Musical Instruments Wind Instruments May 28 2013 1

Musical Instruments Wind Instruments May 28. 2013 1

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

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

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

2. Open Pipes • • • Pressure node at both ends Displacement antinode at both ends Fundamental wavelength is 2 x Length A two foot pipe approximately hits “middle C” (C 4) All harmonics are present (but higher harmonics are excited only when the air flow is big) 5

6 2 b. Open Pipe Harmonics • All harmonics possible (both even and odd) C 1 C 2 G 2 C 3

3. Closed Pipes • • • Pressure antinode at closed end, node at mouth Displacement node at closed end, antinode at mouth Fundamental wavelength is 4 x Length A one foot pipe approximately hits “middle C” (C 4) Only odd harmonics present! 7

8 3 b. Closed Pipe Harmonics • Only ODD harmonics present (n=1, 3, 5, …) Open pipe C 1 C 2 G 2 C 3 Closed pipe

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

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

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

2 a. Flute 12 • Again, 2 foot open pipe, fundamental is C 4 (middle C) • Has extra levers to play sharps/flats (full set of 12 tone holes), allowing one to play all 12 semitones from C 4 to C 5. E 4 • “upper register” to C 4 to C 5, 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) D 5

2 b. Upper Registers 13 • To play even higher, you open up other holes to force the n=3 harmonic D 6 • Another combination forces the n=4 harmonic G 6

2 c. 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 4 x Length Typical Clarinet, fundamental is D 3 17

18 1 b. Closed Pipe Harmonics • Only odd n harmonics • N=1 =4 L C 4 • N=3 =4 L/3 G 5 • N=5 =4 L/6 E 6

1 c. 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 P 5, so G 5 • Next resonance is 5 th harmonic, i. e. 2 octaves plus a M 3, 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 C 1, you’d get a G 2 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 C 1, you would get the E 3) 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

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

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

misc • x 28

29 References • • • http: //www. santafevisions. com/csf/html/lectures/016_instruments_III. htm http: //en. wikipedia. org/wiki/Acoustic_resonance http: //www. phys. unsw. edu. au/jw/pipes. html http: //www. mozart. co. uk/information/articles/woodwindacoustics. htm http: //www. flute-a-bec. com/acoustiquegb. html http: //www. 8 notes. com/flute/fingering/ http: //www. yamaha. co. jp/english/product/winds/down/fingering/index. htm http: //www. phys. unsw. edu. au/jw/saxacoustics. html http: //www. squidoo. com/woodwindfamilyunit