Experimental PVC Shakuhachi Part 1

Hello again,

It's been a while since I made a musical instrument, and I woke up today with a sudden urge to do so.

If you are one of the three or four regular readers of this blog then it will be no surprise to you that I decided to make another shakuhachi. Why? Well, aside from the fact that you can never have too many, I've had an idea knocking around for a few months that I've been wanting to test out.

Firstly, the great majority of shakuhachis are in D. The reason is that shakuhachi means "shaku", which is an old Japanese measurement that is very nearly a foot, and "hachi" which means eight - or in this case "point eight". So a standard shakuhachi is one point eight feet in length, or 54.5cm. A tube this long will usually play a D.

Despite my short time as a student of this instrument, I've acquired three shakuhachis - two bamboo, and one ABS - all in D. I've also accumulated a fair amount of shakuhachi music, some of which is played on shorter pipes (higher pitch) and some on longer (lower notes). Longer shakuhachis sound great. Here's Katsuya Yokoyama playing "San An" on a 2.1 shakuhachi (key of B):

But wait! I hear you cry. Didn't you already make a longer shakuhachi? Well, yes I did, but it's VERY long so the holes are hard to reach, and since I've looked into the subject a little more I think the pipe is too narrow, which makes the low notes very difficult to play, and the tone a bit weird. The third issue is that the pipe (A) has a cylindrical bore, whereas a proper hand-made instrument (B) has a tapered bore:

which is apparently important for tuning the second octave.

So, onto my idea.

I had been thinking for a long time about how to cheaply and easily create a tapered pipe. Cheapness and easiness are essential characteristics of any instrument I make, and a tapered bore profile is an essential characteristic of a shakuhachi.

I read somewhere on this great site that the area of the cross-section of the bore (and how the area changes from one end to the other) is the important element - the shape of the cross-section is not so important. The site contains a lot of suggestions for how to taper a cylindrical pipe, but they are all quite difficult for me to implement without buying extra equipment. And - crucially - adding or removing material to create exact areas is REALLY HARD, and takes a LONG TIME.

Now, there are graphs of bore profiles available on the net. Here's one:

So my problem became: How do I convert a range of diameters like this into a 3D area? The answer which I eventually hit upon was as follows:

Imagine, firstly, a piece of PVC pipe. This is the main body of the shakuhachi. Then, imagine a second pipe fit snugly into the first one. This would make a thicker-walled pipe with a narrower diameter. Like this:

Then, by removing bits of the inner pipe, we can change the cross-sectional area of the bore.

But surely this is the same problem as before! Well, not quite, because we don't have to file away at the inside of the pipe, we can simply cut an area out of it so that, when the shard of smaller pipe is wedged into the larger one, it makes the cross-sectional area equivalent to the desired taper. This is a bit difficult to draw (especially with a mouse) but hopefully this gives some idea:

The clever bit is, because both the pipes have a uniform thickness and diameter, the amount to be cut away can be calculated quite precisely. If you know the maths. This part took me a LONG time, but after several failed attempts here's the "winning formula":

So all that remained was to put this formula into an Open Office spreadsheet and input the values from the shakuhachi bore measurements, and copy the result onto a large piece of paper like this:

 Then cut the paper out and tape it to the inner pipe:

And trace the outline with a permanent marker before removing the template:

That is as far as I've got... Hopefully I'll get some time this week to do a bit more.