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)



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.


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))



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


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.



Paradigmatic Bowed String InstrumentParadigmatic Bowed String Instrument


Anatomy of a Anatomy of a ““StringString””

GuarneriGuarneri ViolaViola

ScrollScroll

FingerboardFingerboardBodyBody

““ff”” HolesHolesBridgeBridge

Tail pieceTail piece

Stradivarius ViolinStradivarius Violin



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


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



String tension is via tuning String tension is via tuning pegs in the scroll.pegs in the scroll.


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



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


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



A rosined horseA rosined horse--hair bow rubs the string.hair bow rubs the string.


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


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.


Horse Hair Horse Hair of Bowof Bow

StringString Slip pointSlip point


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.



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


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



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


Violin cross section Violin cross section

Scroll & Tuning Scroll & Tuning pegspegs

Finger boardFinger board

BodyBodyff--holehole

Sound PostSound Post



Plates are of varying thickness and are Plates are of varying thickness and are ““hingedhinged”” at at the edge (the edge (““PurflingPurfling””))

ThickerThickerThinnerThinner

PurflingPurfling


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



Bridge motions (notice the system asymmetry!)Bridge motions (notice the system asymmetry!)

Sound Sound postpost

BassBass

barbar


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



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


Holographic vibration images Holographic vibration images of violin platesof violin plates



ChladniChladni plates model the vibrational modes of plates model the vibrational modes of Violin plates.Violin plates.


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



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.

phy-2464 physical basis of music - department of physics · 2005. 2. 16. · chladni plates model...

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