Shaku
Design

Designing Your Own Shakuhachi

Updated 4/24/08

Suppose you were to design a car to get good gas mileage and suitable performance. How would you go about it? What parameters would you attend to first and what things would you pay attention to later? Having a clean windshield will improve both mileage and performance, but expending most of your efforts on the windshield won't work out too well. The gas efficiency of a ten-ton vehicle with a 1000 horsepower engine won't improve substantially after cleaning the windshield. The point being to focus on the things which make the most difference first--get the basic parameters right and things will go smoothly.

This page is intended for jinashi flutes, flutes who's bores are left natural.



The Boring Part

In designing a shakuhachi, the biggest thing contributing to the overall performance and sound of the flute is aspect ratio--which is the flute length divided by bore diameter. If you don't get this right, the flute will never do what you want no matter what you do subsequently. See Equivalent Timbre (Equivalent Aspect Ratio --EAR). An EAR of 29-30 is the mean for a shakuhachi, higher numbers brighten the timbre and make the higher registers more available and playable. Lower numbers favor the lower registers and make for a mellow sound. What is commonly referred to as a big bore flute has a lower EAR. Numbers outside of 25-35 start placing you beyond the acoustic range that defines the shakuhachi. Jinashi flutes tend to have EARs under 30 and often much lower. What is often identified as 'the sound of bamboo' is the result of a lower EAR, just as flutes start to sound 'brassy' when the numbers get substantially above 30.

As a point of interest, the word shakuhachi is both singular and plural. One sheep, a herd of sheep. One shakuhachi, an armload of shakuhachi.

Measure/calculate bore size, then decide on an EAR number and consult graph to determine length.

Be aware that you might not be able to build a flute (from a particular piece of bamboo) which has BOTH the timbre (EAR) and pitch you want. Given a piece of bamboo, the bore is set and you should cut the length to achieve a desired timbre, which may result in a pitch that's not anywhere near the one you wanted. Suffice it to say, for example, that it's not possible to have a balanced D flute with a 25mm bore.

There's a story about an emperor in China who came into possession of a remarkable jade boulder. He summoned the royal jade cutter and commanded him to release a dragon from the jade. So the cutter set to work and every year the Emperor would send word, inquiring as to how the carving was coming along. Finally, the piece was finished and the Emperor came to see it. "Where's my dragon?", he asked. The Jade Cutter drew back a silk cover, "There was no dragon, just five butterflies."

Often, this is the way it is with jinashi (natural bore) bamboo flutes. And as such, jinashi flute making (subtraction method) is a much higher art than jiari, where bore subtractions AND additions are made to achieve a standard bore shape. Because each piece of bamboo is different, jinashi construction becomes a problem solving adventure with each and every flute. Those who enjoy solving puzzles are often drawn to and excel at jinashi flutes as they present an endless supply of riddles. Each flute is a new and unique challenge. The jiari method is based on solving the puzzle once and for all time and applying that bore shape over and over. Jiari is mainly an exercise in craftmanship, jinashi is largely an intellectual endeavor. Dragon or butterflies, you never quite know how it'll turn out.

Length-Bore-Note Relationships for EAR=29.5

Don't start your first shak with some impossibly big or long piece of bamboo. Get something with a bore of 18-20mm and a length of 20-24 inches (500mm-600mm) for your first attempts. One end of the bamboo bore will be larger than the other, blow into the big end. Yes, it may seem strange but much about the shakuhachi is strange.

Don't be surprised that your D flute (1.8) isn't exactly 545mm long. Length isn't the only determinant when tuning to a key, bore size contributes, but to a lesser extent. Big bores make flutes shorter, small bores, longer. A flute made of 3/4" Sch40 PVC (bore 20.4mm) with a fundamental of D will be around 533mm long. Methods for determining average bore diameter with irregularly shaped bores: the volume method and the length method.

Cutting the length raises the pitch. Cutting a flute by 6% will raise pitch by one note. Cutting off 1% boosts the pitch by about 15 cents. Often flutes are tuned to themselves rather than an external standard--kind of the sonic equivalent of a free range chicken. What flute holes really do is provide a virtual change to the flute's length. When playing your flute, what you're doing is making virtual cuts to it's length, pitch changes and it's called music. So instead of 'practicing', you could just as well say you are cutting your flute--sit and cut flute.

