When does a cylinder become a cone?

[Tunborough]

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.

[an seanduine]

If memory serves me correctly, the Denners introduced the 'speaker key' and the 'speaker tube' to the chalumeau to effectively create what has become the modern clarinet. The 'speaker tube' corrected the tuning of the twelfth and allowed the register notes to be played more correctly in tune. They also used two tuning holes at the bell end to improve tuning. . .which I guess would be analogous to your bell bulge. When I played clarinet there still seemed to be a little black art in the transition from the mouthpiece through the barrel to the bore proper.

Bob

[Tunborough]

They also used two tuning holes at the bell end to improve tuning.

Good point. However, when I tried that with a cylindrical bore, it didn't help get the third harmonic in tune, with or without a flared bell.

It makes a lot of sense in practice, though. The maker can tune the bottom note by drilling out the tuning holes, rather than shaving off the end of the beautifully-turned bell.

A speaker hole, on the other hand, a small hole around the middle of a cylinder, could produce the first, third and fifth harmonics in tune, even one designed to be always open.

[Driftwood]

I used software to model a hypothetical double-reed instrument

This sounds like interesting software. Where d'ya get it from? Do you need a PhD in Physics to handle it or could an ordinary dummy like me use it?

[Tunborough]

The software is WIDesigner. The latest release, available here on GitHub https://github.com/edwardkort/WWIDesign ... ses/latest, supports whistles, NAFs and flutes. The support for reed instruments isn't ready for prime time yet, but it was enough to produce the results above.

Is it easy to use? Haven't heard a lot of feedback, so I'm not sure. You don't need to understand the physics behind it, but you might be put off by all the details of setting up an instrument and its tuning scheme.

[benoit trémolières]

I'm just this times trying to explain on the french forum that, concerning reed instruments, the theoretical models are not complete!
You can not neglect the reed, or simply simulate it by a resonator volume or else.

Without the reed, for instance, all the calculations about diapason are completly false, because, with the reed, you can produce nearly any pitch you want.
The same with the relative scale.

If you compare with a stringed instrument, the chanter (or the bore) could be compared with the chest and the fretboard, since the reed would be the string and the staple: the bridge.

What could you deduce from the mere chest and fretboard as long as you don't know how strongly the string must be stretched, and how heavy and strong it must be?

If you stretch it very loose, you'll get a very low pitch.
The relative tuning of the scale will be wrong, but this can be fixed by changing the diameter and weight of the string, and removing the bridge at the proper place (what is corresponding with staple dimensions changes).

At the contrary: you can work a lot to adapt the chest and handle with a particular string.

I think that the problem with acoustic theories is that they take too much importance to the bore, and not enough to the rest of the instrument.
What has been said about clarinet's upper part is a good exemple of what reedmaking force us to face with all the time.

Anyway, I find your question accurate and a very interesting one.
Insisting on the huge role of the reed does'nt mean that the rest has no influence.

My idea is, for now, that a particular bore (or chest in a stringed instrument) is more apossible way to obtein a certain sound, than the result of tuning and pitch willings.
The ancient makers naturally deduce that a lower instrument had to be longer and narrower than sharp one, but it's only because it's easier to do (and seems more logical) than to work on the reed.

There's no tuning reasons for a flat-set to be longer or narrower than a concert-pitch.
The same pitch could be reached with another bore dimensions.
But the tone won't be the same at all!

Some makers nowaday are making what could be called "wide bore" B flat chanters.
It works perfectly, but not the same way a narrow one does.
Then, in the end, all the matter is about timber and sound, not tuning and pitch.

Allways the same conclusion: in woodwind instrument making, the reedmaking is very much more than half of the job.
There's no bad chanters: only bad reeds...

[PCL]

Here is a first-pass explanation: http://newt.phys.unsw.edu.au/jw/musFAQ.html#truncate.

The model for a flute doesn't apply to a reed-driven pipe. Put a drone reed in a chanter and listen to the harmonics. I just tried it. A randomly selected baritone reed, made for for Bb pipes, placed in wide bore D chanter (actually a squinnter) gave B for G fingering, overblowing to F# (a diminished fifth). A Bb chanter reed gave a quarter tone flat of G, for G fingering, overblowing to quarter tone flat of F# (a major seventh).

As Craig Fischer says, "The reed is your man."

[Driftwood]

The model for a flute doesn't apply to a reed-driven pipe.

