This graph ties it all together--Note, Length and Aspect Ratio (length divided by bore). If your flute is 545mm long and plays D then it's AR is not quite 31. Every shak which is 545mm long and plays D has this Aspect Ratio. All D shaks 545mm long sound pretty much alike because they all have essentially the same Aspect Ratio. A D flute with an AR of 25 will be about 520mm long--it's that simple. (Another method of determining Aspect Ratio)

Yes, there are things (bore finish, etc.) which can shift Aspect Ratio...a little. But the basic geometry of the bore is the greatest determinant of Aspect Ratio--the timbre--of your flute. What the graph tells you is that for flutes tuned to specific keys the flute's length determines it's timbre. There should be D flutes around which vary in length from, say, 480 to 560mm. That's about a 17% variation in length. Outside that range they won't play too well.

It's obvious from the graph that length isn't the sole determinant of pitch--it's just one factor, Aspect Ratio being the other. At the end of the day it doesn't matter a whole lot about how a shakuhachi's bore is configured--as far as Aspect Ratio goes. A fancy tapered bore with an Aspect Ratio the same as a straight pipe will sound pretty much the same. The octave tuning may be a little different but the fundamental sound characteristics are very similar.

To have flutes made to standard lengths is the same as saying they have standard sound characteristics. If nothing else the graph demonstrates the impact of bore diameter. Aspect ratios above 30 are sharper, clearer, more piercing and favor the higher notes. Below 30 are mellower, softer and favors the lower notes.

So how long is your D flute? Or perhaps more importantly, how long do you want it to be?

Graph of flute length vs. effective bore diameter.

Here's the dance. Suppose you have a D flute and it's average bore diameter is about 17.5mm. You want to open it up a little, lower the AR, get a mellower sound. So you do some filing in the bore. But then it doesn't play D any more--it plays flat. So you cut off some of the length to get D again. And so it goes, following the D curve in the graph above.

Notice that if you opened up the bore of standard D all the way to 22mm it'll play C# (see graph). D length but C# sound. Then if you cut off about 35mm you'd get it back to D. Fat bores are shorter than skinny to produce the same note.

The following graph attempts to make sense of it all.

The Yellow Zone (above) delineates lengths and notes for suitable PVC flutes.

The range of the Zone's Aspect Ratio is 25-33, but this is Equivalent Timbre.

Very playable flutes can be made of thick and thin walled 3/4" PVC, tuned respectively to D and C.

PVC pipe sizes •••• Convert English-Metric •••• 1"=25.4mm

See The Synthesis for a final flute design.

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