PHY2464 - Physical Basis of Music
PHY
-2464
PHY-2464
Physical Basis of Music
Presentation
Presentation 10
10
Plucked
Plucked and
and Struck
Struck String
String
Instruments
Instruments
Adapted
Adapted from
from Sam
Sam Matteson’s
Matteson’s
Unit
Unit 22 Session
Session 22,
22, 23
23
Sam
Sam Trickey
Trickey
Feb.
Feb. 13,
13, 2005
2005
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
Outlook •
Start with a reminder about analyzing
components of musical instrument (cultural
artifact explored “post facto”)
•
Compare basic physics of plucked and struck
stringed instruments
PHY2464 - Physical Basis of Music
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
RECALL! A musical instrument comprises four
primary subsystems:
(1) a mechanical energy source;
(2) a frequency generator;
(3) a frequency filter system;
(4) an antenna.
♩♪♫
~
PHYPHY-2464
f1 f2 f3 f4
~
fn
Pres. 10 Plucked & Struck String Instrum.
Instrum.
RECALL! 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
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
Reminder! The Guitar is a fretted stringed
instrument that is plucked or strummed.
Tuning pegs
Neck
Frets
Strings (6)
Body
Bridge
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
Harp - a stringed instrument that is plucked. Its
strings are of various lengths.
Strings
Traditional
Irish Harp
Sound Board
PHY2464 - Physical Basis of Music
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
The principal pitch of each string in a Pedal Harp is
determined by its length.
Pedal Harp
Strings
Pedals
However, depressing a pedal shortens or lengthens the
string length, raising (or lowering) the pitch incrementally.
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
Pedal Harp: 47 strings (diatonic scale); 7 pedals,
each with 3 positions (flat, natural, sharp)
C string, Position b = C natural. Position a = B sharp;
Position c = C sharp.
PHY2464 - Physical Basis of Music
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
Harpsichord: keyboard stringed instrument whose
strings are plucked. Each string is used for a single
pitch.
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
Though shaped like a modern piano, the harpsichord is smaller, with thinner soundboard &
thinner strings at lower tensions.
PHY2464 - Physical Basis of Music
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
Harpsichord may have one to three additional
strings to vary loudness &/or timbre.
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
Harpsichord action: Plectrum plucks the string on upward
motion; retracts into the jack on downward motion
Damper
Plectrum
String
Key
Jack
PHY2464 - Physical Basis of Music
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
Harpsichord action closeups -
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
Harpsichord action: before and after key is depressed
Plucked
PHY2464 - Physical Basis of Music
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
The jack is constructed so that the plectrum plucks in one
direction of motion, retracts in the other.
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
Hammered Dulcimer
http://www.rtpnet
.org/~hdweb
hdweb//
http://www.rtpnet.org/~
PHY2464 - Physical Basis of Music
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
A Piano is a keyboard stringed instrument whose
strings are hammered. Each string is used for one
pitch only.
Fortepiano
Strings
Piano
Key Board
Sound
Board
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
The Piano strings are hammered by a felt hammer,
actuated by the “action.”
String and Damper
Hammer
Jack Key
PHY2464 - Physical Basis of Music
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
Piano strings, felt hammer, and action.
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
The piano has multiple strings (in the treble) to
provide greater loudness than possible with 1 string.
Multiple Strings
Sound Board
Bridge
Frame
PHY2464 - Physical Basis of Music
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
Piano strings are tensioned by tuning pins in a
strong frame.
Frame
Bass Strings
Tuning Pins
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
Piano hammers are made of felt and wood.
Hammer Head
Felt
Back Check Wood
Pivot hinge
PHY2464 - Physical Basis of Music
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
Timbre: For any struck or plucked string, the point
of impact is crucial for timbre. Specifically, any
frequency which, for that length and density has a
node at the strike point will not be excited.
Example:
A piano string that is of Length L is struck by its
hammer at a point l from the end.
What harmonics are excited and which are missing from the distribution of frequencies (what
might be called the “vibration recipe”)?
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
Specific case: piano string 1.40 m long is struck by
its hammer at a point 20 cm from the end.
What harmonics are excited and which are
missing?
The point where the hammer struck is 20/140 = 1/7
of the total length of the string. Therefore, all
frequencies for which there is a node at that point
will not be excited.
This is the case for n= 7n´ or fn = 7n´f1 (fn = 7f1,
14f1, 21f1 etc) will be missing.
PHY2464 - Physical Basis of Music
PHYPHY-2464
Pres. 10 Plucked & Struck String Instrum.
Instrum.
Clearly by varying string tension, density, and
length, the size of all these instruments can be
varied. But a concert grand piano and a spinet
piano do not sound the same. Why?
At least three facts are relevant: strike points
determine the excited frequency distribution;
sound board sizing plays a role in frequency
filtration; thick strings vibrate somewhat like bars,
hence can be “inharmonic” (overtones not
multiples of fundamental)