1. The Science of Sound Dr. Bill Pezzaglia1
Labrisone (lip vibrating) Instruments
(aka “Brass”)
Updated May 24, 2013

2. Outline Natural Horns Slides Valves References 2
Brass Ensemble Tiger Rag:
Bumble Bee:

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

4. 1. Harmonic Series Bell is a pressure node4
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. 1b. Closed Pipe Harmonics5
1b. Closed Pipe Harmonics
Only odd n harmonics
N=1 =4L
N=3 =4L/3
N=5 =4L/5

6. 1c. Fundamental is wrong f Theory: fn= n f0 n 1 3 5 7 9 11 79 181 3046
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

7. 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

8. 2b. Mouthpiece Shifts Frequencies8
2b. Mouthpiece Shifts Frequencies
Adding a mouthpiece lowers the upper harmonics so that they effectively resemble that of an open pipe

9. 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

10. 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

11. 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. 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. 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. 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. C. Horns with Valves Mechanics of a Valve Playing with Valves17
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
Trumpet (Bugler’s Holiday)

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. 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

22. 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. 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= L added 12.1%
Together they add 18.0%, which is a bit short, so “sharp”

24. 2c. More Problem with Valves24
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. 3. Fixing Problems with Valves25
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. 3c. Add a slide to instrument27
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: re=fvwrel
Tuba Quartet, William Tell
Louie Armstrong, basin street blues
Stars and Stripes (military)
Laughing trombone
Trombone Rag High Sierra Jazz Band x

29. 29
References

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 ?