What the EAR really is, is a general measure of the degree of backpressure a flute will maintain. Getting a flute to jump octaves requires a certain ratio of airspeed to backpressure. Flutes with EARs above 30 have greater backpressure and the airspeed needed to jump octaves is less. With an EAR over 35 one blows quite softly in order to keep the airspeed down so as to remain in first octave. With lower EAR numbers this is reversed. An EAR under 25 (less backpressure) requires forceful blowing (high airspeed) to get an octave jump. The important point here is control of a flute is maintained with airspeed rather than air pressure. In texts on instrument acoustics this is called jet velocity and although velocity and pressure are wrapped up together blowing hard should mean blowing fast. Think of EAR as a direct expression of backpressure--higher number, greater pressure. Lower number, less pressure. Generally, somewhere around 30 is what's considered balanced (first and second octaves both easy to achieve and maintain) for a garden variety, vanilla shak. Other elements of backpressure.

The amount of 'air' a flute uses is determined more by it's EAR than it's general size. A short/small flute with a low EAR requires more air than a long/big flute with a high EAR. If the flute doesn't maintain sufficient backpressure you have to augment it with your blowing, thus low EARs take more 'air'. It follows that a given lungful (volume) of air will play more notes on higher EAR flutes than lower. Those really mellow flutes are breathless in more ways than one.


As a general rule of thumb within the realm of normal flutes, there is a 1 to 5 ratio between the effects of bore and length. If you wished to expand a bore by one mm and keep the same pitch, you'll need to cut five mm from the length.

General, all purpose metric (mm) equation:

Length = (186500/ Hz) - 5 Bore


Getting Holy

Probably the next most important factor is hole size. Consider 10mm on a 1.8 shak as the mean, smaller holes soften the timbre and larger holes harden it. Ending up with holes which are nearly the same size contributes to the holes working well together and a better overall result. Undercutting holes increases venting which is the same as drilling a larger hole. Undercut holes may appear to be the same size as regular holes but acoustically they are larger. Having to undercut a hole means it's in the wrong place and should have been higher on the flute.

Generally, hole sizes can range from 8mm to 12mm. Smaller holes favor micro-tones and 'shading' as the holes work more in concert. Smaller holes favor 'softer' sounds somewhat the same way lower EAR favors darker tones. Larger holes favor a louder, sharper sound as the holes compliment or interfere (however you want to think of it) with each other less than smaller ones. It's generally felt that larger holes allow for a higher cutoff frequency--meaning more sub-harmonics are produced. Larger holes increase the sensation of resonance as they expose more of the finger-pad area to the air-column vibrations, hence the player has a stronger tactile sensation of vibration. So, for resonance go with high EAR first and big holes second. It should be obvious that the air-column vibrates--that's the origin of the sound. That IS the sound. Seen on an oscilloscope the sound wave has a profile--a shape. And shape determines how much 'punch' a wave can deliver. High AR produces a taller, narrower wave--one with more punch and bigger holes deliver a larger amount of impact to the tactile nerve endings in the fingertips.

Think of the whole thing like tsunami. When at sea these waves are often just a few feet tall and sailors are unaware when a wave passes. But as the wave approachs land and the depth of the ocean begins to diminish the wave starts to stand up. A tsunami wave's height is directly related to the depth of the water--the ocean's Aspect Ratio so to speak. When it hits shore the tsunami's power is evident. Shoreline to a tsunami is like a skinny flute is to resonance.

Before leaving the subject of resonance, let's go a step further. Accepting that the receptors for resonance are in the fingertips (and lips); the index fingers are the most sensitive. So if you're going to do anything special to (or near) holes to boost resonance do it to the second and fourth holes. These are the index finger holes and the fourth hole is probably closed a greater percentage of the time than the second--thus that index finger will be in position most often to detect resonance. If there's a single hole to concentrate on in terms of resonance, it's the fourth.

The mouthpiece and edge isn't as critical as many believe. Again, we're talking ballpark figures. The edge needn't be particularly sharp, it doesn't 'split' the air stream, it just defines one side of a shallow 'hole'.


Location, location, location

Now for the perennial question--where do the holes go? It depends on hole size and somewhat on wall thickness. Thicker walls are effectively the same as smaller holes. What we're talking about here is the degree and ease of venting. Below is a chart of generalized percentages which will work fairly well with standard EAR and hole size. Smaller holes--smaller percentage, larger holes, larger percentage.

