PHY-2464 Physical Basis of Music - Department of Physics · 2005. 2. 16. · Chladni plates model...
Transcript of PHY-2464 Physical Basis of Music - Department of Physics · 2005. 2. 16. · Chladni plates model...
PHY2464 - Physical Basis of Music
PHY-2464Physical Basis of Music
PHYPHY--24642464Physical Basis of MusicPhysical Basis of Music
Presentation 11Bowed String Instruments
Adapted from Sam Matteson’s Unit 2 Session 23
Sam TrickeyFeb. 13, 2005
Presentation 11Presentation 11Bowed String Instruments Bowed String Instruments
Adapted from Sam Matteson’s Unit 2 Session 23
Sam TrickeyFeb. 13, 2005
PHYPHY--2464 2464 Pres. 11 Bowed String InstrumentsPres. 11 Bowed String Instruments
Outlook Outlook --•• Start with a reminder about analyzing Start with a reminder about analyzing
components of musical instrument (cultural components of musical instrument (cultural artifact explored artifact explored ““post factopost facto””))
•• Reminder about plucked/struck string Reminder about plucked/struck string instrumentsinstruments
•• Survey basic physics of bowed string instruments Survey basic physics of bowed string instruments with focus on modern orchestral with focus on modern orchestral ““stringsstrings”” (also (also used in jazz, bluegrass, and countryused in jazz, bluegrass, and country--western)western)
PHY2464 - Physical Basis of Music
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Reminder about the four primary subsystems that Reminder about the four primary subsystems that comprise a musical instrument:comprise a musical instrument:
♩♩ ♪♪ ♫♫ ff1 1 ff2 2 ff3 3 ff44fn
~~ ~~
(1) a mechanical energy source;(1) a mechanical energy source;(2) a frequency generator;(2) a frequency generator;(3) a frequency filter system;(3) a frequency filter system;(4) an antenna.(4) an antenna.
PHYPHY--2464 2464 Pres. 11 Bowed String InstrumentsPres. 11 Bowed String Instruments
Fact:Fact: Frequency of nFrequency of nthth harmonic on a string under harmonic on a string under
tension T with linear density tension T with linear density µµ ::
ffnn = [2n/(4L)] = [2n/(4L)] ×× vvstring string
ffnn = [n/(2L)] = [n/(2L)] ×× √√(T/ (T/ µµ))
PHY2464 - Physical Basis of Music
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Reminder! The Reminder! The GuitarGuitar is a fretted stringed is a fretted stringed instrument that is plucked or strummed.instrument that is plucked or strummed.
NeckNeck
BodyBody
Strings (6)Strings (6)
Tuning pegsTuning pegs
BridgeBridge
FretsFrets
PHYPHY--2464 2464 Pres. 11 Bowed String InstrumentsPres. 11 Bowed String Instruments
Fact: the timbre of strings is affected by how and Fact: the timbre of strings is affected by how and where they are driven as well as their where they are driven as well as their mechanical properties.mechanical properties.
Therefore, we expect the timbre of bowed strings Therefore, we expect the timbre of bowed strings to be affected by (1) the properties of strings, to be affected by (1) the properties of strings, (2) bowing, and (3) by the frequency (2) bowing, and (3) by the frequency resonances of the instrument.resonances of the instrument.
PHY2464 - Physical Basis of Music
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Paradigmatic Bowed String InstrumentParadigmatic Bowed String Instrument
PHYPHY--2464 2464 Pres. 11 Bowed String InstrumentsPres. 11 Bowed String Instruments
Anatomy of a Anatomy of a ““StringString””
GuarneriGuarneri ViolaViola
ScrollScroll
FingerboardFingerboardBodyBody
““ff”” HolesHolesBridgeBridge
Tail pieceTail piece
Stradivarius ViolinStradivarius Violin
PHY2464 - Physical Basis of Music
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Family:Family:•• ViolinViolin
•• GG3 3 , D, D4 4 , A, A4 4 , E, E55 (5ths)(5ths)
•• ViolaViola•• CC3 3 , G, G3 3 , D, D4 4 , A, A44
(5(5thth below violin)below violin)
•• CelloCello•• CC2 2 , G, G2 2 , D, D3 3 , A, A33
(8vo below viola)(8vo below viola)
•• Bass (Viol)Bass (Viol)•• EE2 2 , A, A2 2 , D, D3 3 , G, G3 3 (4ths)(4ths)
BowBow
BridgeBridge
StringsStrings
PHYPHY--2464 2464 Pres. 11 Bowed String InstrumentsPres. 11 Bowed String Instruments
Pitch control through variation of the vibrating Pitch control through variation of the vibrating length of the strings by length of the strings by ““fingeringfingering”” –– nono fretsfrets
PHY2464 - Physical Basis of Music
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String tension is via tuning String tension is via tuning pegs in the scroll.pegs in the scroll.
PHYPHY--2464 2464 Pres. 11 Bowed String InstrumentsPres. 11 Bowed String Instruments
String density sets range of each stringString density sets range of each stringDenser wire: lower pitchDenser wire: lower pitch
Less dense wire: Less dense wire: higher pitchhigher pitch
Viola StringsViola Strings
Metal over Metal over ““catgutcatgut”” CC33
GG33
DD44
AA44
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Different pitches can Different pitches can be played on different be played on different strings or on the samestrings or on the samestring.string.
