Chordophones
Physics of
Music
PHY103
Tradeoffs in chordophones
Strings only
• High tension means a lot of stress on the
instrument.
• More massive strings have lower pitches
under lower tension
• However thick strings don’t bend very
easily
– Loss of high frequencies leading to dull or soft timbre.
– Shift of overtones sharpwards
Piano spectrum
347Hz 697Hz 1094Hz
1396Hz
347*2=694
347*3=1041
347*4=1399
Higher harmonics are higher than multiples of
fundamental
Why? Wave equation requires more energy for
shorter waves – non-linear wave equation on string
Are these frequency shifts
important?
Butler(example 2.4).
a) Piano playing C4
b) Piano playing C4 but the partials have been
lowered by digital processing so that their
frequencies are exact integer multiples of
the fundamental.
Pair of tones repeated 3 times.
Loose strings
• Violin D string tuned to an A?
• bowed and plucked
Bass strings
• If you lower the tension too much the tension changes during plucking
or hammering. The pitch changes after the pluck. The strings flop
around leading to buzzing and fast damping.
•  Low notes then requires thick and heavy strings (metal ones) to
prevent these problems.
• Wound strings help reduce problem of loss of high frequencies.
Problems with wound strings: damage to fret-board and fingers
particularly for fretless basses.
• To keep corrosion from reducing high frequency response  plastic
covering. However stretching of plastic may damp string motion
faster.
• If the tension is too low then the string will hit the finger board. This
is less of a problem for a harp but is a big problem for a guitar or lute.
Soprano strings
• Require light strings and high tension (for a
given tension).
• Metallic strings are tiny and kill your
fingers. Many steel string lutes/guitars are
not plucked by hand.
• Gut or nylon strings are softer but damp
faster and are less bright.
Tradeoffs in the strings
• Length/tension/density – ease of play, position of
plucking, having strings of different notes on the
same keyboard or fret-board, strength of
instrument.
• String composition
– metallic – less damping but heavier, harsher and
more damaging to fingers and fret-boards
– Gut or nylon – softer/duller but lighter and
damping faster
Amplification:
• A string by itself is not a very good radiator – it
has a small surface area.
• To increase volume the vibration must be coupled
to something with a larger surface area.
• Box: guitar/zither - vibration passes through
bridge– faces of the box vibrate.
• The surfaces of the box vibrate in modes as does
the air inside.
Amplification (continued)
• Box with holes – air moves in and out
(violin, guitar)
• Box with a membrane (African lutes)
vibrations excited in the membrane too.
The string excites harmonics, some are
amplified more than others depending on
the coupling of the string to box and the
way the box resonates.
Violin spectrum
note the envelope!
spectrum is remarkably harmonic
Cello spectrum
• Again note envelope
Open strings vs fingered on
violin
• open string has
stronger high
frequency harmonics
At different times
Guitar spectrum and decay
Piano Action
• While the 88 key board had been fully developed in the 15th century
the “piano-forte” action was introduced by Christofori in the early 18th
century.
• Originally hammers were covered with soft leather
Modern Piano Action
•
•
Modern piano action is modeled after Crhistofori’s.
Pianists criticize electric keyboards and pianos because they fail to have the sensitivity
and response of the piano action
Stretched octaves and string nonlinearity – Railsback curve
String decay rates
• The more strings, the louder the sound.
• Coupling between strings can influence how
sound is transferred to soundboard
• Slower decays with 2+ strings
Composers write for available instruments
Moonlight Sonata Beethoven
• Evgeny Kissin playing a modern Steinway
• Gayle Martin Henry playing a piano from around 1805 by
the Viennese maker Caspar Katholni
This clip from: http://www.slate.com/id/2245891/
the comparison from the posted article by Jan Swafford!
Modern pianos have bigger keyboards, longer sustain and
more uniform timbre across registers
Composers used the longer sustain and differences in timber
as effects
Examples of Chordophones
Box Zither- Santoor India
• Box zither –
trapezoid box with
many parallel
strings, strings are
struck
• Santoor (Indian)
Music taken from CD
Musical instruments of
the World 1990 CNRS
Vietnamese Board Zither
• 16 steel strings
above an oblong
convex sound
box.
• Strings are
plucked and
pressed to
change the pitch
Class projects 2005 , before
• little koto
• washtub bass
African
Lute
Chad
• Skin below the strings on the gourd.
• Gourd resonator
Tar: Lute from
Azerbaijan
• Belly is covered
with ox pericardium
membrane
• 24 movable frets of
gut?
Harp –ngombi Central Africa
• plucked soft
gut strings
KoraGuinea
• ox tendon
strings slid
up and down
for tuning
• notched
bridge
Mbela- Musical Bow
Central Africa
• What is the
resonant cavity?
Role of sustain in varying how
plucked instruments are played
• Metallic strings with long sustain must be
damped, harder to play (use pluckers)
• Gut strings with short sustain are strummed
rapidly with fingers
Sounding the string
• Plucking finger/plucker
Sound is influenced by position of plucker
• Hammering
Sound is influenced by weight of hammer, material
of hammer and leverage of hammer.
• Bowed –stick/slip continuous excitation. Ability to
control sound quality during the entire tone
For plucked and hammered tones, there is no control
after the note sounds
Hammered/Plucked/Bowed
Which one is which and
how might you expect
the sound would be
different?
Amplification via Pickups
•
•
•
•
Magnetic pickups
Contact pickups
Air pickups (aka microphones)
Optical pickups
Magnetic pickups
– coil typically thousands of winds with thin magnet wire
and with a central iron core. Resonant frequency of
pickup tuned with capacitance of wires and other stuff
to be near ear sensitivity peak (few 2kHz).
– Pickups combined in series and with opposite phases so
hum is cancelled  humbucker
– they work near vibrating metal (strings, gongs …)
Disadvantages: noise pickup, need vibrating metal
Advantages: interesting sound quality, no need for sound
board, good sustain
Contact Pickups
• Typically using piezo-electric material
• Often mounted on or near bridge of a stringed
instrument. Ineffective in wind instruments
unless allowed to move in the air
Advantages: flat frequency response, very cheap,
resistant to noise pickup, no need for sound board
Disadvantages: possibly less dynamic range,
pickups up surface noise, clicks, knocks, scrapes,
plucking
Air pickups
• Microphones
• Most natural sound
• Sensitive to feedback