Hole
9mm
23/64"
9.5mm
3/8"
10mm
25/64"
10.5mm
13/32"
11mm
7/16"
11.5mm
29/64"
5
0.420
0.424
0.427
0.430
0.433
0.435
4
0.481
0.485
0.488
0.491
0.494
0.497
3
0.596
0.599
0.603
0.606
0.609
0.611
2
0.681
0.685
0.688
0.692
0.694
0.697
1
0.778
0.782
0.785
0.788
0.790
0.793

Measure percentage of flute length from top of flute

If you plan on designing more than a few shaks get a metric tape measure and a metric caliper from Ace Hardware.

25.4mm = 1" 1mm = 0.03937" 1 shaku = 303.03mm = 11.93"

For flutes with suitable bores (EAR~29.5) frequency can be calculated from length: Hz =160,045/Length mm and Hz = 528.59/Length Shaku.

Some years ago, Mark Shepard came up with a clever device to quickly lay out the holes of a 'percentage' flute. He stretches out elastic and marks the hole locations on the elastic. Then it can used to locate the holes of any length flute. It helps to epoxy small metal hooks on each end of the elastic so you can hook it onto the bamboo--top and bottom. Once you come up with a hole layout that works well, then transfer it to the elastic and hole layout is accomplished in a jiffy.

'Standard' Parameters

If you get:

1) the EAR about right
2) the hole size about right
3) the hole locations about right
4) and the edge about right--everything else will fall into place.

If you're too far out with any of the these four, finishing the flute in a satisfactory fashion will be an uphill struggle. Getting these four right will account for 95% of your flute's timbre, playability, etc. The rest is just fussing with the finer points.

For Nodal Tuning of Jinashi flutes.

For those who like the look of flute bindings, look to bow string material. High strength, low creep, assorted colors. If you have concern about cracking then a finish should be employed.

In general, both bore and holes should contribute toward the same result. If you want a mellow flute then increase the bore size (lowering the EAR) and go toward the small side with the holes. Having a big bore AND big holes creates a flute which is always operating at cross purposes.

If you can stay within 2% on EAR and hole size and under 1% with hole location things will work out pretty well. If these percentages start rising, expect problems and frustration. If you want a shak that will do all the tricks, jump through all the hoops, a flute that everyone will admire then stick to an EAR of 29-30 and standard hole size for the given bore.

If, on the other hand, you're interested in a particular type of sound then push the parameters in that direction. This flute won't do all things fairly well, but it'll do one or two things stupendously well. The standard balanced shakuhachi is by necessity a compromise--most things are suitable but not exceptional.

Construction PDF:

Making the Japanese Shakuhachi Flute by Ken LaCosse

Ken offers two methods for hole location--one in the text and the other in his drawing. The two methods are slightly different as noted in the table below.

Hole
From Text
From Drawing
5
0.412
0.414
4
0.478
0.480
3
0.578
0.583
2
0.678
0.678
1
0.778
0.778

Measure percentage of flute length from top of flute

Construction Manuals:

Blowing Zen: One Breath, One Mind by Carl Abbott

The Japanese Shakuhachi Flute: Notes on the Craft & Construction by Monty Levenson

Frank's Supply will sell you root-end culms by the dozen.


ShapeShifting Holes

Unless you have an extraordinary ear you'll need a tuner--some standard against which to adjust hole tuning.
The notes your flute should play depend on the basic key it's in.

Katsura Shareware has a Mac Universal Chromatic Tuner for 5 bucks.

Tuner for PC and older Macs.

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

To understand and benefit from the following you'll need to accept the premise that every hole you drill is in the wrong place.

Premise #1: It doesn't matter how much measuring and calculating you do, it doesn't matter how developed your intuition is, it doesn't matter how many hundreds of flutes you've made--the first drilling for holes will be in the wrong place. Maybe many millimeters, maybe a thousandth of a millimeter--but each hole will need to be adjusted. Think of this like golf, the point isn't to always shoot for a hole in one, the point is to complete a number of strokes, each of which advances you steadily closer to the hole. Following is a somewhat systematic method for arriving at proper holes.

Premise #2: Anytime you remove material (drilling, grinding, sanding, etc.) you're increasing venting. Venting and location, that's the thing with holes. It may serve you better to think of venting rather than hole size. Bigger holes vent more than smaller, deeper holes vent less than shallow. Cutting raises the pitch, whether it be the flute's length or holes. Cutting is a one-way street--always upward.

Expanding a hole or moving it upstream has the same effect--raising the pitch
Shrinking a hole or moving it downstream has the same effect--lowering the pitch.

