Place your palm down on a table and spread your fingers. Measure from the center of the tip of your index finger to the center of the tip of your ring finger--check both hands. Now, take half that distance and you'll have the limit of the distance between the holes played by those fingers. For the sake of this discussion let's assume the ergonomic distance is around 60mm. This means that the distance between the first/second and third/fourth holes should be 60mm or less in order to play comfortably. For the distance to the thumb hole take a third of your finger span--or 40mm. Now we have the limiting distances between all the holes except the second and third. Since the second and third holes are played by different hands there isn't any ergonomic limiting distance between them.

The greatest distance between holes in the 'correct' acoustical position is between the third and fourth. As the shakuhachi grows longer this will be the first place to require stretching. We can ask a simple question: At what length do acoustically correct, even-sized holes become a problem as far as spacing? But first, some background: It's makes little difference what sized holes your shak has. Big or small holes, the distance between holes is about the same. It's true! About the only difference big or small holes make (as far as placement goes) is whether the holes will be higher or lower on the shak. Big holes will be lower and smaller higher--but the distance between holes remains nearly the same! So at what length will a shak run into the 60mm limit set above? Surprisingly it's about 1.75 shaku (530mm). Yes Bucky, the standard 1.8 shak is already at or over the 60mm limit in regards to the span between the third and fourth holes. The limit between first and second will be achieved with a 2.06 shak (625mm) and the thumb limit will be maxed out at 2.14 shaku (650mm).

So what to do? Aside from wrecking your hands there's only one answer--different hole sizes. There goes the aesthetics. There are many ways to approach this design problem, but a simple straightforward way is to keep the second and fourth holes at their correct acoustical positions and original sizes. When the third/fourth holes hit the ergonomic limit place the third hole 60mm below the fourth and adjust its size smaller to compensate. Same thing with first/second. Keep the thumb hole within 40mm above the fourth. The size of the first and third holes will diminish, the thumb hole will expand.

What does acoustically correct mean? The short answer is that it satisfies the Benade (or similar) equations. Does acoustical location really matter? The short answer is no--especially if it makes the flute unplayable. At the end of the day your flute will sound better if it's played better and that's only done with comfortable, unstretched fingers. Despite what others may tell you, there is no acoustically compelling reason to place holes outside their ergononomic limit.

Here's the deal. Place the index finger holes where they 'should' go. Place the ring finger and thumb holes where they 'should' go UNTIL they reach their ergonomic limits. Then hold them there and start changing the hole diameter to make things come out right. Not so hard.

It's much easier and more humane to fit flute to the hands than the other way around. If you know what the words 'carpal tunnel' mean from personal experience then it may be time for an ergonomically designed flute. Placing the holes in their ergonomically 'correct' location only happens once, if not, your fingers may be strained every note you play. It's more than a little bizarre that players will deform their hands rather than getting the right flute in the first place. Can't find one? Ask for it, demand it--makers will respond.

The downside of a ergonomically designed shak? The holes won't all be the same size and the spacing will be a little different than you're used to. The upside? Joy pervades the kingdom and the music to go with it.

Happy hands make happy music!

See The Synthesis for a final flute design.

Program for Acoustic Location of holes:

on mouseUp
ask "What flute length?" with 576
put it into TL --Tube Length
ask "What hole diameter?" with 10
put it into Dh --Diameter of holes
put 156521/TL into BaseNote
put 20.5 into Db --Diameter of bore
put 3*1.125 into Wt --Wall thickness
put Wt +(.75*Dh) into Te --Tonehole effective thickness
put 165674 into BigNum
put BigNum/BaseNote into TubeLength --Ideal tube length
put TubeLength-(.3*Db)-TL into MEL --Mouthpiece Equivelent Length
put "32232" into Interval --see Interval page for an explanation
-----------------------------------
put empty into fld "Data"
put empty into temp
put TubeLength into LastLength

repeat with zz=1 to the number of chars of Interval
add char zz of Interval to temp
put BaseNote* 2^(temp/12) into Hz --frequency of hole
put BigNum/Hz into NewLength --Ideal tube length for note
put (LastLength-NewLength)/2 into S
put S*((((((TE/S)*(Db/Dh)^2)*2)+1)^.5)-1) into CF --Correction Factor
put round(NewLength-MEL-CF) into HoleLocation
put zz&"-- "&HoleLocation&" " into line (6-zz) of fld "Data"
put NewLength+CF into LastLength --moving to next hole
end repeat

ask "What's the ergonomic limit?" with 60
put it into ErgoSpan
set numberformat to "0.##"
put (word 2 of line 2 of fld "Data")-(word 2 of line 1 of fld "Data") into ThumbS
put (word 2 of line 3 of fld "Data")-(word 2 of line 2 of fld "Data") into TopS
put (word 2 of line 5 of fld "Data")-(word 2 of line 4 of fld "Data") into BottomS
if ThumbS>(ErgoSpan*2/3)then put " "&(word 2 of line 2 of fld "Data")+ (ErgoSpan*2/3) after line 1 of fld "Data"
if TopS>ErgoSpan then put " "&(word 2 of line 2 of fld "Data")+ ErgoSpan after line 3 of fld "Data"
if BottomS>ErgoSpan then put " "&(word 2 of line 4 of fld "Data")+ ErgoSpan after line 5 of fld "Data"

put TL/25.4&" in." into IInch
Put the short date&return\
&"Pipe Flute--"&BaseNote&"hz"&return\
&"Length--"&round(TL)&"mm "&IInch&return\
&"Aspect Ratio--"&TL/Db&return\
&"Schedule 40 3/4 in."&return\
&"Scale--"&Interval &return\
&"Holes--"&Dh&"mm "&return&return before fld "Data"

put return&return&ThumbS&" Thumb" after fld "Data"
put return&TopS&" Top" after fld "Data"
put return&BottomS&" Bottom" after fld "Data"
end mouseUp

Program output:

7/9/02
Pipe Flute--240.8hz
Length--650mm 25.59 in.
Aspect Ratio--31.71
Schedule 40 3/4 in.
Scale--32232
Holes--10mm

5-- 280
4-- 320
3-- 394 380
2-- 450
1-- 512 510

40 Thumb
74 Top
62 Bottom

Hole locations are in millimeters, measured from the top of the flute. The spans for acoustically located holes are at the bottom of the list. For any span outside the ergonomic limit a second hole location is given. The program example above is set up for schedule 40 3/4" PVC pipe.

Jeremy Bornstein has a page where one may perform the above calculations interactively.