Guitar Strings and Lips: A VERY Loose Model
Sometimes, in order to sort out a very complex system, we have to use some simpler physical models and extrapolate from them to get a picture of how the more complex system could work.
In playing a trumpet, the vibrating lips are the things driving the trumpet. A trumpet is often referred to as a lip reed instrument by physicists.
In this short blog this week. I'll address how the guitar string model might be used to get feel for how trumpeters play the upper register (an unfortunate obsessions with many of us!). To start lets just consider a string.
There are four things that can impact the frequency at which a string will resonate, and lets just consider the fundamental or first harmonic - the main note. These are:
tension of force stretching the string tight
mass per unit length - just think of the mass
diameter or how wide the string is
If you want to look up the physics and math involved, you'll find that there is a set of differential equations that describe the motion of the string with these parameters. The solutions to those equations give rise to all we need to know. You can look this all up in the various physics/acoustics texts, but for the purpose of the blog all we need are the endpoints. Here they are.
All other variables held constant, frequency is proportional the the SQUARE ROOT of the tension.
All other variables held constant, frequency is proportion to the reciprocal or INVERSE of the SQUARE ROOT of mass.
All other variables held constant, frequency is inversely proportional to the length.
All other variables held constant, frequency is inversely proportional to the diameter of the string.
Let's apply the tension and mass concepts to the lips. We have direct control over these when we play. The other two are somewhat determined by the mouthpiece dimensions.
If we do the math, it is pretty easy to see that tension by itself is not likely the way we are able to play the extreme upper register. Most top flight pros can cover about 6 octaves when they play. Heck, let's even back that down to just 5, for good measure. If we assume the frequency is proportional to the square root of tension, each time we want to go up an octave, we have to quadruple the tension. This can get out of hand very quickly. If we want to go up five octaves, the frequency is multiplied by 2^5, or 32. That isn't so bad, is it? Well, that means we have to increase the tension by 32^2, or 1024! So, if you have about 1/2 pound of force int he lips to produce a double pedal C, you'd have to produce a force of 512 pounds in the lips! So, even though there are a couple of other factors involved and that due to the different shape of the lips from strings, it is HIGHLY unlikely that force alone is the driving factor of the high notes.
In short, it isn't about the TENSION in the lips.
Let's consider the mass. Every thing from the preceding paragraph applies except the inverse process mean we have to REDUCE the vibrating mass by 1/1024, or about .0001. While there are practical physical limitations to just how far we can go, this is a much more workable solution. How? By making the so-called lip aperture smaller.
Now reducing the vibrating mass can probably be managed in different ways, depending on the embouchure employed, many folks tend to think of focusing in the middle of the lips as they go way up into the upper register. If seen it addressed in books (there is a discussion and diagram in the Claude Gordon book) and with many successful trumpeters.
Here are a couple of videos that address this. Listen to Jim Manley talk about how close together (about 39 seconds) his lips are when he plays.
Here is another - Rashawn Ross at Monette. On this one, WATCH what he is doing. It is quite effortless.
Are there other factors involved in playing the extreme upper register other than lower the vibrating mass - making the aperture smaller or getting the lips closer together? Of course! Tongue position, and how you move your air can have an impact. The size of the mouthpiece and how it couples to the lead pipe can have an impact. I have already blogged about those things already. Plow through the archives of my blog, and you ought to find something. I just wanted to address the string analogy a bit as many trumpeters do like to use it. I thought a little more back ground on it might serve to help you make a bit more sense out of it.
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