The Science of SoundDr. Bill Pezzaglia

Labrisone (lip vibrating) Instruments

(aka “Brass”)Updated May 24, 2013

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Outline

A. Natural Horns

B. Slides

C. Valves

D. References

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Brass Ensemble Tiger Rag: http://www.youtube.com/watch?v=04PWhO6wd2A&feature=relmfuBumble Bee: http://www.youtube.com/watch?v=xZO5KTJTwhE&feature=relmfu

A. Natural Horns

1. Cylindrical Pipe Harmonics

2. Mouthpiece

3. Bell

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1. Harmonic Series

• Bell is a pressure node• Mouthpiece is pressure antinode• Acts as a “closed pipe”• Fundamental is ¼ length

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Closed End(Mouthpiece)

Open End(Bell)

1b. Closed Pipe Harmonics

• Only odd n harmonics

• N=1 =4L

• N=3 =4L/3

• N=5 =4L/5

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n

Ln

4

79181304428545670

Tube Length: L=1.41mfundamental SHOULD be: f0=c/4L=60.4 Hertz.

f

60.4181302423544664

Theory: fn= n f0

Fundamental wrong due to “edge effects”Rest of harmonics are close to theory

1c. Fundamental is wrong 6

1 3 5 7 911

n cyl

2. Mouthpiece

• A bigger cup has a lower “popping frequency”

• Popping frequency is approximately the highest pitch you can reach (Trumpet is 800 Hz)

• Harmonics near popping frequency are enhanced

• Bigger cup makes it easier to hit lower tones

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2b. Mouthpiece Shifts Frequencies

• Adding a mouthpiece lowers the upper harmonics so that they effectively resemble that of an open pipe

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3. The Bell

• The diameter of the bell limits the highest frequency you can play (cutoff frequency):

•

• Trombone: D=18 cm, f=476 Hz• Trumpet: D=11 cm, f=780 Hz

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D

cfc 4

D

cfc 4

3a. The Bell

• High frequencies reflect closer to the open end than low frequencies.

• Hence effective length of pipe is shorter for low frequencies (raises low frequencies)

• Pulls uplower notes bymore than 20%making themclose to open pipeharmonics

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79181304428545670

What happens when you add the bell

fcyl fbell

93221334449571691

f

144030212621

% change

--229.94.94.83.1

The bell raises all the frequencies; but it raises the low frequencies more than low frequencies.

3b. The Bell raised frequencies

3c. Mouthpiece and Bell

• Adding a mouthpiece and bell, harmonics effectively resemble that of an open pipe

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B. Horns with Slides

1. Harmonics

2. The Slide

3. Add Valves

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1. Harmonics Series

(a) Actual Length 275 cm (270 cm ?)

(b) Actual Fundamental Bb1 (58 Hz)

(c) Lowest note played: Bb2 (116.5 Hz)

Note: would expect fundamental of a closed pipe to be: f=c/(4L)= 31 Hz ! Recall that the frequencies are shifted by mouthpiece and bell. Hence T-Bone behaves like an open pipe of effective length 293 cm.

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2. The Slide

(a) Seven positions of slide, each lowering pitch by 1 semitone (hence lowest note played is E2)

(b) Each lengthens pipe by 5.9%

(c) Hence position 7 has length of(1.059)7L= 1.5 L

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059.1212

3. Add a valve

(a) Some Trombones have a valve that adds an extra meter of pipe to lower fundamental to F1 (fills in the notes between 1st and 2nd harmonic)

(b) Bass Trombone: Fundamental still Bb1,

but bigger bore, with 2 or 3 valves

(c) Contrabass Trombone: Fundamental F1, with valves to go lower yet!

