Frequency Analysis in the Cochlea and Auditory Nerve cont'd

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• Frequency Analysis in the Cochlea and Auditory
  Nerve cont'd
• The Perception of Frequency
• Goldstein, pp. 342 343
• Levine, pp. 367 371
• Roederer, pp. 24 50

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• The spatial position along the basilar membrane
  of the recording hair cells and associated
  neurons determines the primary sensation of
  pitch.
• The musically most important range of frequencies
  (about 20 4000 Hz) covers roughly two-thirds of
  the extension of the basilar membrane (12-35 mm
  from the base).
• Whenever the frequency of a tone is doubled, that
  is, the pitch jumps one octave, the corresponding
  resonance region is displaced by a roughly
  constant amount of 3.5-5 mm, no matter whether
  this frequency jump is from 220 to 440 Hz, or
  from 1760 to 3520 Hz.

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Physiological evidence for place coding

• Tonotopic maps on the chochlea
• Hair cells and auditory nerve fiber tuning

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Tuning curve of a single inner hair cell in the
guinea pig's cochlea

• The hair cell is most sensitive at 18 000 Hz and
  responds well only to a narrow range of
  frequencies above and below this frequency.
• The frequency to which the hair cell is most
  sensitive is called the characteristic frequency.

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Tuning curves for auditory nerve fibers

• Frequency tuning curves of cat auditory nerve
  fibers. They are similar to hair cell tuning
  curves.

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Psychophysical evidence for place coding

• Auditory masking
• single frequency
• masking noise (several frequencies)

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Auditory masking

• (Experiment by Egan Hake, 1950)
• Experiments to determine thresholds for
  frequencies between 100 4000 Hz
• Measure threshold again with narrow band of
  masking noise (combination of frequencies between
  365 and 455Hz and 80 dB SPL) present
• Masking signal constant, frequency of test tones
  varies between 100 4000 Hz

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Result of masking experiment
Increase in test-tone threshold
Increase in test-tone threshold
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Explaining the asymmetry of the function in
terms of basilar membrane vibration patterns
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Just noticeable difference (JND)

• Difference threshold (DL) or just noticeable
  difference (JND) for pitch as a function of
  frequency for four different loudness levels
• For a considerable portion of the auditory range,
  the humans can discriminate between two tones
  that differ in frequency by 3 Hz or less

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• The degree of sensitivity to frequency changes,
  or frequency resolution capability, depends on
  the frequency, intensity, and duration of the
  tone in question and on the suddenness of the
  frequency change.
• It varies greatly from person to person, is a
  function of musical training, and unfortunately,
  depends on the method of measurement employed.

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• Tervaniemi, M. et al. (2005). Pitch
  discrimination accuracy in musicians vs
  nonmusicians an event-related potetial and
  behavioral study. Exp Brain Res, 161, 1-10

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Pitch versus intensity

• Auditory phenomenon Pure tones change in
  perceived pitch as their amplitude is increased
  or decreased.
• Experiment Gulick, 1971
• Standard tone of fixed intensity and frequency
• Task match the pitch of the standard by
  manipulating the frequency of a comparison tone
  of a fixed intensity.

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Result

• Standard 2500 Hz Very loud comparison tones
  had to be of a lower frequency than the standard
  in order to match the standard
• Standard lt 2500 Hz Perceived pitch decreases
  with increasing intensity

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Change of pitch with intensity
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Superposition of two sinusoidal tones of equal
frequency

• Same phase amplitude is the sum of the
  amplitudes of the two components
• Different phases still simple harmonic motion,
  but the amplitude will not be given anymore by
  the sum of the component amplitudes
• destructive interference same amplitude and the
  phase difference is 180

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Superposition of two sinusoidal tones of equal
amplitude
perceived loudness

• If the frequency difference ? f between the two
  components is large enough, we hear two separate
  tones of constant loudness, with pitches
  corresponding to each of the original tones.
• If the frequency difference ? f is smaller than a
  certain amount, we hear only one tone of
  intermediate pitch with modulated or "beating"
  loudness.

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Two pure tones of similar frequency adding
together to produce beats
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• The frequency of the resulting vibration pattern
  of two tones of very similar frequencies f1 and
  f2 is equal to the average value
• The beat frequency (the number of amplitude
  changes per second) is given by
• The closer together the frequencies f1 and f2
  are, the "slower" the beats will result.
• If f2 f1 the beats disappear completely both
  components sound in unison.

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Summary of tone sensation evoked by superposition
of two pure tones of equal amplitude and of
frequency f1 and f2 f1 ? f

• At unison, we hear one single tone of pitch
  corresponding to f1 and a loudness that will
  depend on the particular phase difference between
  the two tones.
• When we slightly increase the frequency f2, we
  continue hearing one single tone, but of slightly
  higher pitch, corresponding to the average
  frequency f.
• The loudness of this tone will be beating with a
  frequency ? f.
• These beats increase in frequency as f2 moves
  away from f1.

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Summary cont'd

• When the frequency differences ? f exceeds a
  particular value, the beat sensation disappears,
  giving way to a quite characteristic roughness or
  unpleasantness of the resulting tone sensation.
• When ? f surpasses a so-called limit of frequency
  discrimination, we suddenly distinguish two
  separate tones, of pitch corresponding to f1 and
  f2 (roughness still persists)
• Surpassing a yet larger frequency difference,
  called the critical band, the roughness sensation
  disappears and both pure tones sound smooth and
  pleasing.

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Critical bands

• How well can the hearing system discriminate
  between individual frequency components?
• Whether or not two components that are of similar
  amplitude and close together in frequency can be
  discriminated depends on the extent to which the
  basilar membrane displacements due to each of the
  two components are clearly separated or not.

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• The limit for pitch discrimination and the
  critical band depend strongly on the average
  frequency (f1 f2)/2 of the two tones (called
  the center frequency).
• The limit for frequency discrimination is roughly
  30 times larger than the JND for frequency
  resolution. That is,
• We can detect very minute frequency changes of a
  single pure tone, but it takes an appreciable
  frequency difference between two pure tones
  sounding simultaneously, to hear out each
  component separately.

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Implications for music

• Tuning instruments to avoid beats
• Critical bands (listen to "holy" tones in
  usc_s05_3_sound.ppt)
• Critical bands ! consonance and dissonance of
  musical intervals