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PHY2464 - The Physical Basis of Music

PHY-2464Physical Basis of Music

PHYPHY--24642464Physical Basis of MusicPhysical Basis of Music

Presentation 17Brass Instruments

Adapted from Sam Matteson’s Unit 3 Session 29

Sam TrickeyMar. 13, 2005

Presentation 17Presentation 17Brass InstrumentsBrass Instruments

Adapted from Sam Matteson’s Unit 3 Session 29

Sam TrickeyMar. 13, 2005

PHYPHY--2464 2464 Pres. 17 Brass InstrumentsPres. 17 Brass Instruments

Brass instruments: Brass instruments: •• Characterized by “buzzing” the lips in a mouth pieceCharacterized by “buzzing” the lips in a mouth piece

•• KEY FACT KEY FACT ––Pipe is Pipe is closedclosed atat mouthpiecemouthpiece endend to an excellent to an excellent approximationapproximation

••There are There are valvedvalved and and valvelessvalveless brass instrumentsbrass instruments••There are “brasses” made with little or no metal.There are “brasses” made with little or no metal.



Brass Instruments of the OrchestraBrass Instruments of the Orchestra

French HornFrench Horn

TromboneTromboneTrumpetTrumpet

Piccolo TrumpetPiccolo Trumpet

EuphoniumEuphonium


Brass InstrumentsBrass Instruments•• The lips produce a pulsation in the The lips produce a pulsation in the pressurepressure

admitted to the pipe. The pressure standing admitted to the pipe. The pressure standing wave feeds back to control oscillations of the wave feeds back to control oscillations of the playerplayer’’s lips.s lips.

♩♩ ♪♪ ♫♫ ff1 1 ff2 2 ff3 3 ff44fn

~~ ~~

LipLip--valve valve pulsationspulsations

Standing wave frequenciesStanding wave frequencies

FeedbackFeedback



The Origins of Brass:The Origins of Brass:

ShofarShofar

SerpentSerpentSackbutSackbutOcleidexOcleidex


The Lip ValveThe Lip ValveBrass instruments are played by the playerBrass instruments are played by the player’’s lips. s lips.

Breath pressure, muscle tension, and pressure feedback Breath pressure, muscle tension, and pressure feedback from the pipe determine the frequency of the opening and from the pipe determine the frequency of the opening and closing of the lips.closing of the lips.

Louis Armstrong Louis Armstrong –– trumpet trumpet (1901(1901--1971)1971)



Lip ValveLip ValveEmbouchureEmbouchure


Lip ValveLip Valve

•• The lips of the player act as a valve that admits The lips of the player act as a valve that admits pressure pulses into the pipe.pressure pulses into the pipe.

•• The frequency is determined by the breath air The frequency is determined by the breath air pressure, the lip tension and the resonances of pressure, the lip tension and the resonances of the pipe.the pipe.



Brass Instruments Brass Instruments are stopped pipes.are stopped pipes.

•• The playerThe player’’s lips s lips produce a displacement produce a displacement node (pressure node (pressure antinodeantinode) ) at the mouthpiece.at the mouthpiece.

•• A displacement antiA displacement anti--node node (pressure node) exists at (pressure node) exists at the bell.the bell.

Winton Marsalis Winton Marsalis TrumpetTrumpet


The elements of a The elements of a valvelessvalveless brass instrument are brass instrument are illustrated by the illustrated by the HosaphoneHosaphone™™

http://http://rothroth--music.com/music.com/hosaphonehosaphone



The MouthpieceThe MouthpieceCupCup Back BoreBack Bore


The MouthpieceThe Mouthpiece

The The cup volumecup volume and and the the diameter diameter of the of the constriction leading to constriction leading to the back bore are more the back bore are more important than the important than the shape of the cavity.shape of the cavity.

Cup VolumeCup Volume

DiameterDiameter



Resonance for Combination PipesResonance for Combination Pipes

ConeCone Cone with Cone with mouthpiecemouthpiece

ff

The Brass mouthpiece The Brass mouthpiece lowers the high lowers the high frequency resonances.frequency resonances.


The pitch is changed by pipe length and excitation The pitch is changed by pipe length and excitation of resonances.of resonances.

By means of slides By means of slides and valves the and valves the length is changed.length is changed.




Horns can be played by Horns can be played by exciting the exciting the resonances onlyresonances only..

The “Natural Horns”The “Natural Horns”

No valves (a coiled No valves (a coiled hosaphonehosaphone™™))



Resonance for Combination PipesResonance for Combination Pipes

0/100%0/100% 20/80%20/80% 25/75%25/75% 50/50%50/50%40/60%40/60% 100/0%100/0%

ff

Pedal TonePedal Tone

Cone/ Cylinder %


Recall Key FACT Recall Key FACT -- For a stopped conical pipeFor a stopped conical pipe

ffnn ≈≈ nn v / 2(Lv / 2(L′′ + c)+ c)

if c << if c << λλ

LL′′ = L + 0.6 r= L + 0.6 r

cc

LL′′

0.6 r0.6 r

d=2rd=2r



Resonances for Combination Bores in Resonances for Combination Bores in Brass InstrumentsBrass Instruments

Key FACT: A 50% cylindrical Key FACT: A 50% cylindrical -- 50% conical 50% conical bore has a nearly harmonic series.bore has a nearly harmonic series.


CylindricalCylindrical--Conical InstrumentsConical Instruments

French French HornHorn TromboneTrombone

CornetCornet

ConeCone

CylinderCylinder



TrumpetTrumpet--like Instrumentslike Instruments

CornetCornet

TrumpetTrumpet

FlFlüügelhorngelhorn

Various instruments Various instruments have different lengths have different lengths of cylindrical and of of cylindrical and of conical pipe.conical pipe.


The BellThe Bell

a = a = aaoo exp(m x)+ bexp(m x)+ b

“m” is called “m” is called the “flare constant.”the “flare constant.”

Larger m means more Larger m means more rapid flare.rapid flare.

xx

Exponential HornExponential Horn



The BellThe BellBessel HornsBessel Horns

xx

aa

a = a = aaoo ee--((εεxx)) +b+b

Called “Bessel Horns” Called “Bessel Horns” because the standing wave because the standing wave follows a Bessel Function.follows a Bessel Function.


SummarySummary•• Brass instruments are stopped pipesBrass instruments are stopped pipes•• The pipe bore is a combination of cylindrical and The pipe bore is a combination of cylindrical and

conical or flared, designed to give resonances conical or flared, designed to give resonances that are harmonic.that are harmonic.

•• Brass instruments are excited by lipBrass instruments are excited by lip--valves. valves. •• The playerThe player’’s lips are a soft reed.s lips are a soft reed.•• The pitch is determined by feedback from the The pitch is determined by feedback from the

resonances of the pipe.resonances of the pipe.•• The pitch is changed by exciting various The pitch is changed by exciting various

overtones and by changing the length of the pipe.overtones and by changing the length of the pipe.

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