Physics of Music Lecture 12 Brass Instruments

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Physics of MusicLecture 12Brass Instruments

• Prof. Charles Hyde-Wright
• Old Dominion University
• November 12, 2002
• Berg Stork, Chapter 11

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Brass Instruments

• Very ancient
• Animal horns
• Shells
• Hollowed out tree branch (didgeridoo)
• Some Renaissance instruments used keys to modify
  pitch.
• All modern (western) brass instruments use valves
  and slides to produce a full range of notes.

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Sound Production in Brass Instruments

• Buzzing lips are primary source of sound and
  pitch
• Mass and tension both effect pitch
• Frequency square root (tension/mass)
• Acoustic resonance in tube shapes the sound
• Selects the fundamental and harmonic series
• Suppresses all other frequencies from sounding.
• Acoustically, Tube is closed at lip end, open at
  bell end.

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PVC Brass

• Buzz lips into 92cm long tube
• Fundamental frequency and odd harmonics expected
  at
• (344 m/s) / (4 0.92 m) 94 Hz
• 394Hz 282 Hz, 594Hz 470 Hz,
• Observed and all integer harmonics, but odd
  harmonics are stronger
• 95 Hz, 186 Hz, 281 Hz, 377 Hz, 470.6 Hz

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PVC Brass with Mouthpiece

• Buzz lips into PVC tube with rubber-stopper
  mouthpiece. Length beyond mouthpiece is 90cm
• Mouthpiece resonance suppresses fundamental at 95
  Hz.
• fundamental at 281 Hz
• Weak 2nd Harmonic at 568 Hz
• Strong 3rd harmonic at 851 Hz

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Brass Acoustics Bell

• Bell enhances coupling of standing wave to
  exterior room.
• Brass instruments are loud!
• Larger coupling lowers the Q-value, broadens the
  resonance, makes it easier for player to lip up
  or down a note into (or out of) tune.
• Bell shortens the effective length of instrument
  for low frequencies,
• Lower frequencies are shifted up

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Brass Acoustics Mouthpiece

• Mouthpiece resonance (typically 800 Hz) combine
  with resonances in tube to shift higher
  frequencies down.

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Harmonic Series of Brass

• Instead of frequency ratios
• 1357
• Brass harmonic series is
• 2345
• Fundamental is missing (almost unplayable)
• If B-flat is lowest playable note (trumpet,
  trombone)
• 2nd playable note is ratio 3/2 perfect fifth F
• 3rd playable note is ratio 4/2 to B-flat B-flat
  one octave above
• 4th playable note is ratio 5/2 to B-blat
  perfect third above 3rd note D
• 5th playable note is F

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Chromatic Scale of Wind Instruments

• The flute, oboe must fill in 12 notes of
  chromatic scale in one octave leap from
  fundamental to 2nd harmonic.
• The Clarinet must fill in 19 chromatic notes
  between fundamental and next harmonic at 3x
  fundamental (Octave Fifth)
• Brass instruments need only fill in 7 chromatic
  notes in the perfect Fifth interval from lowest
  (playable tone) to next harmonic

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Chromatic Scale ofTrombone

• Trombone has 7 slide positions.
• Each position lengthens the trombone by 5.95
  (lowers pitch by half-step).
• Size of Trombone and size of trombonist must
  match, so that trombonists arms will reach far
  enough to extend length by
• (1.0595)6-1 21/2 -1 1.414-1 41
• All increases are equal percentage, therefore
  increasing absolute length.

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Chromatic Scale of Trumpet

• Trumpet has 3 valves.
• Each valve adds a different length of tubing to
  the trumpet
• The valves can be activated individually of
  together (tubing adds).
• Actual length of tubing is a tuning compromise.

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Trumpet Valves

• Basic trumpet length L0 F (harmonic)
• 2nd valve (middle) Add length L0(5.95) E
• 1st valve, alone Add length L0(12.25) E-flat
• 1st 2nd adds length 18.2 lt 18.92 3 half
  steps D
• Without retuning, the D will be sharp
• Lengthen the tubing on 1 2, and require
  trumpet player to lip the E E-flat back up,
  while lipping the D down a little.
• 3rd valve alone give 4 semitones D-flat.
• 5, 6, 7 semitones obtained (poorly) with
• Valves 23, 13, 123, respectively.
• Equip trombone with mini-slide on valve 3
• Require trumpet player to adjust lips on every
  note.