Undercutting is the same as expanding a hole because both increase venting. Undercutting on the upstream or downstream sides move the effective center of the hole in that direction. So, undercutting on the upstream side is both increasing hole size and moving the hole upstream--both things raise the pitch. Can you undercut and lower the pitch? No. Undercutting on the downstream side does move the hole downstream (thereby lowering the pitch), but this is offset by the increase in hole size. It's the ratio of hole expansion versus hole movement and hole movement is smaller compared to hole expansion

Undercutting upstream doubly raises the pitch.
Undercutting downstream raises the pitch at a slower rate.

Because the bamboo bore isn't cylindrical and because the inside of all bamboo is different, accept that you're flying in fog, make your best guess and drill. What we're trying for here is to get within a few millimeters. To drill close enough to the correct location in order to be able to ShapeShift the hole into the right place. The trick is to drill a pilot hole of a size such that if it's in the right location it'll sound one note lower then it'll end up being.

Assuming a D Flute: Drill a pilot hole at the #1 hole location (the one at the bottom) where you think it should go, but drill it 1/2 the size you'll want on the finished flute. The first hole on a finished D flute will sound F. If you drill it 1/2 size and it sounds E then you know the hole is in the right location and you can go ahead and expand it. If the note is above E the hole location is too high and you should expand it on the downstream side. If the note is below E then the hole location is too low and expansion should only be on the upstream side. Drilling a pilot hole 1/2 size should sound one note lower (than the finished note) if the location is right. The method isn't perfect, but with a little practice this Pilot Hole Method will inform you about location and which way a hole needs to be shapeshifted. Use pilot holes on the remaining holes the way you did on the first. Pilot notes for a D flute: E, F#, G#, B, C#.

The outer hole edges are usually finished with a fairly crisp profile, inner edges should be chamfered more.

Premise #3: Holes don't exist in isolation, they work together. As hole size increases the less do the holes cooperate to create pitch. Small holes acoustically chain together more, so the effects of fingering and cross fingering becomes more pronounced. If you really like the sound and shades of tricky fingering then tend toward smaller holes. Larger holes favor half-holeing, smaller holes fingering.

Premise #4: Flute building is an exercise in compromise. Try as you might, you can't have everything in one flute. There is the issue of visual versus aural. Do you want the same identical hole sizes or equal hole spacing? Or should your flute follow more acoustical principles? Flute making is a matter of compromising, judgment, and intention.


Once you've gotten a grip on the four elements detailed above (EAR, hole size, hole location, edge) and are familiar with their effects, you can step out of the beginner category and start creating your own particular shakuhachi. For the most part, that journey will be about investigating the subtly of the interplay among the four elements. The general concept of venting will serve you well in most circumstances. For example, changing the slickness of the bore surface changes venting and changing the venting of the bore is the same as changing its size. So, by changing the surface roughness at the choke point (for example), one can effectively expand or shrink the bore at that location. Ordinarily, changing bore venting at particular locations along its course is done by adding material to the bore at these places and this is the way jiari flutes are built. It's not commonly realized that the pressure wave in the bore of a shak is moving at the speed of sound--Mach 1, so thinking like a supersonic designer could lead to any number of impressive effects.


Bamboo/Urushi Vibrations

There is a view that any flute material which is fairly stiff, hard, air-tight and used in thicknesses not given to incidental flexure produces about the same results as any other. So aluminum foil is out, being too thin. Pine isn't particularly hard, oak isn't air-tight. Foam-rubber's lack of stiffness makes it attractive for other purposes.

But let's look at the opposite belief, that the peculiar sound of the shakuhachi comes primarily from bamboo/urushi vibrations.

A quick review:

Areophones are instruments in which the sound is produced by the vibration of air. They are classified according to how the vibration is generated, and include flutes, reeds, cup mouthpiece instruments, and free areophones.

Idiophones are instruments made of naturally sonorous material, sounded in a variety of different ways. They include: xylophone, mirimba, gong, bell, glockenspiel, etc. These are the ‘percussion’ instruments.

Membranophones are instruments in which the sound is made by the vibration of a stretched membrane or skin--drums and mirlitons.

Chordophones are instruments in which the sound is made by vibrating strings. There are five basic types: bows, lyres, harps, lutes, and zithers.

