Physics 1251 The Science and Technology of Musical Sound Unit 3 Session 30 MWF The Timbre of Wind Instruments Unit 3 Session 30 MWF The Timbre of Wind Instruments

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments What is the physical difference between a Cornet, Trumpet and Flugel Horn? Cornet Trumpet Flugel Horn The fraction of the horn that is cone/cylinder/flare. Trumpet – most cylindrical Trumpet – most cylindrical Cornet -- more conical Cornet -- more conical Flugel Horn – most conical Flugel Horn – most conical

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments 1′ Lecture: The pitch of a wind instrument is determined by the length and shape of its air column. The pitch of a wind instrument is determined by the length and shape of its air column. The effective length of the air column is controlled with holes, valves and slides. The effective length of the air column is controlled with holes, valves and slides. Feedback from the resonances of the pipe select the frequency of oscillation of the jet, reed or lip-valve. Feedback from the resonances of the pipe select the frequency of oscillation of the jet, reed or lip-valve. The excitation, transmission and emittance of the sound in the horn determine the timbre of the instrument. The excitation, transmission and emittance of the sound in the horn determine the timbre of the instrument.

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments Transverse Flute 80/20 The flute is driven by air flow against the edge of the embrochure hole. 80/20 A pressure node exists at the open hole. Embrochure Air flow

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments The Single Reed 80/20 The reed opens and closes like a valve, pressurizing the pipe when open, closing due to the Bernoulli effect when the air flows. 80/20 A pressure anti-node exists at the reed. Air flow Reed Tonguing

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments The Double Reed 80/20 The reed opens and closes like a valve, pressurizing the pipe when open, closing due to the Bernoulli effect when the air flows. 80/20 A pressure anti-node exists at the reed. Air flow Reed Tip Pressure Pulses

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments The Lip Valve 80/20 Brass instruments are played by the player’s lips that form a lip valve. 80/20 A pressure anti-node exists at the player’s lips. Louis Armstrong – trumpet ( )

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments Comparison of Wind Instruments Brass f Pedal Tone Other Woodwinds ClarinetFlute f1f1f1f1 2f 1 3f 1 4f 1 5f 1 f1f1f1f1 3f 1 5f 1 f1f1f1f1 2f 1 3f 1 4f 1 6f 1 f 1 = v/2L f 1 = v/4L f 1 = v/2(L+c) L c f o = f o = (1+ξ)v/4(L+c) f1f1f1f1 fOfOfOfO 2f O 3f O 4f O 5f O 6f O

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments Comparison of Wind Instruments (cont’d.) Brass Other Woodwinds ClarinetFlute f 1 = v/2L f 1 = v/4L f 1 = v/2(L+c) L c f o = f o = (1+ξ)v/4(L+c) Open Cylinder N p – N p f n = nf 1 f 1 = v/2L Stopped Cylinder A p – N p f 2n-1 = (2n-1)f 1 f 1 = v/4L Stopped Cone A p – N p f n = nf 1 f 1 = v/2(L+c) Stopped Combination A p – N p f n = nf 0 f 0 = (1+ξ)v/4(L+c)

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments 80/20 In the flute, feedback from the acoustic standing wave locks the frequency of the oscillation if the edge tone is near the fundamental frequency. Displacement wave f edge = 0.2 v jet /b f n = n v/ 2L; f edge ≈ f n

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments 80/20I In reed instruments, feedback from the pressure standing wave locks the frequency of the oscillation of the reed. Pressure wave f 2n-1 = (2n-1) v/ 4L′ f 2n-1 = (2n-1) v/ 4L′ Pressure inverts L′ = L d 0.3 d

Physics 1251Unit 3 Session 30 The Timbre of Wind 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

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments Feedback from Resonaces 80/20 The pitch of a wind instrument is determined by the influence on the jet/reed/lip-valve of feedback from the pressure/displacement standing waves in the pipe. 80/20 The pitch of a wind instrument is determined by the influence on the jet/reed/lip-valve of feedback from the pressure/displacement standing waves in the pipe.

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments Wind Instruments A jet produces a fluctuating air flow, while a reed or the lips produce pressure pulsations, the frequencies of which are controlled by feedback from standing waves in the horn. A jet produces a fluctuating air flow, while a reed or the lips produce pressure pulsations, the frequencies of which are controlled by feedback from standing waves in the horn. ♩ ♪ ♫ f 1 f 2 f 3 f 4 f 1 f 2 f 3 f 4 fn fn ~ ~ Flow fluctuations or Pressure pulsations Standing waves in horn Feedback

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments Effect of Excitation The mode of excitation of the horn significantly influences the harmonic recipe of the air column. The mode of excitation of the horn significantly influences the harmonic recipe of the air column. The harmonics will only be as strong as the excitation of the jet/reed/lip-valve. The harmonics will only be as strong as the excitation of the jet/reed/lip-valve.

