Musical Instruments Wind Instruments May

Wind Instruments A.Flue Pipes B.Flutes C.Reeds D.References 2

A. Flue Pipes 1)Vortex Oscillation 2)Open-End Pipes 3)Closed-End Pipes 3

1. Von Karman vortex street Stream of air oscillates from one side of the sharp edge to the other 4

2. Open Pipes 5 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 are excited only when the air flow is big)

2b. Open Pipe Harmonics All harmonics possible (both even and odd) 6 C1 C2 G2 C3

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! 7

3b. Closed Pipe Harmonics Only ODD harmonics present (n=1, 3, 5, …) 8 Open pipeClosed pipe C1 C2 G2 C3

B. Flutes 1.The Recorder 2.The Flute 9

1a. Recorder x 10 opening holes effectively makes the cylinder shorter (moves antinode up). Plays the “diatonic” scale

1b. Recorder Resonances 11 A very high note can be played by opening a hole midway, forcing a pressure node, hence exciting a higher harmonic (“upper register” note)

2a. Flute 12 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 to force a pressure node, hence play the n=2 harmonic (i.e. play notes an octave higher with nearly same fingering) E4 D5

2b. Upper Registers 13 To play even higher, you open up other holes to force the n=3 harmonic Another combination forces the n=4 harmonic D6 G6

2c. Flute Fingering Charts 14

C. Reeds 1.Reed Acoustics 2.Harmonics (Clarinet) 3.Conical Bores 15

history Simple reed instruments were invented by the Egyptians 16

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 17

1b. Closed Pipe Harmonics Only odd n harmonics N=1 =4L N=3 =4L/3 N=5 =4L/6 18 C4 G5 E6

1c. Reed Pipe Timbre Cylindrical bore (Clarinet) only allows odd harmonics. Waveform is approximately “square” (as reed opens/closes its like a binary “on/off” pulse) Square waves are made of only odd harmonics. 19

2. Reed Pipe Fingerings Example: let fundamental (lower register) be a C 4 Next resonance (“middle register”) is 3 rd harmonic, i.e. octave plus P5, so G 5 Next resonance is 5 th harmonic, i.e. 2 octaves plus a M3, so E 6 20

Clarinet Fingerings 21

Clarinet Fingering: Low Register Like recorder, opening holes effectively makes the cylinder shorter (moves antinode up). 22

Clarinet Fingering: Upper Register Opening the register key makes an antinode that reinforces the 3 rd harmonic, and suppresses the fundamental (so instead of playing a C1, you’d get a G2 which is a twelfth above the fundamental). 23

Clarinet Fingering: High Notes To get very high notes, opening some other holes forces the 5 th harmonic to dominate! (so instead of playing the fundamental C1, you would get the E3) 24

3. Conical Bore Cylindrical bore (Clarinet) only allows odd harmonics. Saxophone, Oboe have a “conical bore” which allows for all the harmonics, but this is complicated to explain why. Hence upper register of these instruments utilizes the 2 nd harmonic (more similar to fingering for the flute). 25

Sax Fingering 26 Saxophone is a modern instrument, invented 1840 by Adolphe Sax. its mouthpiece is similar to clarinet

3c. Double Reeds Oboes and Bassoons have a “double reed” Both have conical bores 27

misc x 28

References