1. Physics 1251 The Science and Technology of Musical Sound Unit 3 Session 29 MWF Brass Instruments Unit 3 Session 29 MWF Brass Instruments

2. Physics 1251Unit 3 Session 29 Brass Instruments What pitch (frequency) does a clarinet play if the length from the reed to a hole is 19.5 cm (including end corrections, i.e. L′= 0.195 m) at 20 C? f = v/4L′ for a stopped cylinder; v =343 m/s f = 343/(4 ‧ 0.195) = 440 Hz.

3. Physics 1251Unit 3 Session 29 Brass Instruments 1′ Lecture: Brass instruments are stopped pipes, that have a bore that is a combination of cylindrical and conical or flared. Brass instruments are stopped pipes, that have a bore that is a combination of cylindrical and conical or flared. Brass are excited by lip-valves. Brass are excited by lip-valves. The pitch is determined by feedback from the resonances of the pipe. The pitch is determined by feedback from the resonances of the pipe. The pitch is changed by exciting various overtones and by changing the length of the pipe. The pitch is changed by exciting various overtones and by changing the length of the pipe.

4. Physics 1251Unit 3 Session 29 Brass Instruments Brass Instruments of the Orchestra French Horn Trombone Trumpet Piccolo Trumpet Euphonium

5. Physics 1251Unit 3 Session 29 Brass Instruments Brass Instruments The lips produce a pulsation in the pressure admitted to the pipe; the pressure standing wave feeds back to control the oscillations of the plays lips. The lips produce a pulsation in the pressure admitted to the pipe; the pressure standing wave feeds back to control the oscillations of the plays lips. ♩ ♪ ♫ f 1 f 2 f 3 f 4 f 1 f 2 f 3 f 4 fn fn ~ ~ Lip-valve pulsations Standing wave frequencies Feedback

6. Physics 1251Unit 3 Session 29 Brass Instruments The Origins of Brass: Shofar Serpent Sackbut Ocleidex

7. Physics 1251Unit 3 Session 29 Brass Instruments The Lip Valve 80/20 Brass instruments are played by the player’s lips. Breath pressure, muscle tension and pressure feedback from the pipe determine the frequency of the opening and closing of the lips. Louis Armstrong – trumpet (1901-1971)

8. Physics 1251Unit 3 Session 29 Brass Instruments Lip Valve Embouchure

9. Physics 1251Unit 3 Session 29 Brass Instruments Lip Valve The lips of the player act as a valve that admits pressure pulses into the pipe. The lips of the player act as a valve that admits pressure pulses into the pipe. The frequency is determined by the breath air pressure, the lip tension and the resonances of the pipe. The frequency is determined by the breath air pressure, the lip tension and the resonances of the pipe.

10. Physics 1251Unit 3 Session 29 Brass Instruments 80/20 Brass Instruments are stopped pipes. The player’s lips produce a displacement node (pressure antinode) at the mouthpiece. The player’s lips produce a displacement node (pressure antinode) at the mouthpiece. A displacement anti-node (pressure node) exists at the bell. A displacement anti-node (pressure node) exists at the bell. Winton Marsalis Trumpet

11. Physics 1251Unit 3 Session 29 Brass Instruments The Mouthpiece Cup Back Bore

12. Physics 1251Unit 3 Session 29 Brass Instruments The Mouthpiece 80/20 The Cup Volume and the diameter of the constriction leading to the back bore are more important than the shape of the cavity. Cup Volume Diameter

13. Physics 1251Unit 3 Session 29 Brass Instruments Resonance for Combination Pipes Cone Cone with mouthpiece f 80/20 The Brass mouthpiece lowers the high frequency resonances.

14. Physics 1251Unit 3 Session 29 Brass Instruments The pitch is changed by pipe length and excitation of resonances. By means of slides and valves the length is changed.

15. Physics 1251Unit 3 Session 29 Brass Instruments

16. Horns can be played by exciting the resonances only. The “Natural Horns” No valves

17. Physics 1251Unit 3 Session 29 Brass Instruments Resonance for Combination Pipes 0/100% 20/80% 25/75%50/50%40/60% 100/0% f Pedal Tone Cone/ Cylinder %

18. Physics 1251Unit 3 Session 29 Brass Instruments Resonances for Combination Bores in Brass Instruments 80/20 A 50% cylindrical ‒ 50% conical bore has a nearly harmonic series.

19. Physics 1251Unit 3 Session 29 Brass Instruments Cylindrical-Conical Instruments French Horn Trombone Cornet Cone Cylinder

20. Physics 1251Unit 3 Session 29 Brass Instruments Trumpet-like Instruments Cornet Trumpet Flugel Horn Various instruments have different lengths of cylindrical and of conical pipe.

21. Physics 1251Unit 3 Session 29 Brass Instruments The Bell a = a o exp(m x)+ b 80/20 m is called the “flare constant.” Larger m means more rapid flare. x Exponential Horn

22. Physics 1251Unit 3 Session 29 Brass Instruments The Bell Bessel Horns x a a = a o e -(εx) +b 80/ 20 Called “Bessel Horns” because the standing wave follows a Bessel Function.

23. Physics 1251Unit 3 Session 29 Brass Instruments Summary: Brass Instruments are stopped pipes. Brass Instruments are stopped pipes. The pipe bore is designed to give resonances that are harmonic. The pipe bore is designed to give resonances that are harmonic. The pedal tone (the lowest note) is not harmonic. The pedal tone (the lowest note) is not harmonic. The player’s lips are a soft reed. The player’s lips are a soft reed. The pitch is changed by changing the length and exciting resonances. The pitch is changed by changing the length and exciting resonances.