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C. Horns with Valves

1. Mechanics of a Valve

2. Playing with Valves

3. Fixing Problems with valves

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• French Horn: http://www.youtube.com/watch?v=I6DjQ1-T3z8

• French Horn: http://www.youtube.com/watch?v=dRHvQJu6qU8&feature=related

• Trumpet (Bugler’s Holiday)http://www.youtube.com/watch?v=OkYcKfqFNmM

1. How a Valve Works(a) Adds a section of pipe when pressed

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1b. Valve Tuning

• Each valve has a little piece of pipe that you can slide to tune that valve individually

• Note the Rotary Valves have advantage of being “faster” and require less finger movement (Joseph Riedlin 1832). Standard for French Horns and expensive tubas

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1c. Valve Types• Square Piston valve invented by Stotzel 1815

• Cylindrical Pistons most common today

• Rotary Valves have advantage of being “faster” and require less finger movement (Joseph Riedlin 1832). Standard for French Horns and expensive tubas

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2. Playing with Valves

(a) Standard is 3 valves• Valve 1 adds 2 units (2 semitones lower)• Valve 2 adds 1 unit (1 semitone lower)• Valve 3 adds 3 units (3 semitones lower)

• A “unit” of length would add 5.9% to the fundamental length of the instrument

• In principle, combinations of these valves can add 0 through 6 units of length, equivalent to the 7 positions of trombone

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2b. Problem with Valves

• In principle, valve 3 is equivalent to pressing valves 1 & 2

• But you will find Valve 1 & 2 play 10 cents higher than valve 3

• Correctly tuned Valve 3:

– Valve 3: new length is (1.059)3L=1.188 L, added 18.8%

• Whereas

– Valve 2: new length is (1.059)1L=1.059 L, added 5.9%

– Valve 1: new length is (1.059)2L=1.121481 L added 12.1%

– Together they add 18.0%, which is a bit short, so “sharp”

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2c. More Problem with Valves

• No matter how you tune the valves you cannot make the 7 combinations match equal temperament.

• If valves 1, 2, 3 are each individually tuned to equal temperament pitches, then the combination of all 3 will be sharp by a full quarter tone (51 cents)!

• The problem is that valves are additive, whereas the equal temperament tuning is multiplicative.

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NN )059.0(1059.1

3. Fixing Problems with Valves

(a) Chromatic Valves

• Ideally you’d have 11 valves, each tuned to equal temperament semitone

• But, you only have 10 fingers, and you need some of them to hold the instrument!

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3b. Add 4th and 5th Valve

• You can add some extra valves to give more possible fingerings and reduce the overall error

• 4th valve drops the pitch a perfect 4th (5 semitones).

• 5th and 6th valves are sometimes used also! (function varies with instrument)

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3c. Add a slide to instrument

• A “trigger” or “throw” is a small slide added to tubing of a valve that can be adjusted while playing.

• Trumpet: on the first valve slide, operated by the player's thumb, used to adjust the higher F, D and B .♭

• Trumpet: on the third valve slide, operated by the player's fourth finger, used to adjust the lower D, C♯, A , G, and F♯.♭

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Performances• Playing two trumpets at once: http://www.youtube.com/watch?v=ouGfTqX-phk&featu

re=fvwrel • Tuba Quartet, William Tell

http://www.youtube.com/watch?v=0IZgQc_NMvI• Louie Armstrong, basin street blues

http://www.youtube.com/watch?v=qRjT4h7F_jw • Stars and Stripes (military)

http://www.youtube.com/watch?v=a-7XWhyvIpE • Laughing trombone

http://www.youtube.com/watch?v=6BFr3xgPS_M • Trombone Rag High Sierra Jazz Band

http://www.youtube.com/watch?v=VfjYXqVWUQk• x

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References• http://www.santafevisions.com/csf/html/lectures/016_instruments_III.htm• http://ccrma.stanford.edu/CCRMA/Courses/150/brasses.html• http://en.wikipedia.org/wiki/Brass_instrument• http://www.phys.unsw.edu.au/jw/brassacoustics.html

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Things to do• Cylindrical pipe: adding mouthpiece and bell, what is now the relationship of the

fundamental to the length? Is it somewhere between C/4L and C/2L ?