Chordophones

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Chordophones

• Physics of Music PHY103

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Tradeoffs in chordophonesStrings only

• High tension means a lot of stress on the
  instrument.
• More massive strings have lower pitches under
  lower tension
• However thick strings dont bend very easily
• Loss of high frequencies leading to dull or soft
  timbre.
• Shift of overtones sharpwards

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Piano spectrum
3472694 34731041 34741399
347Hz
1094Hz
697Hz
1396Hz
Higher harmonics are higher than multiples of
fundamental Why? Wave equation requires more
energy for shorter waves non-linear wave
equation on string
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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.

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Loose strings

• Violin D string tuned to an A?
• bowed and plucked

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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.

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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.

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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

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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.

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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.

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Violin spectrum
note the envelope! spectrum is remarkably harmonic
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Cello spectrum

• Again note envelope

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Open strings vs fingered on violin

• open string has stronger high frequency harmonics

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Guitar spectrum and decay
At different times
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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

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Modern Piano Action

• Modern piano action is modeled after
  Crhistoforis.
• Pianists criticize electric keyboards and pianos
  because they fail to have the sensitivity and
  response of the piano action

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Stretched octaves and string non-linearity
Railsback curve
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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

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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

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Examples of ChordophonesBox 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
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Vietnamese Board Zither

• 16 steel strings above an oblong convex sound
  box.
• Strings are plucked and pressed to change the
  pitch

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Class projects 2005 , before

• little koto
• washtub bass

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African LuteChad

• Skin below the strings on the gourd.
• Gourd resonator

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Tar Lute from Azerbaijan

• Belly is covered with ox pericardium membrane
• 24 movable frets of gut?

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Harp ngombi Central Africa

• plucked soft gut strings

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Kora-Guinea

• ox tendon strings slid up and down for tuning
• notched bridge

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Mbela- Musical Bow Central Africa

• What is the resonant cavity?

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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

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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

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Hammered/Plucked/Bowed
Which one is which and how might you expect the
sound would be different?
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Amplification via Pickups

• Magnetic pickups
• Contact pickups
• Air pickups (aka microphones)
• Optical pickups

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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

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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

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Air pickups

• Microphones
• Most natural sound
• Sensitive to feedback