Example:Example:
““Air on the GAir on the G--StringString””
J.S. BachJ.S. Bach
PHYPHY--2464 2464 Pres. 11 Bowed String InstrumentsPres. 11 Bowed String Instruments
The sound post transfers vibration from the top The sound post transfers vibration from the top plate to bottom plate and supports bridgeplate to bottom plate and supports bridge..
Sound postSound postTop plateTop plate
Bottom plateBottom plate
PHY2464 - Physical Basis of Music
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A rosined horseA rosined horse--hair bow rubs the string.hair bow rubs the string.
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The Action of the BowThe Action of the Bow
The bow alternately pulls The bow alternately pulls the string, then releasesthe string, then releasesit when the string wave it when the string wave reaches the bow:reaches the bow:Stick Stick ––Slip mechanismSlip mechanism
PHY2464 - Physical Basis of Music
The StickThe Stick--Slip Mechanism causes the string to Slip Mechanism causes the string to vibrate when rubbed by the bow.vibrate when rubbed by the bow.
PHYPHY--2464 2464 Pres. 11 Bowed String InstrumentsPres. 11 Bowed String Instruments
Horse Hair Horse Hair of Bowof Bow
StringString Slip pointSlip point
PHYPHY--2464 2464 Pres. 11 Bowed String InstrumentsPres. 11 Bowed String Instruments
Where else do we meet Where else do we meet ““slipslip--stickstick””??••The The ““squeeksqueek”” of basketball shoes on the court.of basketball shoes on the court.
••The singing wine glass.The singing wine glass.
••The Hindu prayer bell.The Hindu prayer bell.
PHY2464 - Physical Basis of Music
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A complicated wave shoots down the string when the A complicated wave shoots down the string when the string slips from the bow.string slips from the bow.
Moving BowMoving BowScrollScroll BridgeBridge
Waveform envelopeWaveform envelope
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The coupling of the strings to the top and bottom The coupling of the strings to the top and bottom plates will accentuate or attenuate various plates will accentuate or attenuate various frequencies.frequencies.
♩♩ ♪♪ ♫♫ ff1 1 ff2 2 ff3 3 ff44fn
~~ ~~Top & bottom plates plus cavity Top & bottom plates plus cavity
acoustics filter harmonicsacoustics filter harmonics
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The response of the body and air cavityThe response of the body and air cavitydetermine the filtering of the harmonics.determine the filtering of the harmonics.
BridgeBridgeSound holeSound hole
Truss rodTruss rod
BodyBody
NeckNeckRecall Recall –– guitarguitar
crosscross--sectionsection
PHYPHY--2464 2464 Pres. 11 Bowed String InstrumentsPres. 11 Bowed String Instruments
Violin cross section Violin cross section
Scroll & Tuning Scroll & Tuning pegspegs
Finger boardFinger board
BodyBodyff--holehole
Sound PostSound Post
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Plates are of varying thickness and are Plates are of varying thickness and are ““hingedhinged”” at at the edge (the edge (““PurflingPurfling””))
ThickerThickerThinnerThinner
PurflingPurfling
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The bridge is The bridge is essentialessential to transforming the lateral to transforming the lateral motion of the string into vibrations of the top plate.motion of the string into vibrations of the top plate.
BridgeBridge
PHY2464 - Physical Basis of Music
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Bridge motions (notice the system asymmetry!)Bridge motions (notice the system asymmetry!)
Sound Sound postpost
BassBass
barbar
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Vibration is transmitted to the body and air cavity by Vibration is transmitted to the body and air cavity by the action of the Bridge.the action of the Bridge.
Rocking Rocking motionmotion
Helmholtz Helmholtz ResonanceResonance
Sound postSound post
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The The ““vibration recipevibration recipe”” (spectrum) determines the (spectrum) determines the timbre of a stringed instrument.timbre of a stringed instrument.
Log(
Am
plitu
de) d
BLo
g(A
mpl
itude
) dB
Frequency HzFrequency Hz
BowedBowed
PluckedPlucked
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Holographic vibration images Holographic vibration images of violin platesof violin plates
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ChladniChladni plates model the vibrational modes of plates model the vibrational modes of Violin plates.Violin plates.
PHYPHY--2464 2464 Pres. 11 Bowed String InstrumentsPres. 11 Bowed String Instruments
Summary:Summary:•• ffnn = [n/(2L)] = [n/(2L)] ‧‧ √√(T/ (T/ µµ))•• The bow works by the SlipThe bow works by the Slip--stick mechanism.stick mechanism.•• The timbre of a bowed stringed instrument is The timbre of a bowed stringed instrument is
determined by its harmonic recipe.determined by its harmonic recipe.•• The harmonic recipe of a bowed stringed The harmonic recipe of a bowed stringed
instrument is determined by its modes of instrument is determined by its modes of excitation, the harmonics of a string, and the excitation, the harmonics of a string, and the natural frequency response of the instrument as a natural frequency response of the instrument as a wholewhole
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Summary:Summary:•• A violin, viola, cello and bass are stringed A violin, viola, cello and bass are stringed
instruments with a finger board played by instruments with a finger board played by bowing.bowing.
•• The string vibrates the bridge which vibratesThe string vibrates the bridge which vibratesthe top plate.the top plate.
•• The sound post transmits the vibration to the The sound post transmits the vibration to the back plate.back plate.
•• The timbre of the violin family is strongly The timbre of the violin family is strongly affected by the modes of vibration of the affected by the modes of vibration of the instrument.instrument.