PowerPoint Presentation

Musical Instruments

WindInstruments

May 29. 2012

Wind Instruments

A.Flue Pipes

B.Flutes

C.Reeds

D.References

A. Flue Pipes

1)Vortex Oscillation

2)Open-End Pipes

3)Closed-End Pipes

1. Von Karman vortex street

Stream of air oscillates fromone side of the sharpedge to the other

2. Open Pipes

•Pressure node at both ends

•Displacement antinode at both ends

•Fundamental wavelength is 2x Length

•A two foot pipe approximately hits “middle C” (C4)

•All harmonics are present (but higher harmonics areexcited only when the air flow is big)

2b. Open Pipe Harmonics

•All harmonics possible(both even and odd)

3. Closed Pipes

•Pressure antinode at closed end, node at mouth

•Displacement node at closed end, antinode at mouth

•Fundamental wavelength is 4x Length

•A one foot pipe approximately hits “middle C” (C4)

•Only odd harmonics present!

3b. Closed Pipe Harmonics

•Only ODD harmonicspresent (n=1, 3, 5, …)

Open pipe

Closed pipe

B. Flutes

1.The Recorder

2.The Flute

1a. Recorder

•opening holes effectively makes the cylinder shorter(moves antinode up).

•Plays the “diatonic” scale

1b. Recorder Resonances

A very highnote can beplayed byopening a holemidway,forcing apressure node,hence excitinga higherharmonic(“upperregister” note)

2a. Flute

•Again, 2 foot open pipe, fundamental is C4 (middle C)

•Has extra levers to play sharps/flats (full set of 12 tone holes),allowing one to play all 12 semitones from C4 to C5.

•“upper register” to C4 to C5, you open a hole near center toforce a pressure node, hence play the n=2 harmonic (i.e. playnotes an octave higher with nearly same fingering)

2b. Upper Registers

•To play even higher, you open up other holes to force the n=3harmonic

•Another combination forces the n=4 harmonic

2c. Flute Fingering Charts

C. Reeds

1.Reed Acoustics

2.Harmonics (Clarinet)

3.Conical Bores

history

Simple reed instrumentswere invented by theEgyptians

1. Reed Pipe Acoustics

•Reed open and closes, sending pulses of pressure waves.Hence mouthpiece is a pressure antinode

•Open end is a pressure node

•Hence behaves like a closed pipe

•Fundamental wavelength is 4x Length

•Typical Clarinet, fundamental is D3

1b. Closed Pipe Harmonics

•Only odd n harmonics

•N=1 =4L

•N=3 =4L/3

•N=5 =4L/6

1c. Reed Pipe Timbre

•Cylindrical bore (Clarinet) only allows odd harmonics.

•Waveform is approximately “square” (as reedopens/closes its like a binary “on/off” pulse)

•Square waves are made of only odd harmonics.

2. Reed Pipe Fingerings

•Example: let fundamental (lower register) be a C4

•Next resonance (“middle register”) is 3rd harmonic, i.e. octaveplus P5, so G5

•Next resonance is 5th harmonic, i.e. 2 octaves plus a M3, so E6

Clarinet Fingerings

Clarinet Fingering: Low Register

•Like recorder, opening holes effectively makes thecylinder shorter (moves antinode up).

Clarinet Fingering: Upper Register

•Opening the register key makes an antinode that reinforces the 3rdharmonic, and suppresses the fundamental (so instead of playing aC1, you’d get a G2 which is a twelfth above the fundamental).