When does a cylinder become a cone?
Posted: Wed Aug 10, 2016 7:58 pm
The people who need to know these things probably understand all this already, but I've been curious for a while ...
I've read that a cylindrical-bore reed instrument like a clarinet overblows at the 12th (3rd harmonic), while a conical-bore instrument like an oboe or uilleann chanter overblows at the octave (2nd harmonic). So how does it suddenly switch from the 3rd harmonic to the 2nd just because the bottom end gets a bit bigger.
Turns out, it doesn't. It's a gradual change. I used software to model a hypothetical double-reed instrument in D4 with a 6mm diameter bore at the top, as the bore at the bottom went up from 6mm diameter. The length of the pipe also had to increase, starting from under 200 mm, to keep the fundamental at D4.
With a 6mm cylinder, the second register was actually sharp of the 12th (A5), by about 2 1/2 semitones (almost to C6). It gradually got flatter as the bore at the bottom increased. It got down to A5 when the bottom was around 8 mm diameter, and down to D5 (the second harmonic) around 22 mm diameter and 400 mm long. It kept going down from there, although more slowly. At 40 mm, it still wasn't down as far as C#5.
For none of these cones were the higher registers in tune with the higher harmonics. I tried adding a flared bell at the end; that didn't help much at all. However, a cone with a bulb or bulge at the bottom, worked like a charm, getting all of the first 5 harmonics reasonably well in tune. The result looked a whole lot like an oboe d'amore or cor anglais.
I've read that a cylindrical-bore reed instrument like a clarinet overblows at the 12th (3rd harmonic), while a conical-bore instrument like an oboe or uilleann chanter overblows at the octave (2nd harmonic). So how does it suddenly switch from the 3rd harmonic to the 2nd just because the bottom end gets a bit bigger.
Turns out, it doesn't. It's a gradual change. I used software to model a hypothetical double-reed instrument in D4 with a 6mm diameter bore at the top, as the bore at the bottom went up from 6mm diameter. The length of the pipe also had to increase, starting from under 200 mm, to keep the fundamental at D4.
With a 6mm cylinder, the second register was actually sharp of the 12th (A5), by about 2 1/2 semitones (almost to C6). It gradually got flatter as the bore at the bottom increased. It got down to A5 when the bottom was around 8 mm diameter, and down to D5 (the second harmonic) around 22 mm diameter and 400 mm long. It kept going down from there, although more slowly. At 40 mm, it still wasn't down as far as C#5.
For none of these cones were the higher registers in tune with the higher harmonics. I tried adding a flared bell at the end; that didn't help much at all. However, a cone with a bulb or bulge at the bottom, worked like a charm, getting all of the first 5 harmonics reasonably well in tune. The result looked a whole lot like an oboe d'amore or cor anglais.