Physics 1251 The Science and Technology of Musical Sound Unit 3 Session 29 MWF Brass Instruments Unit 3 Session 29 MWF Brass Instruments

Physics 1251Physics 1251The Science and The Science and

Technology of Musical Technology of Musical SoundSound

Physics 1251Physics 1251The Science and The Science and

Technology of Musical Technology of Musical SoundSound

Unit 3Unit 3

Session 29 MWFSession 29 MWF

Brass Instruments Brass Instruments

Unit 3Unit 3

Session 29 MWFSession 29 MWF

Brass Instruments Brass Instruments

Physics 1251Physics 1251 Unit 3 Session 29Unit 3 Session 29Brass InstrumentsBrass Instruments

What pitch (frequency) does a What pitch (frequency) does a clarinet play if the length from the clarinet play if the length from the reed to a hole is 19.5 cm (including reed to a hole is 19.5 cm (including end corrections, i.e. Lend corrections, i.e. L′= 0.195 m′= 0.195 m) at ) at 20 C? 20 C?

f = v/4Lf = v/4L′ for a stopped cylinder′ for a stopped cylinder; ;

v =343 m/s v =343 m/s

f = 343/(4 f = 343/(4 ‧ ‧ 0.195) = 440 Hz. 0.195) = 440 Hz.


11′ Lecture:′ Lecture:

• Brass instruments are stopped pipes, Brass instruments are stopped pipes, that have a bore that is a combination of that have a bore that is a combination of cylindrical and conical or flared.cylindrical and conical or flared.

• Brass are excited by lip-valves. Brass are excited by lip-valves.

• The pitch is determined by feedback The pitch is determined by feedback from the resonances of the pipe.from the 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 overtones and by changing the length of the pipe.the pipe.


Brass Instruments Brass Instruments of the Orchestraof the Orchestra

French HornFrench Horn

TromboneTromboneTrumpetTrumpet

Piccolo TrumpetPiccolo Trumpet

EuphoniumEuphonium


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

pressurepressure admitted to the pipe; the admitted to the pipe; the pressure standing wave feeds back to pressure standing wave feeds back to control the oscillations of the plays lips.control the oscillations of the plays lips.

♩ ♪ ♫♩ ♪ ♫ ff1 1 f f2 2 f f3 3 f f44

fn

~~ ~~

Lip-Lip-valve valve pulsatiopulsationsns

Standing wave frequenciesStanding wave frequencies

FeedbacFeedbackk


The Origins of Brass:The Origins of Brass:

ShofarShofar

SerpentSerpentSackbutSackbutOcleidexOcleidex


The Lip ValveThe Lip Valve80/2080/20Brass instruments are played by the Brass instruments are played by the

player’s lips. player’s lips.

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

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


Lip Valve Lip Valve EmbouchureEmbouchure


Lip ValveLip Valve

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

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


80/2080/20Brass Instruments Brass Instruments are stopped pipes.are stopped pipes.

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

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

Winton Marsalis Winton Marsalis Trumpet Trumpet


The MouthpieceThe MouthpieceCupCup Back Back

BoreBore


The MouthpieceThe Mouthpiece

80/2080/20The The Cup VolumeCup Volume and the and the diameter diameter of of the constriction the constriction leading to the back leading to the back bore are more bore are more important than the important than the shape of the cavity.shape of the cavity.

Cup Cup VolumeVolume

DiameterDiameter


Resonance for Combination PipesResonance for Combination Pipes

ConeCone Cone with Cone with mouthpiecemouthpiece

ff

80/2080/20The Brass The Brass mouthpiece lowers mouthpiece lowers the high frequency the high frequency resonances.resonances.


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

slides and slides and valves the valves the length is length is changed.changed.



Horns can be played Horns can be played by excitby exciting the ing the resonances only.resonances only.

The “Natural Horns”The “Natural Horns”

No valvesNo valves


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 Pedal ToneTone

Cone/ Cylinder %


Resonances for Combination Bores Resonances for Combination Bores in Brass in Brass InstrumentsInstruments

80/2080/20A 50% cylindrical A 50% cylindrical ‒ 50% conical bore ‒ 50% conical bore has a nearly harmonic series.has a nearly harmonic series.


Cylindrical-Conical InstrumentsCylindrical-Conical Instruments

French French HornHorn TrombonTrombon

ee

CornetCornet

ConeCone

CylinderCylinder


Trumpet-like InstrumentsTrumpet-like Instruments

CornetCornet

TrumpeTrumpett

Flugel HornFlugel Horn

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


The BellThe Bell

a = aa = aoo exp(m x)+ exp(m x)+ bb

80/2080/20m is called m is called the “flare the “flare constant.”constant.”

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

xx

Exponential HornExponential Horn


The BellThe BellBessel HornsBessel Horns

xx

aa

a = aa = aoo e e-(-(εεx)x) +b +b

80/80/2020Called “Bessel Called “Bessel Horns” because the Horns” because the standing wave follows a standing wave follows a Bessel Function.Bessel Function.


Summary:Summary:• Brass Instruments are stopped Brass Instruments are stopped

pipes.pipes.

• The pipe bore is designed to give The pipe bore is designed to give resonances that are harmonic.resonances that are harmonic.

• The pedal tone (the lowest note) is The pedal tone (the lowest note) is not harmonic.not harmonic.

• The player’s lips are a soft reed.The player’s lips are a soft reed.

• The pitch is changed by changing The pitch is changed by changing the length and exciting resonances.the length and exciting resonances.

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Physics 1251 The Science and Technology of Musical Sound Unit 3 Session 29 MWF Brass Instruments Unit 3 Session 29 MWF Brass Instruments