Editor's note: Published in The Instrumentalist, April 1977. I was not able to scan or accurately reproduce the diagrams to which reference is made herein because of the condition of the source material, though the descriptions are clear enough for one to understand the points, I think. Comments in square brackets [ ] are my attempts to describe the missing diagram or photograph to assist in comprehension.
The designer of instruments and mouthpiece must have a thorough knowledge of physics, but it is also helpful for the player and teacher to understand some of the basic principles.
In order to produce a sound on the trumpet (or any other brass instrument), air (1) is expelled under pressure through the lips, (2) further compressed in the cup of the mouthpiece, until it reaches the throat (3) of the mouthpiece, where it sets up a pattern in the air already in the instrument.
It is not necessary for the air to move through the instrument. I have demonstrated this at clinics by having a tuba player blow smoke into his instrument. He can play for over a minute before any smoke begins to trickle out of the bell. The pattern set up by the player in the air is more like what happens when you drop a rock in the lake--the energy impulse travels along lifting and depressing the water (making slight waves, but does not move the water to another area. The pattern can be shown as a [wave like] graph, with P = maximum pressure (like the swell of the wave in the water), and R = rarefaction, i.e. minimum pressure (like the valley of the wave).
Remember that this is a graph of pressure, not a picture of air movement. The pattern of air set up in the instruments concludes with a rarefaction just beyond the bell where a standing wave is formed, reflecting back through the instrument [creating a reverse wave pattern where the pressure, P and R, are on opposite sides].
These pressure rarefaction points are called nodes (places of "no movement"--as the air pulsates against the pipe there is a momentary pause in the motion).
The nodal pattern is different for different notes, the number of nodes increasing with higher pitches.
Tubing is required to contain the vibrating air only at the pressure points. So it would be possible to play on a pipe full of holes--as long as those holes did not come at the pressure points...and we only had to produce one pitch.
I have often given demonstrations of this phenomenon, using a C trumpet and playing three notes, G [treble clef, in the staff], C [third space] and E [fourth space]. When the G is played, the nodal pattern is such that a pressure point falls exactly at the place in the tube where the water key hole is located. When this key is opened, the hole in the pipe stops the tone. This fact is no surprise to anyone who has ever lost the cork on the water key. But when the C is played, the nodal pattern is different, and water key hole in the tubing comes at the taper-off of the pressure point. This time when the water key is opened, it raises the pitch of the note a whole step (you could use it as a trill key!).
When E is played, the pattern is once again different. This time there is absolutely no disturbance to the tone. In fact, in that area 5/8 inch of tubing could be cut out of the instrument and you could play E's all day.
Once the nodes of various pitches are located, their placement--and therefore the pitch--can be changed by altering the rate of taper in the tube. It only takes .001 to .002 inch, but it must be done exactly at the pressure point of the note you want to affect. And you must find the single pressure point in order to accomplish this. Altering the tubing at a multiple pressure point will adversely affect other notes with the same pressure point.
Practical Applications of Physical Principles
If the pitch of notes can be altered by changing the taper of pipe only .001 to .002 of an inch, imagine what a little dirt can do. And then consider what effect years of accumulation will have!
I remember one of my very fine students was having terrible troubles getting a sound. One day when I left the student for a few minutes he picked up an aluminum mouthpiece I had been experimenting with and had left on the desk. When I cam back he asked if I would sell him the mouthpiece. He said, " I can play so beautifully on this." I picked up his mouthpiece and found it so full of dirt that I could hardly see a pinhole through it. A mouthpiece cleaning was all he needed--and I've never let him forget it!
I recommend oiling the valves by putting the oil into the leadpipe (rather than directly on the valves) and allowing it to work its way through the instrument. Because the inside is coated with oil, erosion of the metal is stopped and food particles are easy to flush out once a week. Just run warm water through and every particle of dirt will come out easily. Also the valves stay lubricated all day because the oil continues to run down into that area. I see many instruments with tiny holes starting to appear in the mouthpipe--the first sign of erosion. Anyone who uses this method of oiling can keep his instrument for a hundred years without having it wear out.
The cleaning aspect is only one rather obvious practical application of a physical principle. There are many others. For example, braces on trumpets should not be located at pressure points (remember the water key hole), where they can deaden the vibration of the tubing that is then in contact with the air.
Also, anything that can cause turbulence (interruption of the nodal pattern) will adversely affect the tone. One common turbulence trouble spot is the area where the mouthpiece fits into m receiver. Sometimes there is a gap, or the inside diameters of the mouthpiece backbore and the leader pipe are different. This crucial areas should like like this: [trumpet mouthpiece backbore and leadpipe seamlessly connect without gap or without differences in wall width so that the opening of the mouthpiece and the receiver are identical].
