PHY2464 - The Physical Basis of Music
PHY
-2464
PHY-2464
Physical Basis of Music
Presentation
Presentation 15
15
Recorders,
Recorders, Pan
Pan Flutes
Flutes and
and
Organ
Organ Flue
Flue Pipes
Pipes
Adapted
Adapted from
from Sam
Sam Matteson’s
Matteson’s
Unit
3
Sessions
26
Unit 3 Sessions 26 &
& 27
27
Sam
Sam Trickey
Trickey
Mar.
Mar. 1,
1, 2005
2005
PHYPHY-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
PHYPHY-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 NONNON-zero bending
stiffness. Notice the similarity to edgeedge-tone behavior.
PHYPHY-2464
Pres. 15 Recorders, …
Edge Tone
fedge = 0.4 vjet / 2 b = 0.2 vjet /b
b
vjet
u
b
u = 0.4 vjet
PHY2464 - The Physical Basis of Music
PHYPHY-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
PHYPHY-2464
Pres. 15 Recorders, …
Flue and Fipple of a Recorder
Recorder
Mouthpiece
Fipple
Air Column
Flue
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 15 Recorders, …
Recorder (A Baroque Flute)
fn = n v/2L
Fipple
L
What happens
when you “over
blow?”
PHYPHY-2464
The instrument
jumps to a new
register, n=2 or 3.
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
Leff
f n′ = n ‧ v/2Leff
PHY2464 - The Physical Basis of Music
PHYPHY-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.
♩
PHYPHY-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
PHYPHY-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
PHYPHY-2464
Pres. 15 Recorders …
Primitive Flute “cluster”
cluster” – panpan-pipes or pan flute
This pipe plays an octave above the scale shown
http://www.panflutejedi
.com/jean--paulhttp://www.panflutejedi.com/jean
paul-tutorial.html
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 15 Recorders …
Organ Pipes
Open Pipes
PHYPHY-2464
Pres. 15 Recorders …
Organ Pipes
Pipe Organs use both
open and stopped (one
end closed) pipes in
different ranks because
the timbre is different
for each. “Rank”
Rank” ≈ a
complete scale of the same
timbre
Open
Pipes
Stopped
Pipes
PHY2464 - The Physical Basis of Music
PHYPHY-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
Feedback
♩♪♫
~
PHYPHY-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”
f1 f2 f3 f4
fn
PHY2464 - The Physical Basis of Music
PHYPHY-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
pipeorgan/Pages/
/Pages/SoundCharac
SoundCharac.html
.html
http://www.ibiblio.org/
We will come back to reed pipes in the context of
orchestral reed instruments.
PHYPHY-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…
1,2,3,4….
• Stopped flue pipes have only f2n(2n-1) v/ 4L
2n-1 = (2n• 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.