standard utaguchi is that it 'stalls' easily.

The Reynolds Number (Rn, which is proportional to inertial force/viscous force in fluids), named after Osborne Reynolds, should be of interest to flute players. The Reynolds Number of air changes according to air speed. In recorders the number is typically in the range of one to two thousand and the air jet remains laminar across the width of the instrument mouth. For large organ pipes, and the high notes on flutes, however, the Reynolds Number can exceed 3000, and turbulent noise makes a significant contribution to the sound. Most end-blown flutes have that distinctive air-rush sound and it’s an indication of a higher Reynolds Number.

Air streams change dramatically with different speeds (Reynolds Numbers). Within the range of most flute playing there are three phases: At very low speeds the air stream is steady and quiescent, like a candle flame. A little faster (Rn—40 to 2000) and the flow is laminar. Even faster (Rn>2500) the air stream becomes turbulent and generates a particular quality of sound.

There isn’t a smooth transition from one phase to another, it’s rather sudden and the sound of the shakuhachi (and most end-blown flutes) is distinguished by the rapid transitions from laminar flow to turbulent and back again. These shifts are generated by changes in air-stream pressure/speed. Want more of that air-rush sound? Pump up the pressure. Less? Drop the pressure. What you’re really doing is shifting the Reynolds Number of the air stream.

In avionics, the wing can do something which is referred to as 'stall'. When a wing stalls the lift characteristics suddenly collapse and the craft begins to fall from the sky. This is usually caused by the 'angle of attack' becoming too great. If the angle of attack is kept within a certain range everything works fine, but if it goes over a critical value then turbulence ensues, the wing quits lifting, and quick thinking and/or a parachute is needed.

When a flute suddenly loses sound it’s because the blowing edge has stalled. The angle of attack of the air stream to the edge is out of synch and the resonance and whole sound envelope vanishes. The edges of end-blown flutes have a narrow range of angle of attack and thus are considered hard to play. There isn’t as great a latitude as with other instruments.

This condition can be rectified and to do so we need to look at airfoils which are harder to stall. In particular, the Kline/Fogelman Airfoil. By adopting some anti-stall geometry we can expand the sweet spot of the end-blown edge, making it easier and less frustrating to play. What we’ll attempt to do is create an edge which is more tolerant of swings and variation in angle of attack. Adopting the design below will substantially improve your flute's stability (blowing edge stall characteristics). As a demonstration, you should be able to jog and play your flute at the same time.


Cut away (blue) showing anti-stall geometry on the inside of the tube


There is nothing quite so fine as messing about with utaguchi. --Peter Riley



Putting it all together:

C Flutes 262 hz. 606mm
Hole Locations (in mm) for Various Sizes
Schedule 40 (thin wall) 3/4" PVC & the Oval Utaguchi
Hole
9.5 mm
3/8"
9.9 mm
25/64"
10.3 mm
13/32"
5
258
260
261
4
295
297
298
3
364
366
367
2
416
418
419
1
475
476
478
Ro
606
606
606

Since they're all the same length, hole size will define the character of the sound of your C flute. Smaller holes will make it soft, quiet and mellower--larger holes do just the opposite. If you want to do a fine job then drill holes one size smaller and carefully expand (file) the holes (starting from the bottom) until they come into tune. 606mm is the TOTAL length which pitches the flute to C. The aspect ratio of these flutes is 29.5 which makes the Equivalent Aspect Ratio 28.9--putting them on the mellow (dark) side of things.

For extra credit, slightly undercut the holes along with the foot opening. Use acetone on a folded paper towel to smooth, clean, and finish.

Schedule 80 (thick wall) C Flutes 611mm
3/4" PVC & the Oval Utaguchi
Hole
9.5 mm
3/8"
9.9 mm
25/64"
10.3 mm
13/32"
5
272
273
274
4
309
310
311
3
377
378
379
2
428
430
431
1
486
487
488
Ro
611
611
611

The aspect ratio of these schedule 80 C flutes is 33.2 which make the Equivalent Aspect Ratio 32.6--placing them on the bright side.


Acoustical comparison of the two pipes

See The Synthesis for a final flute design.


Top of Page