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments Lip Valve Embouchure

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments The Mouthpiece 80/20 The Cup Volume and the diameter of the constriction leading to the back bore are the most important factors in determining the frequency spectrum of the mouthpiece. Cup Volume Diameter

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments Driven Pipe Vibration Recipe A A A Pipe Spectrum Mouthpiece Spectrum Driven Pipe Spectrum Frequency

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments Effect of the Pipe A pipe is three dimensional; therefore, 3-D modes of oscillation are possible in the pipe. A pipe is three dimensional; therefore, 3-D modes of oscillation are possible in the pipe. 80/20 Only those modes with frequency above a Cut-off Frequency f c will exist in the pipe. 80/20 Only those modes with frequency above a Cut-off Frequency f c will exist in the pipe. f > f c for propagation.

Modes of Vibration of a Column of Air Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments (0,0) (1,0) (2,0) D Cut Off Frequency f c = q n m v/D; for f < f c no propagation q 00 = 0; q 10 = 0.59; q 20 = 0.97

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments Effect of Modes on Spectrum More modes implies more intensity. More modes implies more intensity. Most influential in high f harmonics. Most influential in high f harmonics. Shape and relative diameter of pipe influence modes. Shape and relative diameter of pipe influence modes. Thus, a square organ pipe has a different timbre than does a round organ pipe because of the modes. Thus, a square organ pipe has a different timbre than does a round organ pipe because of the modes.

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments Reflections from the array of holes in a woodwind affect the relative strength of the high frequency harmonics in the pipe. Displacement wave Reflections from holes (closed and open)

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments Effect of Holes on Transmission Larger holes have greater effect. Larger holes have greater effect. A “high pass filter:” Low frequencies tend to be reflected more and high frequencies transmitted more. A “high pass filter:” Low frequencies tend to be reflected more and high frequencies transmitted more. The holes make a “brighter” sounding instrument. The holes make a “brighter” sounding instrument.

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments Reflections from joints and imperfections affect the relative strength of the high frequency harmonics in the pipe. Reflections

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments Filtering of Wind Instrument Sound The vagaries of transmission of the various frequency components in the pipe produce a filtering effect on the frequency spectrum of the sound. The vagaries of transmission of the various frequency components in the pipe produce a filtering effect on the frequency spectrum of the sound. ♩ ♪ ♫ f 1 f 2 f 3 f 4 f 1 f 2 f 3 f 4 fn fn ~ ~ Transmission through horn

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments Radiation of Sound from Wind Instruments The radiation characteristics of the bell “shape” the harmonic recipe and strongly influence the timbre of the instrument. The radiation characteristics of the bell “shape” the harmonic recipe and strongly influence the timbre of the instrument. ♩ ♪ ♫ f 1 f 2 f 3 f 4 f 1 f 2 f 3 f 4 fn fn ~ ~ Radiation Characteristics

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments 80/20 The diameter of the mouth and the flare rate of the bell determine the radiation characteristics of brass instruments. Cornet Trumpet Flugel Horn The larger the bore diameter, the more intense the low frequency harmonics.The larger the bore diameter, the more intense the low frequency harmonics. The more rapid the flare, the more the low frequencies are reflected, and thus, the more high frequency harmonics are radiated.The more rapid the flare, the more the low frequencies are reflected, and thus, the more high frequency harmonics are radiated.

Physics 1251Unit 3 Session 30 The Timbre of Wind 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

Physics 1251Unit 3 Session 30 The Timbre of Wind 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.

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments Mutes The French Horn player’s hand modifies the radiation characteristics of the horn, as well as the effective flare. The French Horn player’s hand modifies the radiation characteristics of the horn, as well as the effective flare. Mutes reduce the effective area of the horn and, therefore, reduce the intensity. Mutes reduce the effective area of the horn and, therefore, reduce the intensity. Mutes tend to reduce more the first and second harmonic of the pipe than higher frequency harmonics due to their internal modes of oscillation. Mutes tend to reduce more the first and second harmonic of the pipe than higher frequency harmonics due to their internal modes of oscillation. Mutes make brass sound “thin and reedy.” Mutes make brass sound “thin and reedy.”

Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments Summary: The pitch of a wind instrument is determined by the length and shape of its air column. The pitch of a wind instrument is determined by the length and shape of its air column. Feedback from the resonances of the pipe select the frequency of oscillation of the jet, reed or lip-valve. Feedback from the resonances of the pipe select the frequency of oscillation of the jet, reed or lip-valve. The excitation, transmission and emittance of the sound in the horn determine the timbre of the instrument. The excitation, transmission and emittance of the sound in the horn determine the timbre of the instrument.