The Science of Sound Dr. Bill Pezzaglia 1 Labrisone (lip vibrating) Instruments (aka “Brass”) Updated May 24, 2013

Outline Natural Horns Slides Valves References 2 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 A. Natural Horns Cylindrical Pipe Harmonics Mouthpiece Bell

1. Harmonic Series Bell is a pressure node 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)

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

1c. Fundamental is wrong f Theory: fn= n f0 n 1 3 5 7 9 11 79 181 304 6 Tube Length: L=1.41m fundamental SHOULD be: f0=c/4L=60.4 Hertz. f Theory: fn= n f0 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

2. Mouthpiece 7 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

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

3. The Bell 9 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

3a. The Bell 10 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 up lower notes by more than 20% making them close to open pipe harmonics

3b. The Bell raised frequencies What happens when you add the bell f f f % change cyl bell 79 181 304 428 545 670 93 221 334 449 571 691 14 40 30 21 26 -- 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 3c. Mouthpiece and Bell Adding a mouthpiece and bell, harmonics effectively resemble that of an open pipe

13 B. Horns with Slides Harmonics The Slide Add Valves

1. Harmonics Series Actual Length 275 cm (270 cm ?) 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 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 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!

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

French Horn: http://www.youtube.com/watch?v=I6DjQ1-T3z8 Trumpet (Bugler’s Holiday) http://www.youtube.com/watch?v=OkYcKfqFNmM

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

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

1c. Valve Types 21 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

2. Playing with Valves 22 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 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”

2c. More Problem with Valves 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.

3. Fixing Problems with Valves 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 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)

3c. Add a slide to instrument 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 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

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

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 ?