Experimentation continues, this time with 1/2″ CTS CPVC tubing and elbows.

Step one, of course, is to figure out how to get a mouthpiece on. I have a 3/4″ to 1/2″ reducer and if the 3/4″ end were reamed out a little I could fit a soprano clarinet mouthpiece into it. And I might try that at some point, but for now I found something easier was to put a few wraps of electrical tape around a tube, and then it fit inside the tenon of an alto clarinet mouthpiece. Which I have one of. Yeah, yeah, laugh it up.

So then I started measuring frequencies using various combinations of four lengths of tubing. As before, I found a linear relationship between $1/f$ and $L$, but with a coefficient corresponding to a very low speed of sound — 322 m/s. Again, I don’t understand the cause of that.

Next I compared frequencies for a tube with and without 13 street elbows added, and came up with a figure of about 33 mm for the elbow bore length.

Now, the configuration I showed in a drawing in the previous post has holes separated by about two elbows for half steps and four elbows for whole steps — about 66 and 132 mm respectively. Given that Pollak’s Mr Curly, which is in the contrabass clarinet range, uses about 145 mm for a whole step, 132 mm might be too long for a whole step in the contra-alto clarinet range. But I’ve been messing around with these elbows and I think I can get configurations without too much stretch having smaller bore separations than that, based on planar and right angle serpentine geometries, and switching over to helical geometry at the lower end. In fact I might not have to have my half steps in the positions I mentioned before, between holes 1 and 2 and holes 4 and 5; I might be able to put them at holes 2/3 and 5/6, like on a standard clarinet.

So I tested that. The all-fingers-down note (one of them, that is) of a contra-alto clarinet is written F, sounding A♭1, about 51.9 Hz. Fortuitously, putting all four tubing pieces plus two ells together gives me about 54 Hz, pretty close.

So I drilled holes in four elbows — 10 mm diameter in two and 6 mm in the other two. Putting pairs of them in the appropriate spot between tubes gives a frequency of around 100 Hz with both holes open — close to the all-fingers-up note on a contra-alto. Now the question is, how many elbow lengths between holes are needed to produce semitones and whole tones? If I need spacings smaller than the minimum you can get, I’ll have to abandon the contra-alto idea and aim for making a lower pitched instrument instead. If I can handle the spacings at the top end, on the other hand, the ones further down should be manageable.

So for various combinations of elbow-with-hole, $n$ elbows-without-holes, elbow-with-hole, I measured the frequencies with both holes open and top hole closed, bottom hole open.

One surprising finding was that if the top hole is 6 mm, I can play a note on that, but if the bottom hole is 6 mm and the top hole is closed, it refuses to sound a note in the bottom register. That’s true whether there are three, two, one, or zero elbows in between. Evidently the small hole is acting like a register hole, but only in positions past the first elbow!  A 10 mm hole in those positions works fine, though — until you half-hole it, and it overblows. Presumably once you get far enough down the bore a 6 mm hole will work again, but I haven’t verified that yet. Lesson: holes much smaller than 10 mm may or may not work, depending on where they are.

So I got results only for two 10 mm holes, and for 6 mm above 10 mm. At a distance of 1 elbow the two notes are about 65 and 45 cents apart, respectively (where 100 cents is a semitone). Not too surprisingly, at a separation of 2 elbows the intervals are about twice that, 126 and 87 cents: too wide and too narrow for a semitone, but clearly you can move the tuning around by tens of cents by changing the hole diameter a little (8 mm might be safe) or by moving it a fraction of an elbow length. A 3 elbow separation gives 186 and 120 cents, and 4 elbows, 249 and 169 cents. In those cases I can probably correct a too-short bore separation with short inserts of tubing without affecting the stretch. Further down the instrument the needed separations will get larger, and those too can be accomplished with tubing inserts, I think.

So this seems encouraging. Not that getting a good set of hole positions and sizes is going to be trivial, but these results suggest it may well be possible! And the good thing about building with elbows is, if you have a hole that’s too big or in the wrong place, you can just yank out that elbow and try again. Big advantage over grenadilla logs there!