PHY2464 - The Physical Basis of Music
PHYPHY-2464-2464 Physical Basis of Music
PresentationPresentation 1515 Recorders,Recorders, PanPan FlutesFlutes andand OrganOrgan FlueFlue PipesPipes AdaptedAdapted fromfrom SamSam Matteson’sMatteson’s UnitUnit 33 SessionsSessions 2626 && 2727 SamSam TrickeyTrickey Mar.Mar. 1,1, 20052005
PHY-2464 Pres. 15 Recorders, …
Reminder: Take a different look at flutes
More advanced treatment of how a flute works. Focus on the graphical representations –
http://www.phys.unsw.edu.au/~jw/fluteacoustics.html PHY2464 - The Physical Basis of Music
PHY-2464 Pres. 15 Recorders, …
Revisit fipples - or
Why does a flag wave?
http://www.maths.soton.ac.uk/staff/fitt/sailer.html Gives a simulation presuming a small initial angle of the breeze with respect to the plane of the flag (initially flat). The flag has NON-zero bending stiffness. Notice the similarity to edge-tone behavior.
PHY-2464 Pres. 15 Recorders, …
Edge Tone
fedge = 0.4 vjet / 2 b = 0.2 vjet /b
b b u = 0.4 vjet u vjet PHY2464 - The Physical Basis of Music
PHY-2464 Pres. 15 Recorders, …
Selection & stabilization of frequency: Feedback from the acoustic standing wave locks the frequency of the oscillation if the edge tone is near the fundamental frequency of the pipe.
Displacement wave
fedge = 0.2 vjet /b ; fn = n v/ 2L; fedge ≈ fn
PHY-2464 Pres. 15 Recorders, …
Flue and Fipple of a Recorder Recorder Mouthpiece
Fipple Flue
Air Column PHY2464 - The Physical Basis of Music
PHY-2464 Pres. 15 Recorders, …
Recorder (A Baroque Flute)
fn = n v/2L Fipple
L What happens The instrument when you “over jumps to a new blow?” register, n=2 or 3.
PHY-2464 Pres. 15 Recorders, …
How does one “play” the notes?
• By effectively changing the length of the air column.
• Opening holes introduces reflections that change the standing wave length. Displacement wave f n′ = n ‧ v/2Leff Leff PHY2464 - The Physical Basis of Music
PHY-2464 Pres. 15 Recorders, …
Cross Fingering The position and size of the open holes modify the effective length of the air column and consequently the pitch.
♩ ♩ ♯♩ ♩ ♯♩ ♩
PHY-2464 Pres. 15 Recorders, …
Why does the size of the hole matter? Remember acoustic impedance: Z =p/U Impedance = pressure/flow
Displacement →Flow U:
Z Z ′ PHY2464 - The Physical Basis of Music
PHY-2464 Pres. 15 Recorders, …
The Intonation Problem of Flutes:
• Only about 1% of the energy of the air stream produces sound. • Playing louder requires more air flow. • More air flow means higher jet velocity • Edge tone goes sharp • Worse in Recorder than in Transverse Flute • Player must “lip” tone into tune
PHY-2464 Pres. 15 Recorders …
Primitive Flute “cluster” – pan-pipes or pan flute
This pipe plays an octave above the scale shown
http://www.panflutejedi.com/jean-paul-tutorial.html PHY2464 - The Physical Basis of Music
PHY-2464 Pres. 15 Recorders …
Organ Pipes
Open Pipes
PHY-2464 Pres. 15 Recorders …
Organ Pipes
Pipe Organs use both open and stopped (one Open Pipes end closed) pipes in different ranks because the timbre is different for each. “Rank” ≈ a Stopped Pipes complete scale of the same timbre PHY2464 - The Physical Basis of Music
PHY-2464 Pres. 15 Recorders … Four-component mechanical model • Organ is a set of “boxes of whistles” as far as flue pipes are concerned. • Wind source (blower), “stop action” and “key action” to select pipes, swell shades, room acoustics Standing wave frequencies Flow Instability Standing wave frequencies Feedback ♩ ♪ ♫ f1 f2 f3 f4 fn ~ ~
PHY-2464 Pres. 15 Recorders …
• Elements of a mechanical action (“tracker”) pipe organ We will examine these on a local tracker organ on a field trip. • Other actions use magnets and air motors to actuate valves and stops.
From “Smithsonian Magazine” PHY2464 - The Physical Basis of Music
PHY-2464 Pres. 15 Recorders … Flue pipe – roughly, a one-note recorder or whistle. The fipple in a whistle is the mouth in a flue pipe To see more on flue pipes click on “The Organ and How It Works” → “Pipes” →“Flue Pipe Construction” at http://panther.bsc.edu/~jhcook/OrgHist/begin.htm Also see http://www.ibiblio.org/pipeorgan/Pages/SoundCharac.html We will come back to reed pipes in the context of orchestral reed instruments.
PHY-2464 Pres. 15 Recorders …
Summary: • Flutes, whistles, open flue pipes are open columns of air, with fn = n v/2L, n = 1,2,3,4…. • Stopped flue pipes have only f2n-1 = (2n-1) v/ 4L • Flue pipes are excited by flow instabilities of the air steam in the embochure hole, fipple, or mouth. • The frequency range is selected by the edge tone. • The pitch is determined by the effective length of the pipe. • Open holes determine the effective length of the pipe.