Leaks also disturb the nodal pattern and affect intonation. Valves can be kept airtight by holding the tolerance on the pistons under .001 (.0005 inch on each side of the piston). This permits free movement of the valves and still gives good acoustical qualities. But regardless of the condition of the instrument, some players seem to be able to adjust and play beautifully. For example, when Rafael Mendez became associated with Olds, he asked them to build a new instrument that would be equal to the old Besson he had played for years. They tried everything they knew to please him, but they could not succeed. Finally one of the workmen took the valves out of the Besson, measured them, and found a surprisingly large clearance of over .008 Inch (the result of years of wear). He then made an instrument with similarly loose valves and Mendez was thrilled with the result. He was again performing on a totally inadequate instrument, but he was happy. He had overcome the problems caused by the leaky valves throughout years of practice (nobody ever practiced harder than Mendez), and for him it was just right.
As physical principles are applied to the manufacture and maintenance of instruments, we gradually learn more and produce better equipment. But it continues to amaze me that people can and do adjust to almost anything. It's true with mouthpieces, too. I have some that were used by the greatest players of the past--Liberati, Arban--and they are horrible things, so far from being physically correct. Yet these people played beautifully on them.
Three major parts of the mouthpiece affect its sound and performance qualities: rim, cup and throat/backbore. Within each major area there are sub-categories such as width, size, shape, etc. All of these elements react with each other to affect the qualities of the mouthpiece here.
Only the most important variables are included here. In each case certain tendencies are discussed. For example, as a rim is made wider, it becomes increasingly more comfortable; as it is made narrower it provides increasingly more flexibility. Other elements are treated similarly. Obviously, there are many different measurements usable for every element, and literally millions of combinations are possible.
Width: wider = comfort, narrower = flexibility
Distance between the high points on the rim can vary according to the shape of the contour [and] affects how large the mouthpiece feels on the lips.
The edge ("bite") [is the] point at which convex rim blends into the concave cup and affects the precision of the attack.
Contour: flatter = comfort, but the constant contact holds lips in a fixed position, and thus reduces flexibility; rounder = most flexible, varying contact according to the amount of pressure, but tires the player sooner--useful for those who play with pressure or for beginners (who need to feel the action of the lips).
Depth (Volume): deeper = better lower tones, richer darker sound, accommodates thicker lips, allows more lip to vibrate (producing more full and resonant tone) and "helps" (forces?) player to develop endurance and lip control; shallower = brighter tone, easier to produce high notes (use with higher instruments, e.g. when doubling B flat and D trumpets use mouthpiece for D that is .025 inch more shallow than B flat, with other dimensions the same."
Shape: flatter = improved attack, coarser tone; steeper = better quality of sound, but at extreme (French horn shape) it is colorless on the trumpet.
Double Cup: shallower cup, for support in upper register; wider cup, for full tone.
The tube leading from the cup to the end of the mouthpiece has two areas blended together. The throat is straight [parallel]. The backbore begins when the tube begins to flare. The amount of taper depends on the size and length of the throat, as well as the diameter of the leader pipe (which the mouthpiece must match).
Throat size (ranges from large to small, drill sizes of 18 to 30); larger = mellow sound; smaller = brilliant sound.
Length (throat length ranges from 1/8 to 3/4 inch): longer throat (shorter backbore) = loss of tonal center, loss of resonance, increase in intonation control, sharp in high register; shorter throat (longer backbore) = harder to control, flat in high register.
Backbore shape: flared = full tone, more difficult to control; straight = thin tone, more easily controlled, blowing resistance increased.
In Marseilles, France they are now working on a 75 foot long trumpet that will produce a "note" at 4 Hz (four vibrations per second). No one can hear 4 Hz of course, but with massive energy input (perhaps 350 times that of a 75 piece orchestra playing at its loudest intensity) the vibrations from this instrument could destroy an entire city the size of Chicago--just like the story of Joshua and the Battle of Jericho, where the walls came a-tumblin' down.
The people who are building this trumpet first discovered the power of highly energized low frequency sounds when they moved into a new laboratory and found that workers were getting stomach aches from ventilators that were putting out 37 Hz. They built a modified version at 17 Hz and had to shut it off instantly because the walls were cracking and everyone was doubling up on the floor.
For those interested in further study of the physics of brass instruments, take a look at these sites:
How Brass Instruments Work, by Scott Whitener
Musical Acoustics (the Trumpet), by Rod Nave, Georgia State University
Physics of the Trumpet
Why Do Sounds Sound the Way They Do? by Pat Gary (former SMU student)
How Brass Instruments are Built: Art, Craft, Perhaps Even Science, by Robert W. Pyle
The Physics of the Didjeridu, by Dr. William Robertson
Introduction to the Acoustics of Brass Instruments, University of New South Wales
Trumpet Acoustics, by Arthur Benade
Essays on Trumpet Physics, by Nick Drozdoff
A Virtual Reconstruction of the Trumpet, by Lamberto Tronchin and Alessandro Cocchi
Trumpet Spectra Analysis, by John T. Lynch
Simulation of Brass Instruments, by Paul Anglmayer
Richard Smith Technical Papers
Bibliographies for yet further research:
Trumpet References (containing many listings for acoustics and physics)
Arthur H. Benade Archive
If you are aware of other sites relevant to the topic, please let me know.
Links checked and updated July 2006.