phy-2464 physical basis of music - department of physics

PHY2464 - Physical Basis of Music

PHY-2464Physical Basis of Music

PHYPHY--24642464Physical Basis of MusicPhysical Basis of Music

Presentation 10Plucked and Struck String

Instruments Adapted from Sam Matteson’s

Unit 2 Session 22, 23 Sam TrickeyFeb. 13, 2005

Presentation 10Presentation 10Plucked and Struck StringPlucked and Struck String

Instruments Instruments Adapted from Sam Matteson’s

Unit 2 Session 22, 23 Sam TrickeyFeb. 13, 2005

PHYPHY--2464 2464 Pres. 10 Plucked & Struck String Pres. 10 Plucked & Struck String InstrumInstrum..

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””))

•• Compare basic physics of plucked and struck Compare basic physics of plucked and struck stringed instruments stringed instruments



RECALL!RECALL! A musical instrument comprises four A musical instrument comprises four primary subsystems:primary subsystems:

♩♩ ♪♪ ♫♫ 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.


RECALL!RECALL! Frequency of nFrequency of nthth harmonic on a string harmonic on a string

under tension T with linear density under tension T with linear density µµ ::

ffnn = [2n/(4L)] = [2n/(4L)] ×× vvstringstring

ffnn = [n/(2L)] = [n/(2L)] ×× √√(T/ (T/ µµ))



Reminder!Reminder! The 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


HarpHarp -- a stringed instrument that is plucked. Its a stringed instrument that is plucked. Its strings are of various lengthsstrings are of various lengths..

Traditional Traditional Irish HarpIrish Harp

StringsStrings

Sound BoardSound Board



The principal pitch of each string in a The principal pitch of each string in a Pedal HarpPedal Harp is is determined by its length.determined by its length.

Pedal HarpPedal Harp

However, depressing a pedal shortens or lengthens the However, depressing a pedal shortens or lengthens the string length, raising (or lowering) the pitch incrementally.string length, raising (or lowering) the pitch incrementally.

StringsStrings

PedalsPedals


Pedal HarpPedal Harp:: 47 strings (diatonic scale); 7 pedals, 47 strings (diatonic scale); 7 pedals, each with 3 positions (flat, natural, sharp)each with 3 positions (flat, natural, sharp)

C string, Position b = C natural. Position a = B sharp; C string, Position b = C natural. Position a = B sharp; Position c = C sharp. Position c = C sharp.



Harpsichord: keyboard stringed instrument whose Harpsichord: keyboard stringed instrument whose strings are plucked. Each string is used for a single strings are plucked. Each string is used for a single pitch. pitch.


Though shaped like a modern piano, the Though shaped like a modern piano, the harpsiharpsi--chord is smaller, with thinner soundboard & chord is smaller, with thinner soundboard & thinner strings at lower tensions.thinner strings at lower tensions.



Harpsichord may have one to three additional Harpsichord may have one to three additional strings to vary loudness &/or timbre.strings to vary loudness &/or timbre.


Harpsichord action: Plectrum plucks the string on upward Harpsichord action: Plectrum plucks the string on upward motion; retracts into the jack on downward motionmotion; retracts into the jack on downward motion

KeyKey

JackJackStringStringPlectrumPlectrum

DamperDamper



Harpsichord action Harpsichord action closeupscloseups --


Harpsichord action: before and after key is depressedHarpsichord action: before and after key is depressed

PluckedPlucked



The jack is constructed so that the plectrum plucks in one The jack is constructed so that the plectrum plucks in one direction of motion, retracts in the other.direction of motion, retracts in the other.


Hammered DulcimerHammered Dulcimer

http://www.http://www.rtpnetrtpnet.org/~.org/~hdwebhdweb//



A A PianoPiano is a keyboard stringed instrument whose is a keyboard stringed instrument whose strings are hammered. Each string is used for one strings are hammered. Each string is used for one pitch only.pitch only.

StringsStrings

Key BoardKey Board

Sound Sound BoardBoard

FortepianoFortepiano PianoPiano


The Piano strings are hammered by a felt hammer, The Piano strings are hammered by a felt hammer, actuated by the actuated by the ““action.action.””

JackJack KeyKey

HammerHammer

String and DamperString and Damper



Piano strings, felt hammer, and actionPiano strings, felt hammer, and action..


The The pianopiano has multiple strings (in the treble) to has multiple strings (in the treble) to provide greater loudness than possible with 1 string.provide greater loudness than possible with 1 string.

Multiple StringsMultiple Strings

Sound BoardSound Board BridgeBridge FrameFrame



Piano strings are tensioned by tuning pins in a Piano strings are tensioned by tuning pins in a strong frame.strong frame.

FrameFrame

Tuning PinsTuning Pins

Bass StringsBass Strings


Piano hammers are made of felt and wood.Piano hammers are made of felt and wood.

Pivot hingePivot hinge

Hammer HeadHammer Head

Back CheckBack CheckFeltFelt

WoodWood



Timbre: For any struck or plucked string, the point Timbre: For any struck or plucked string, the point of impact is crucial for timbre. Specifically, any of impact is crucial for timbre. Specifically, any frequency which, for that length and density has a frequency which, for that length and density has a node at the strike point will node at the strike point will notnot be excited.be excited.

Example: Example: A piano string that is of Length L is struck by its A piano string that is of Length L is struck by its hammer at a point l from the end.hammer at a point l from the end.What harmonics are excited and which are missWhat harmonics are excited and which are miss--inging from the distribution of frequencies (what from the distribution of frequencies (what might be called the “vibration recipe”)?might be called the “vibration recipe”)?


Specific case:Specific case: piano string 1.40 m long is struck by piano string 1.40 m long is struck by its hammer at a point 20 cm from the end.its hammer at a point 20 cm from the end.What harmonics are excited and which are What harmonics are excited and which are missing?missing?

The point where the hammer struck is 20/140 = 1/7 The point where the hammer struck is 20/140 = 1/7 of the total length of the string. Therefore, all of the total length of the string. Therefore, all frequencies for which there is a node at that point frequencies for which there is a node at that point will not be excited.will not be excited.

This is the case for n= 7nThis is the case for n= 7n´́ or for fnn = 7n= 7n´́ff11 (f(fnn = 7f= 7f11, , 14f14f11, 21f, 21f11 etc) will be missing.etc) will be missing.



Clearly by varying string tension, density, and Clearly by varying string tension, density, and length, the size of all these instruments can be length, the size of all these instruments can be varied. But a concert grand piano and a spinet varied. But a concert grand piano and a spinet piano do not sound the same. Why?piano do not sound the same. Why?

At least three facts are relevant: strike points At least three facts are relevant: strike points determine the excited frequency distribution; determine the excited frequency distribution; sound board sizing plays a role in frequency sound board sizing plays a role in frequency filtration; thick strings vibrate somewhat like bars, filtration; thick strings vibrate somewhat like bars, hence can be hence can be ““inharmonicinharmonic”” (overtones not (overtones not multiples of fundamental)multiples of fundamental)

phy-2464 physical basis of music - department of physics

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