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The Science of Sound Dr. Bill Pezzaglia

1. The Science of Sound Dr. Bill Pezzaglia. Labrisone (lip vibrating) Instruments (aka “Brass”) Updated May 23, 2012. 2. Outline. Natural Horns Slides Valves References. Brass Ensemble Tiger Rag: http://www.youtube.com/watch?v=04PWhO6wd2A&feature=relmfu

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The Science of Sound Dr. Bill Pezzaglia

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  1. 1 The Science of SoundDr. Bill Pezzaglia Labrisone (lip vibrating) Instruments (aka “Brass”) Updated May 23, 2012

  2. 2 Outline • Natural Horns • Slides • Valves • References Brass Ensemble Tiger Rag: http://www.youtube.com/watch?v=04PWhO6wd2A&feature=relmfu Bumble Bee: http://www.youtube.com/watch?v=xZO5KTJTwhE&feature=relmfu

  3. 3 A. Natural Horns • Cylindrical Pipe Harmonics • Mouthpiece • Bell

  4. 4 1. Harmonic Series • Bell is a pressure node • Mouthpiece is pressure antinode • Acts as a “closed pipe” • Fundamental is ¼ length Closed End (Mouthpiece) Open End (Bell)

  5. 5 1b. Closed Pipe Harmonics • Only odd n harmonics • N=1 =4L • N=3 =4L/3 • N=5 =4L/6

  6. 6 1c. Fundamental is wrong Tube Length: L=1.41mfundamental SHOULD be: f0=c/4L=60.4 Hertz. Theory: fn= n f0 f n cyl 1 3 5 7 9 11 79 181 304 428 545 670 60.4 181 302 423 544 664 Fundamental wrong due to “edge effects” Rest of harmonics are close to theory

  7. 7 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

  8. 8 2b. Mouthpiece Shifts Frequencies • Adding a mouthpiece lowers the upper harmonics so that they effectively resemble that of an open pipe

  9. 9 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

  10. 10 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

  11. 3b. The Bell raised frequencies What happens when you add the bell f f % change f bell cyl 79 181 304 428 545 670 93 221 334 449 571 691 14 40 30 21 26 21 -- 22 9.9 4.9 4.8 3.1 The bell raises all the frequencies; but it raises the low frequencies more than low frequencies.

  12. 12 3c. Mouthpiece and Bell • Adding a mouthpiece and bell, harmonics effectively resemble that of an open pipe

  13. 13 B. Horns with Slides • Harmonics • The Slide • Add Valves

  14. 14 1. Harmonics Series • Actual Length 275 cm (270 cm ?) • Actual Fundamental Bb1 (58 Hz) • 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.

  15. 15 2. The Slide • Seven positions of slide, each lowering pitch by 1 semitone (hence lowest note played is E2) • Each lengthens pipe by 5.9% • Hence position 7 has length of(1.059)7L= 1.5 L

  16. 16 3. Add a valve • 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) • Bass Trombone: Fundamental still Bb1, but bigger bore, with 2 or 3 valves • Contrabass Trombone: Fundamental F1, with valves to go lower yet!

  17. 17 C. Horns with Valves • Mechanics of a Valve • Playing with Valves • Fixing Problems with valves

  18. French Horn: http://www.youtube.com/watch?v=I6DjQ1-T3z8 • French Horn: http://www.youtube.com/watch?v=dRHvQJu6qU8&feature=related

  19. 19 1. How a Valve Works • Adds a section of pipe when pressed

  20. 20 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

  21. 21 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

  22. 22 2. Playing with Valves • 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

  23. 23 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”

  24. 24 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.

  25. 25 3. Fixing Problems with Valves • 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!

  26. 26 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)

  27. 27 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♯.

  28. 28 Performances • Playing two trumpets at once: http://www.youtube.com/watch?v=ouGfTqX-phk&featu re=fvwrel

  29. 29 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

  30. 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 ?

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