Absolutely. In very crude terms, the "down-time" between air pulses starting down a whistle and those going down a reed pipe is usually very different (i.e. a shorter period of time) because the pulses are created by a different method. And this affects the sound frequency coming out of a given length of pipe.

[Tunborough]

I'm just this times trying to explain on the french forum that, concerning reed instruments, the theoretical models are not complete!
You can not neglect the reed, or simply simulate it by a resonator volume or else.

No argument there. At the moment, WIDesigner models the reed with two parameters; you have to set these based on how the reed you have in hand behaves in a real pipe. Those two parameters were enough to describe the behaviour of a real reed in a real smallpipe chanter.

That's one of the reasons the WIDesigner reed model isn't ready for a release: we need to test whether those two parameters are enough to model other reeds.

[Tunborough]

The model for a flute doesn't apply to a reed-driven pipe.

Just to be clear ... the reed model in WIDesigner is separate from the whistle/flute models. They share a model for bores and toneholes, but use totally different mechanisms for modelling the driving source and calculating playing frequencies. Very roughly speaking, flutes resonate when the head sees a low acoustic impedance (low pressure, high flow), reeds resonate when the head sees a high acoustic impedance (high pressure, low flow).

[benoit trémolières]

I must apologise:I've got a slight tendency to over react as soon as I hear about improving things from the bore and holes...
So many people, since a long time, have been driven to look this way, because the basics of musical acoustics theories are always treating of this dimension first.
Experiencing the reedmaking, I noticed that, in the facts, these theories was all the time challenged by practice.

But your purpose was not about improving...
Sorry.

[Tunborough]

I must apologise:I've got a slight tendency to over react as soon as I hear about improving things from the bore and holes...
So many people, since a long time, have been driven to look this way, because the basics of musical acoustics theories are always treating of this dimension first.
Experiencing the reedmaking, I noticed that, in the facts, these theories was all the time challenged by practice.

But your purpose was not about improving...
Sorry.

No apology necessary, your reaction was quite reasonable. While the aim would be to improve the bore and toneholes, we can only do that if we know what the reed is really doing, not what theories say it should be doing. After all, the theory says a cylinder overblows at the twelfth, and as noted in the OP, I don't believe that any more.

And I'm nowhere near being able to improve the reed.

[PCL]

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.

Another way to think about it is this: In a bore closed at one end, the standing pressure wave has a maximum at the reed and a minimum at the open end. These boundary conditions must apply for all of the harmonics. If a closed cylindrical bore were to overblow to the octave, there would be another pressure maximum at the open end, which is impossible because it is atmospheric pressure there. The boundary conditions require that the closed cylinder must overblow odd-numbered harmonics, hence a twelfth instead of an octave.

A conical bore "modifies" the profile of the pressure wave because it introduces a pressure gradient. This moves the nodal point created by overblowing down the bore, towards the open end. When things are right (the reed!), this point is halfway along the bore, so it overblows the octave.

In a real instrument, there are pesky things like finger holes, staples, etc. The bore must be modified to counter their effects, as best we can.

For a more mathematical description of the fundamentals, see here: http://www.mozart.co.uk/information/the ... ustics.htm.

[Tunborough]

For a more mathematical description of the fundamentals, see here: http://www.mozart.co.uk/information/the ... ustics.htm.

That page propagates the claim that, "The clarinet ... overblows at the twelfth, where all the others overblow at the octave." The point of the OP was that isn't true. For starters, a vibrating reed isn't the perfect closed end that the simplistic mathematics assumes. A real reed in a cylinder is likely to overblow sharp of the twelfth. The simplistic analysis of cones, on the other hand, falls apart when it assumes the standing wave has to be a sinusoid. It doesn't. Only certain cones will overblow at the octave. Shallow cones will overblow sharp of the octave, broader cones will overblow flat.

[benoit trémolières]

And the place where the cone is cutted is of crucial importance too!
We have a man in France that achieve a bore calculating program (http://la.trompette.free.fr/Ninob/Tutt.pdf), who pretend that the inner volume of the reed acts like a resonator at the upper end, that balances the octaves (or fifth).
But it appears in my own experience that the vibrating abilities of the blades can completly set aside this claim.

As usual, this theorie is neglecting the fact that the blades behavior doesn't follow the tubes acoustic laws.
And because (as demonstrated by patrick Murray:http://www.tuftl.tufts.edu/musicenginee ... n_reed.pdf) nobody really knows how they work, there's actually no way of modelising it, and really introduce this dimension in calculations.