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In response to a question about bad notes on a natural horn crook, both John and Dave have taken a crack at an answer.
Behind-the-scenes we also heard from Brian Holmes a.k.a. the “Cabbage.”
The initial question:
My question is why a natural horn instrument with a certain crook might have a bad note. What is the explanation, the physic behind it? … For example, on my Courtois horn, the top G on the C-crook is terribly sharp in pitch, and has a very poor tone quality.
My first thought was that it might not be clean inside (after all, it’s more than 200 years old!), or maybe a dent was interfering with the vibrations. But I got both the crook cleaned and the dents removed, and the “wolf” note is still there.
Mr. Holmes has been a member of the Physics Department of San Jose State University for fourteen years. His interests include the physics of music and sports, and physics education. A sought-after speaker, his topics include musical acoustics and sports physics.
Mr. Holmes offered his own opinion on this topic and given his background and expertise, we thought that it would be interesting to pass it on to our readers. It is reproduced here with permission.
In response, Brian Holmes
* * *
I’m not sure I understand what Dave means by “equalizing.” And I do not understand the physics whereby such equalization would produce a shortening of the air column. Let me offer another explanation.
Sound consists of oscillating pressure. Without sound, the pressure in the horn would be one atmosphere. With sound, the pressure in the air oscillates, sometimes above atmospheric pressure, sometimes below. When I play concert A, these oscillations occur 440 times a second (different on a natural horn played at “authentic” pitch.)
I buzz my lips in the mouthpiece. The resulting sound travels down the horn and reaches the bell. At the bell, the pressure wave inverts (that is, high pressures are converted to low pressures, and vice versa) and reflects back up the horn toward the mouthpiece. (Only 1% of the sound actually leaves the bells and goes into the room.)
Notice that I didn’t explain why the pressure inverts. But let me point out that if there were a wall at the end of the horn (you can simulate this by closing the bell with your hand) then the reflected pressure wave would not invert.
(Let me know if you crave a detailed explanation of the inverting/noninverting of the reflected waves.)
Imagine that you are a tiny insect living inside the horn. (There may be plentiful green goo to dine on.) You will be in the presence of an outgoing and a returning sound wave. At certain locations, the high pressure regions of an outgoing wave exactly line up with low pressure regions of the returning wave. In these locations, the two waves cancel, and the insect will hear little sound. These locations are called pressure nodes. In other locations, the high pressure regions of the outgoing and returning waves will line up, as will the low pressure regions. In these regions, the two waves reinforce, making the sound louder; these spots are called anti-nodes.
When you play a note on your horn, there is a standing wave inside. As the insect walks from the mouthpiece to the bell, it will notice a succession of nodes and antinodes.
Now suppose that there is a tiny leak in the side of the horn. This makes it more difficult for pressure to oscillate there: if the pressure rises above one atmosphere, the air rushes out the hole. And if the pressure falls below one atmosphere, the air rushes in from outside the hole.
Here is the result. Suppose you have a standing wave in the horn, and you open a hole in the side. If the standing wave has a pressure node where the hole is, the hole will have no effect on the pitch of the note. If the standing wave has a pressure node near where the hole is, then opening the hole causes the node to move toward the hole, changing the pitch of the note.
(I have a trumpet on which I demonstrate this effect. If I open the spit valve, the note G is unaltered. This means the standing wave for G has a node at the location of the hole. Meanwhile, the note A flat gets flatter, and the note F sharp gets sharper. )
Suppose, instead of a hole, you have a tiny dent. Then the tendency will be for pressure nodes to move away from the dent. And once again, the effect will be different for different notes.
My guess, therefore, is to look for some imperfection in the tubing of the crook that is causing the mischief. Since the other crooks behave acceptably, I suspect either a small obstruction (a dent, blob of solder, or a joint between tubing of different diameters) or a small leak. But it’s easy enough to test a crook for a leak.
