PHY2464 - Physical Basis of Music
PHY
-2464
PHY-2464
Physical Basis of Music
Presentation
Presentation 11
11
Bowed
Bowed String
String Instruments
Instruments
Adapted
Adapted from
from Sam
Sam Matteson’s
Matteson’s
Unit
2
Session
Unit 2 Session 23
23
Sam
Sam Trickey
Trickey
Feb.
Feb. 13,
13, 2005
2005
PHYPHY-2464
Pres. 11 Bowed String Instruments
Outlook •
Start with a reminder about analyzing
components of musical instrument (cultural
artifact explored “post facto”)
•
Reminder about plucked/struck string
instruments
•
Survey basic physics of bowed string instruments
with focus on modern orchestral “strings” (also
used in jazz, bluegrass, and country-western)
PHY2464 - Physical Basis of Music
PHYPHY-2464
Pres. 11 Bowed String Instruments
Reminder about the four primary subsystems that
comprise a musical instrument:
(1) a mechanical energy source;
(2) a frequency generator;
(3) a frequency filter system;
(4) an antenna.
♩♪♫
~
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f1 f2 f3 f4
~
fn
Pres. 11 Bowed String Instruments
Fact: Frequency of nth harmonic on a string under
tension T with linear density µ :
fn = [2n/(4L)] × vstring
fn = [n/(2L)] × √(T/ µ)
PHY2464 - Physical Basis of Music
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Pres. 11 Bowed String Instruments
Reminder! The Guitar is a fretted stringed
instrument that is plucked or strummed.
Tuning pegs
Neck
Frets
Strings (6)
Body
Bridge
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Fact: the timbre of strings is affected by how and
where they are driven as well as their
mechanical properties.
Therefore, we expect the timbre of bowed strings
to be affected by (1) the properties of strings,
(2) bowing, and (3) by the frequency
resonances of the instrument.
PHY2464 - Physical Basis of Music
PHYPHY-2464
Pres. 11 Bowed String Instruments
Paradigmatic Bowed String Instrument
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Pres. 11 Bowed String Instruments
Anatomy of a “String”
Stradivarius Violin
Scroll
Fingerboard
Body
Bridge
“f” Holes
Tail piece
Guarneri Viola
PHY2464 - Physical Basis of Music
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Pres. 11 Bowed String Instruments
Family:
Violin
•
•
G3 , D4 , A4 , E5 (5ths)
Viola
•
•
C3 , G3 , D4 , A4
(5th below violin)
Bridge
Bow
Cello
•
•
C2 , G2 , D3 , A3
(8vo below viola)
Strings
Bass (Viol)
•
•
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E2 , A2 , D3 , G3 (4ths)
Pres. 11 Bowed String Instruments
Pitch control through variation of the vibrating
length of the strings by “fingering” – no frets
PHY2464 - Physical Basis of Music
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String tension is via tuning
pegs in the scroll.
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String density sets range of each string
Viola Strings
Denser wire: lower pitch
C3
Metal over “catgut”
G3
D4
Less dense wire:
higher pitch
A4
PHY2464 - Physical Basis of Music
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Different pitches can
be played on different
strings or on the same
string.
Example:
“Air on the G-String”
J.S. Bach
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The sound post transfers vibration from the top
plate to bottom plate and supports bridge.
Top plate
Sound post
Bottom plate
PHY2464 - Physical Basis of Music
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Pres. 11 Bowed String Instruments
A rosined horse-hair bow rubs the string.
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The Action of the Bow
The bow alternately pulls
the string, then releases
it when the string wave
reaches the bow:
Stick –Slip mechanism
PHY2464 - Physical Basis of Music
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Pres. 11 Bowed String Instruments
The Stick-Slip Mechanism causes the string to
vibrate when rubbed by the bow.
Horse Hair
of Bow
String
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Slip point
Pres. 11 Bowed String Instruments
Where else do we meet “slip-stick”?
•The “squeek” of basketball shoes on the court.
•The singing wine glass.
•The Hindu prayer bell.
PHY2464 - Physical Basis of Music
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Pres. 11 Bowed String Instruments
A complicated wave shoots down the string when the
string slips from the bow.
Moving Bow
Scroll
Bridge
Waveform envelope
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The coupling of the strings to the top and bottom
plates will accentuate or attenuate various
frequencies.
♩♪♫
~
f1 f2 f3 f4
~
Top & bottom plates plus cavity
acoustics filter harmonics
fn
PHY2464 - Physical Basis of Music
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Pres. 11 Bowed String Instruments
The response of the body and air cavity
determine the filtering of the harmonics.
Recall – guitar
Neck
cross-section
Truss rod
Sound hole
Bridge
Body
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Violin cross section
Finger board
Scroll & Tuning
Body
pegs
f-hole
Sound Post
PHY2464 - Physical Basis of Music
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Plates are of varying thickness and are “hinged” at
the edge (“Purfling”)
Purfling
Thicker
Thinner
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The bridge is essential to transforming the lateral
motion of the string into vibrations of the top plate.
Bridge
PHY2464 - Physical Basis of Music
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Bridge motions (notice the system asymmetry!)
Bass
bar
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Sound
post
Pres. 11 Bowed String Instruments
Vibration is transmitted to the body and air cavity by
the action of the Bridge.
Rocking
motion
Helmholtz
Resonance
Sound post
PHY2464 - Physical Basis of Music
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Pres. 11 Bowed String Instruments
Log(Amplitude) dB
The “vibration recipe” (spectrum) determines the
timbre of a stringed instrument.
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Plucked
Bowed
Frequency Hz
Pres. 11 Bowed String Instruments
Holographic vibration images
of violin plates
PHY2464 - Physical Basis of Music
PHY-2464 Pres. 11 Bowed String Instruments
Chladni plates model the vibrational modes of
Violin plates.
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Summary:
•
fn = [n/(2L)] ‧ √(T/ µ)
•
The bow works by the Slip-stick mechanism.
•
The timbre of a bowed stringed instrument is
determined by its harmonic recipe.
•
The harmonic recipe of a bowed stringed
instrument is determined by its modes of
excitation, the harmonics of a string, and the
natural frequency response of the instrument as a
whole
PHY2464 - Physical Basis of Music
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Pres. 11 Bowed String Instruments
Summary:
•
A violin, viola, cello and bass are stringed
instruments with a finger board played by
bowing.
•
The string vibrates the bridge which vibrates
the top plate.
•
The sound post transmits the vibration to the
back plate.
•
The timbre of the violin family is strongly
affected by the modes of vibration of the
instrument.