PipesVoicePercussionReviewUnit 3 Pipes, Voice and PercussionEssential Facts and ConceptsPipes- Open (cylindrical) pipes: fundamental frequency f1 = v/2L’ ,ov= 343+0.6 (T-20C) the speed of soundoL’ = length of pipe (with end correction δL = 0.3 DiameteroHarmonics: all present fn =n f1- Stopped (cylindrical) pipes: fundamental frequency f1 = v/4L’,ov= 343+0.6 (T-20C) the speed of soundoL’ = length of pipe = end correctionoHarmonics: only odd present fn =(2n-1) f1- Conical pipes: fundamental frequency f1 = v/2(L’+c)oCones are stopped pipe but act like open pipes.ov as aboveoL’+c = length of cone plus end correction.- Standing WavesoStanding waves result from the combination of the wave traveling down the pipe and the wave reflected from the end and holes.oWoodwinds and brass change pitch by changing the length of the pipe and by exciting different harmonics.- ImpedanceoThe impedance is the ratio of the pressure fluctuation to the flow fluctuation: Z =p/UoWhen the impedance Z changes abruptly there are reflections of sound.oTherefore there are reflections at the ends (open and stopped) and from holes along the pipe.oThe holes produce (by wave interference) standing waves for a pipe of an effectively shorter pipe.- Sounding the pipeoFlue and Fipple pipes:oThe transverse flute (and other fipple woodwinds) and flue pipe are sounded by the edge tone of the fipple or embouchure.oEdge tone occurs because Bernoulli principle causes turbulent oscillation.oBernoulli principle: higher velocity air is a lower pressure.oPressure node near the open fipple.oThe frequency of the edge tone is fedge = 0.2 vjet /b, where vjet is thevelocity of the jet of air and b is the width of the opening in the fipple.oThe transverse flute is an open cylindrical pipe in which the standing waves in the pipe produced by reflections from the endsand holes feedback to control the precise frequency of the edge tone.oReed PipesoReeds are soft reeds if their they are responsive to feedback, i.e. they have a broad resonance; the reeds are hard reeds if they are unresponsive to the feedback because they have a sharp resonance.oReeds work by Bernoulli principle: higher velocity air is a lower pressure.oPressure anti-node at the reed.oThe clarinet reed is a soft reed.oThe clarinet is a stopped cylindrical pipe. Fundamental frequency = v/4lL’ Only odd harmonics for first few overtones oOther woodwinds: sax, oboe, bassoon, etc have conical bore. Fundamental frequency = v/2(L’+c) All harmonics present.oAll orchestral woodwind instruments have soft reeds.oBrassoBrass instruments are stopped pipes with combinations of cylindrical and conical pipes with a pronounced bell and a mouthpiece.oThe pipe is sounded by buzzing lips.oThe lips are a soft reed/valve.oPressure anti-node at the players lips.oThe pitch is changed primarily by changing the length of the pipe with slides and valves and by exciting different harmonics. oThe combination produces a nearly complete harmonic series expect that the lowest harmonic is not the fundamental of the series.oThe lowest frequency of the pitch is inharmonic and is called the “pedal tone.”oThe trumpet, cornet and Flugel horn are examples of similar instrument in which the percentage of conical tubing varies. (More cone for Flugel, less of cornet, least for trumpet).oThe mouthpiece cup volume and diameter of the tapered back-boredetermine the resonance frequencies of the mouth piece, similar to a Helmholtz resonator.oThe “flare constant” m in “exponential horns” determines how fast the bell opens up; a large m means an abrupt widening; a small m a gentle taper.oA Bessel horn is a slightly different kind of horn, similar to French Horns in shape.oTimbre of PipesoThe shape and diameter of the pipe determine the cutoff frequency for 3-D modes of oscillations of the air.oOnly frequencies higher than the cutoff frequencies can participate in the 3-D modes.oThe shape and size of the pipe and any bell affect the harmonic recipe and therefore the timbre of the pipe.oMutes filter the sound of the pipe, changing its timbre.oThe French Horn player’s hand changes the timbre of the pipe as well as changing its effective length.oThe finish of the inside of the bore and the edges of holes and joints affect the harmonic recipe in fine instruments.Voice- The vocal tract is the instrument of the human voice.- Sound originates in from the modulation of air by the vocal folds located in the larynx.- The vocal folds are hard reeds, not responsive to the standing waves in the vocal tract.- The pitch of the voice is determined by the density, length and tension (external and internal) of the vocal folds.- The vocal tract produces broad resonances called “formants” at about 500 Hz, 1500 Hz and 2500 Hz.- The intelligibility of speech is due to the relative frequency of the first two formats.- In singing the formants are modified from speech to produce matched resonance and harmonics of the vocal fold frequencies.- The singer’s formant is the third formant (~2500 Hz) that permits a singer to produce a significant amount of acoustic energy at a very high frequency that has little competition from other instruments by modification of the vocal tract.Percussion- Percussion instruments are instruments that are struck.- Percussion instruments produce sound from the vibration of their natural modes of oscillation.- Most percussion instruments do not have pitch.- Pitch results from a harmonic series.- The fundamental frequency of a circular membrane scales as the inverse of the diameter and the thickness and as the square root of theratio of the surface tension and the areal density, that is, the bigger the drum head or the thicker or the more dense the material the lower is the fundamental frequency. The tighter the stretch, on the other hand, the higher the range.- Bars and flexing sheets are dispersive (velocity of the wave depends on frequency) in their behavior.- For circular disks, the fundamental frequency depends on the inverse square of the diameter and is also proportional to the thickness.- The stiffer the bar or disk, the higher the range; the longer bar or largerdiameter the lower the range.- The natural modes of membranes, circular sheets of metal and rectangular bars are not harmonic (whole number rations of the fundamental).- Air lowers the range of real drum heads.- Timpani achieve approximate pitch by (1) air loading; (2) resonances ofthe air in the kettle;