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

Outline A.Natural Horns B.Slides C.Valves D.References 2 Brass Ensemble Tiger Rag: Bumble Bee:

A. Natural Horns 1.Cylindrical Pipe Harmonics 2.Mouthpiece 3.Bell 3

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

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

Tube Length: L=1.41m fundamental SHOULD be: f 0 =c/4L=60.4 Hertz. f Theory: f n = n f 0 Fundamental wrong due to “edge effects” Rest of harmonics are close to theory 1c. Fundamental is wrong 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 7

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

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 9

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 up lower notes by more than 20% making them close to open pipe harmonics 10

What happens when you add the bell f cyl f bell ff % change 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 12

B. Horns with Slides 1.Harmonics 2.The Slide 3.Add Valves 13

1. Harmonics Series (a)Actual Length 275 cm (270 cm ?) (b)Actual Fundamental B b 1 (58 Hz) (c)Lowest note played: B b 2 (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. 14

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) 7 L= 1.5 L 15

3. Add a valve (a)Some Trombones have a valve that adds an extra meter of pipe to lower fundamental to F 1 (fills in the notes between 1 st and 2 nd harmonic) (b)Bass Trombone: Fundamental still B b 1, but bigger bore, with 2 or 3 valves (c)Contrabass Trombone: Fundamental F 1, with valves to go lower yet! 16

C. Horns with Valves 1.Mechanics of a Valve 2.Playing with Valves 3.Fixing Problems with valves 17

French Horn: T3z8 T3z8 French Horn: Ju6qU8&feature=related Ju6qU8&feature=related

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

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 20

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 21

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 22

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) 3 L=1.188 L, added 18.8% Whereas –Valve 2: new length is (1.059) 1 L=1.059 L, added 5.9% –Valve 1: new length is (1.059) 2 L= L added 12.1% –Together they add 18.0%, which is a bit short, so “sharp” 23

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. 24

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! 25

3b. Add 4 th and 5 th Valve You can add some extra valves to give more possible fingerings and reduce the overall error 4 th valve drops the pitch a perfect 4 th (5 semitones). 5 th and 6 th valves are sometimes used also! (function varies with instrument) 26

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 ♯. 27

Performances Playing two trumpets at once: re=fvwrelhttp:// re=fvwrel 28

References

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 ?