PHY2464 - The Physical Basis of Music
PHY
-2464
PHY-2464
Physical Basis of Music
Presentation
Presentation 17
17
Brass
Brass Instruments
Instruments
Adapted
Adapted from
from Sam
Sam Matteson’s
Matteson’s
Unit
Unit 33 Session
Session 29
29
Sam
Sam Trickey
Trickey
Mar.
Mar. 13,
13, 2005
2005
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Pres. 17 Brass Instruments
Brass instruments:
• Characterized by “buzzing” the lips in a mouth piece
• KEY FACT –
Pipe is closed at mouthpiece end to an excellent
approximation
•There are valved and valveless brass instruments
•There are “brasses” made with little or no metal.
PHY2464 - The Physical Basis of Music
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Pres. 17 Brass Instruments
Brass Instruments of the Orchestra
Euphonium
Piccolo Trumpet
Trumpet
Trombone
French Horn
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Pres. 17 Brass Instruments
Brass Instruments
•
The lips produce a pulsation in the pressure
admitted to the pipe. The pressure standing
wave feeds back to control oscillations of the
player’s lips.
LipLip-valve
Standing wave frequencies
pulsations
Feedback
f1 f2 f3 f4
♩♪♫
~
~
fn
PHY2464 - The Physical Basis of Music
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Pres. 17 Brass Instruments
The Origins of Brass:
Shofar
Ocleidex Sackbut
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Serpent
Pres. 17 Brass Instruments
The Lip Valve
Brass instruments are played by the player’
player’s lips.
Breath pressure, muscle tension, and pressure feedback
from the pipe determine the frequency of the opening and
closing of the lips.
Louis Armstrong – trumpet
(1901(1901-1971)
PHY2464 - The Physical Basis of Music
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Pres. 17 Brass Instruments
Lip Valve
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Embouchure
Pres. 17 Brass Instruments
Lip Valve
•
The lips of the player act as a valve that admits
pressure pulses into the pipe.
•
The frequency is determined by the breath air
pressure, the lip tension and the resonances of
the pipe.
PHY2464 - The Physical Basis of Music
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Pres. 17 Brass Instruments
Brass Instruments
are stopped pipes.
•
The player’
player’s lips
produce a displacement
node (pressure antinode)
antinode)
at the mouthpiece.
•
A displacement antianti-node
(pressure node) exists at
the bell.
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Winton Marsalis
Trumpet
Pres. 17 Brass Instruments
The elements of a valveless brass instrument are
illustrated by the Hosaphone™
http://roth-music.com/hosaphone
PHY2464 - The Physical Basis of Music
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Pres. 17 Brass Instruments
The Mouthpiece
Back Bore
Cup
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Pres. 17 Brass Instruments
The Mouthpiece
The cup volume and
the diameter of the
constriction leading to
the back bore are more
important than the
shape of the cavity.
Cup Volume
Diameter
PHY2464 - The Physical Basis of Music
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Pres. 17 Brass Instruments
Resonance for Combination Pipes
The Brass mouthpiece
lowers the high
frequency resonances.
f
Cone
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Cone with
mouthpiece
Pres. 17 Brass Instruments
The pitch is changed by pipe length and excitation
of resonances.
By means of slides
and valves the
length is changed.
PHY2464 - The Physical Basis of Music
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Pres. 17 Brass Instruments
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Pres. 17 Brass Instruments
Horns can be played by
exciting the resonances only.
The “Natural Horns”
No valves (a coiled
hosaphone™
hosaphone™)
PHY2464 - The Physical Basis of Music
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Pres. 17 Brass Instruments
Resonance for Combination Pipes
f
Pedal Tone
Cone/
Cylinder
%
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0/100%
20/80%
25/75%
40/60%
50/50%
100/0%
Pres. 17 Brass Instruments
Recall Key FACT - For a stopped conical pipe
fn ≈ n v / 2(L′ + c)
if c << λ
L′ = L + 0.6 r
L′
d=2r
c
0.6 r
PHY2464 - The Physical Basis of Music
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Pres. 17 Brass Instruments
Resonances for Combination Bores in
Brass Instruments
Key FACT: A 50% cylindrical - 50% conical
bore has a nearly harmonic series.
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Pres. 17 Brass Instruments
Cylindrical-Conical Instruments
Cone
French
Horn
Cornet
Trombone
Cylinder
PHY2464 - The Physical Basis of Music
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Pres. 17 Brass Instruments
Trumpet-like Instruments
Various instruments
have different lengths
of cylindrical and of
conical pipe.
Flü
Flügelhorn
Cornet
Trumpet
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Pres. 17 Brass Instruments
The Bell
a = ao exp(m x)+ b
“m” is called
the “flare constant.”
Larger m means more
rapid flare.
Exponential Horn
x
PHY2464 - The Physical Basis of Music
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Pres. 17 Brass Instruments
The Bell
Bessel Horns
a
a = ao e-(εx) +b
x
Called “Bessel Horns”
because the standing wave
follows a Bessel Function.
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Pres. 17 Brass Instruments
Summary
• Brass instruments are stopped pipes
• The pipe bore is a combination of cylindrical and
conical or flared, designed to give resonances
that are harmonic.
• Brass instruments are excited by lip-valves.
• The player’s lips are a soft reed.
• The pitch is determined by feedback from the
resonances of the pipe.
• The pitch is changed by exciting various
overtones and by changing the length of the pipe.