Physics of Music Lecture 11

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Physics of MusicLecture 11

• Woodwind Instruments
• Berg Stork Chapter 10.
• Prof. Charles Hyde-Wright
• Old Dominion University

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Wind Instruments

• Woodwinds
• Resonant Tube
• Sound made by
• Edge tone
• Recorder, Flute, Organ
• Single Reed
• Clarinet, Saxophone, Organ
• Double Reed
• Oboe, English Horn, Bassoon,
• Shawm, Krummhorn

• Brass
• Resonant Tube
• Sound made by lips
• Trumpet, Trombone, French horn,

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Early Woodwinds

• 9000 year old clay flute from China
• Pre-historic clay, bone flutes
• Bamboo flutes

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Medieval RenaissanceWoodwinds

• Capped Reed Krummhorn, etc
• Double reed enclosed in a box, musician blows
  into wind way.
• Fipple flutes Tabor flute, Recorder, whistle.
• Musician blows into wind way, tone is generated
  by turbulence at an edge
• Early instruments had cylindrical bores.
• Conical bores developed to modify tone and give
  more flexibility in laying out fingering holes
• Simple holes (8 on recorder) almost no keys
• Every instrument came in a family of different
  sizes
• Soprano, Tenor, Alto, Baritone, Bass All
  dimensions scaled

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Tabor FlutePlayed by minstrels while
simultaneously beating a drum and dancing.

• Very narrow cylindrical bore.
• Fundamental does not sound
• Harmonic series is 2/21, 3/2, 2, 5/2, 3
• E.g. C5 G5 C6 E6 G6
• Over blow to select any note from harmonic
  series.
• With end covered by hand, harmonics
• ¾, 5/4, 7/4,
• G4, E5, B-flat/A5,
• Two finger holes near end can fill in missing
  notes
• Tube Open C, D, D
• (Like a trumpet)

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Recorder Resonance

• Turbulence of edge tone creates noise (all
  frequencies stimulated
• Negative amplitude reflection of pressure wave
  from end of tube interferes with edge tone
  turbulence.
• (twice length of recorder)/(speed of sound) time
  for pressure wave to reflect off end and come
  back to source.
• This reflected wave will reinforce those
  frequencies in the edge tone with
• Frequency n S/(2L), n1,2, 3 harmonic series

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Recorder Fingering

• Pressure wave is zero at each end
• 7 finger holes 1 thumb hole
• Opening the last hole effectively shortens the
  instrument (try E5 E6 B7) //0 //0
  /0/0.
• If the hole is smaller than the bore (or only
  partially opened) the effective length of the
  instrument is a little longer than the distance
  to the finger hole
• Last two finder holes are double, small holes.
• Blowing harder favors the 2nd or 3rd harmonic
  over the fundamental (shifts the pink noise).
• This is further enhanced by opening the thumb
  hole, which favors the creation of a node halfway

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Fingering
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BaroqueRecorder Conical Bore voicing
fingering

• Recorder has (inversed tapered) conical bore,
  narrowing at far end.
• Moves effective position of pressure node beyond
  length L of recorder.
• Antinode of 2nd harmonic moves towards end.

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RecorderForked Fingering

• A full chromatic scale requires many forked
  fingerings
• Opening the next to last finger has less effect
  than opening the last two fingers.
• Every half step must shift the effective length
  of the instrument by 5.75(even though we have
  fat fingers).
• We want to find 12 half steps with only eight
  fingers

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Double Reeds

• Older than single reeds (except organ)
• Krummhorn Capped reed
• Shawm Lips directly on reed, no keys
• Oboe, Bassoon, English Horn
• Fingerings enhanced by keys to add more
  combinations of hole positions and sizes.
• Keys extend hand reach for Bassoon.

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Reeds Source of Vibration

• Flow of air through reed opening drops the
  pressure (Bernoulli effect)
• Reeds are forced together by over pressure on
  outside
• With the air flow cut-off, the Bernoulli effect
  stops, the reeds rebound by their elasticity.
• Stiffness and mass of reed, set a broad resonance
  (range of frequencies) for the reed vibrations.
• Reflections of sound waves in tube reinforces
  the vibrations at the frequencies of the tube
  resonances (fundamental and harmonics).
• Reed acts as closed end. But reed in Conical
  tube acts like open end of cylindrical tube
• Oboe, Bassoon,
• Integer harmonics 1,2,3
• 2nd harmonic is one octave above
  fundamental(first harmonic).

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Single ReedsChalumeau, Clarinet, Saxophone

• Single Reed in cylindrical bore
• 2nd Harmonic at 3 x fundamental frequency
• Need 19 fingerings for Octave Fifth Difficult!
• Chalumeau is early precursor.
• Double holes for pitch control (like recorder)
• Register key (now optimal placement is 1/3)
• One or two keys for fingers.
• Chalumeau is played upside down (reed on top).
• Acoustics require much less air pressure
• Diameter of bore? Shape of mouthpiece??

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Clarinet

• Most recent of modern symphonic instruments.
• Mozart is earliest composerbut not for modern
  clarinet (also J.Christian Bach)
• Low register of clarinet is Chalumeau
• Middle register is clarinet register
• High register dominated by complicated fingerings

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Transposing Instrument

• Clarinet C is actually B-flat on piano
• Simplest scale on clarinet is defined to be
  C-major scale.
• Size of hands dictates that Clarinet C-Major
  scale is shifted down 1 whole step on piano to
  B-flat major

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Fingering of Clarinet Flute

• Böhm system circa 1850
• Rings and keys
• Each finger activates several pads.
• Combinations of fingers are not the same as the
  sum of the individual fingers.
• Clarinet acoustics is also affected by the
  chamfering given to individual finger and pad
  holes.

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Modern Flute

• Thin Walled cylindrical Tube
• Bohm fingering mechanism
• Head piece length adjusted.