Many in the shakuhachi world don't classify the shak as an areophone, they classify it as an idiophone--an instrument who's tone derives from the material from which it's constructed, bamboo and urushi. Further, they often posit that bamboo and urushi of bygone eras was of higher ‘quality’--implying that the sonorous qualities are superior in some way. This bamboo/urushi contingent sometimes classifies the shak as a chordophone by comparing it to violins, guitars and the like.

It's surprising that the bamboo/urushi group is generally made up of musicians and other experts who usually have wide exposure to different kinds and types of instruments. They, if anyone, should have a deep appreciation for the four general types of phonic instruments and the principles underlying each.

It's a mystery. If the shakuhachi isn't an areophone, what is it? Makers usually proceed with the idea that a shak is an areophone, but are repeatedly told that they're wrong in this assumption. If the shakuhachi world can't agree on the most fundamental principle of where the sound comes from, then there's something badly wrong with the whole endeavor. If the shak is an areophone this means that many of the leading lights in the shak world have been wrong their entire careers about the most basic fact of their instruments which implies that their opinions on other shakuhachi matters should be treated with caution.

If the shakuhachi is an ideophone or has important ideophonic qualities then the makers have been barking up the wrong tree the whole time and have never understood what they were doing.

The shakuhachi seems to attract and engender non-critical thinkers or this thing would have been settled long ago. It's kind of like clinging to the biplane era of flight after aeronautics moved on and insisting that flight itself arises because of the properties of canvas and wood. For a pilot to not comprehend or understand the basis of flight is worrying.

Some teachers steadfastly maintain that when, say, a wooden and bamboo flute sound differently, the difference is solely attributable to material. Why would they think so? Are the two bores identical? Same taper, same choke point, same hole size, same undercuts, same hole locations, same bore surface roughness, same chimney heights, and so on? Only after one has undertaken detailed measurements to guarantee similarity is he justified in making the pronouncement that disparate flute materials sound differently. Otherwise, it's just a case of very lazy thinking.

On the other hand, let's assume for a moment that the materials conjecture is true, that bamboo/urushi is at the heart of the shakuhachi sound. The people who believe this should already have done exhaustive resonant material tests. This should have become the Holy Grail, the search for the ultimate resonant flute material. But it hasn't happened. The Irish flute people swear that certain hardwoods are the best and won't even consider bamboo. Shakuhachi people believe only in bamboo and shun hardwoods. Go figure.

Where does the shakuhachi reside, in the flute or the activity? Shakuhachi collectors are compelled to believe in the bamboo/urushi theory, otherwise what are they hoarding? Object or activity? Settle that one for yourself.

Actually, the bamboo/urushi people don't really believe that the sound of a shakuhachi arises from the physical vibrations of bamboo/urushi. There are so many ways to test this that any moderately curious person would know it to be ridiculous within minutes. What the bamboo/urushi crew is claiming is much more subtle and profound. That the spirit of suizen only resides in bamboo/urushi and as such can only be called forth from bamboo/urushi. The idea that the soul of Honkyoku could happily reside in PVC (or any other disgusting equivalent) blows the lid off the whole belief structure surrounding the shakuhachi. Once cracked (no pun intended), the entire edifice would collapse. The bamboo/urushi crowd isn't claiming vibration on literal scientific grounds (otherwise, they'd demonstrate such), their claim is more quasi-religious and therefore faith-based. They feel vibrations in their finger tips and lips, they are touching bamboo/urushi--ipso facto, the bamboo/urushi must be vibrating. It moves, it's alive, and it sings. How could it be otherwise? They're really talking about what they percieve to be the spirit of bamboo/urushi. It's a subjective thing. Enlightenment from a single note? Yeah, right.

The bamboo/urushi camp claims that bamboo adds an intangible quality essential for understanding shakuhachi and it's probably true in the same sense that context provides an intangible element to any experience. However, an 'intangible quality' is different from discernable tonal effects both by type and degree. Bamboo/urushi is doubtlessly REQUIRED to fulfill the traditional aspects of shakuhachi, but for little else. When bamboo/urushi is examined as an issue of fashion everything clears up. It's really the question of whether clothes make the man.

Suffice it to say that if you believe sonorous materials play a role in flute sound then little on this page is of much use to you for the purposes of flute building. The path would then be to develop tests to identify and quantify the vibratory qualities of bamboo/urushi and proceeding from the results.

Should you particularly care about this discussion of bamboo/urushi then contemplate ideophones and notice how different notes are created on an ideophone. That should clear it up.

Here's a short article that sums up the whole debate.

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