1. Acoustics of Brass Instruments
Jonathan Julius

2. Introduction Already Covered What this presentation will cover
Resonance of a closed pipe
Bell Effect
Cylindrical Vs Conical
What this presentation will cover
Mouth Piece Effect
Valves Versus Slides

3. Anatomy of a Brass Mouthpiece
Already covered woodwind mouthpieces in class, but the brass mouth piece doesn’t have the moving reed or create the open pipe of the flute.
Without a mouthpiece the bore of the pipe inhibits the musicians ability to produce a quality sound with ease. –demo it with trombone- In addition to producing a bad sound, the exposure to the sharp sides would tear up the mouth of the player.
A brass mouthpiece consists of a cup, throat and backbore. The rim is generally cushioned with additional material for player comfort.

4. Mouth Piece Resonance Helmholtz Resonator
Each mouth piece has own resonant frequency
Lowers Frequency Above Resonance
Creates a range of frequencies instrument can play well
Deeper Cup -> Lower Resonance -> Darker Sound
Mouth Piece Effect:
The cup creates a volume of air that acts as a compliance, the throat an inertance, and the backbore expands the bore diameter to that of the instrument. These components create an inductor, capacitor, and resistor system that creates a resonance. Each mouthpiece has its own unique resonance. This effectively diminishes the effect of higher frequencies within the timbre of the instrument creating a darker tone. It essentially lowers the higher harmonics bringing them more into a classically oriented series. When playing within the resonance, it is done so with ease, but when the player attempts to play higher it is more difficult to do so. This, combined with the effect of the bell, is what gives brass instruments its characteristic sound.

5. Overall Effect
First Graph: Impedance for frequencies for a cylindrical pipe the length of a trumpet
Second Graph: Added effect of a mouth piece
Third Graph: Added effect of Bell. Note the addition of even harmonics.
Note: The cylindrical pipe
Image: The Acoustics of Brass Musical Instruments, Moore.

6. Different Factors and Effects
From Yamaha’s Guide of Brass Mouthpieces:
Cup Depth
More depth = Darker tone, harder to play high range
Cup Shape
U v V shape, V = Darker tone, hard to play high range
Rim Thickness
Wide Rim easier for high notes
Throat
Long narrow throat = Bright Tone
Backbore
Narrower backbore = Bright Tone
Cup Width- Smaller cup width allows smaller portion of lips to vibrate increasing ease of hitting higher notes but the total volume of sound is reduced.
Cup Depth- A deeper cup decreases the resonance frequency of the mouth piece. By doing so, with the mechanisms we’ve discussed, it produces a darker tone, but makes it harder to produce higher notes.
Cup Shape: The cup can taper in two different ways as the metal gets deeper. In broad terms the two shapes are notated as u or v shapes. U shapes increase the resonance frequency, while V shapes decrease. This effect isn’t as pronounced on cylindrical brass, but most commonly effect French Horn Mouth pieces.
Rim Thickness: A thicker rim creates more surface area in contact with your lips. This makes it easier to reach higher notes and the extra cushioning grants more endurance. However the more surface area your lips touch the harder it is to shift frequencies and therefore there is a lose in tonal flexibility.
Throat + Backbore: This section narrows and focuses the air you produce creating resistance. The more resistance, the more brilliant the tone and harder to play high, i.e. increases the resonance.

7. The convenience of valves
Condenses Space
No need to manually shrink massive amounts of tubing.
Better Legato Sounded
Slides lead to “Drunken Slurs”
French horn and tuba consist of 20 feet and 18 feet of tubing respectively. The tuba plays at a low range, but the French Horn ranges from the bass clef to the treble clef. An attempt to manually adjust the length of tubing to achieve that range would be near impossible, therefore valves allow for French horns to function with ease.

8. Out of Tune Valves On Trumpet
First Valve Lowers 1 Semitone (Adds 8.3cm of tubing)
Second Valve Lowers 2 Semitones (Adds 17.2cm of tubing)
Third Valve Lowers 4 Semitones
In order to lower 3 Semitones needs 26.5 cm of tubing
First + Second Valve adds 25.5 cm
Valve Instruments have tuning pipes for different valves
To lower a trumpet 1 semitone you have to increase the length by 6%. For two that increase is 12.25%. So when you press the first valve, if you want to lower the current state of the trumpet by two semitones of the length of the trumpet plus the 6% added on by the first valve, the second valve is only tuned to increase the base length by 12.25%

9. Conclusion Mouth Pieces lower high frequencies in timber
At trade off of ability to play higher frequencies
Valves are more convenient and allow better shaping of sound
Slides are more in tune and allow better shaping of pitch
Questions?
Possible questions:
Materials of mouth pieces from : “Silver mouthpieces produce far-carrying, dark, and heavy sound, but it does not harmonically resonate as much as brass. Stainless mouthpieces produce very brilliant sound and would be suit lead performances. Titanium produces a solid and bright tone and does not occur an allergic reaction, however, the sound actually becomes very light. Plastic mouthpieces are cheap and have a lot of colors. It would be fun to collect them.”

10. Sources http://newt.phys.unsw.edu.au/jw/brassacoustics.html#mouthpiece
University of New South Wales
Moore’s “The Acoustics of Brass Musical Instruments”