Auditory Theory: Acoustics

Lecture 010 Hearing V

Reading Assignment for Lecture 011

Before next lecture please read Sections

• 3.3 Hearing notes 136

pages 136 to 144 of Acoustics and Psychoacoustics. We may have a brief quiz on these sections at the beginning of the next class.

Brain Bullets

• Pitch
  • Pitch relates to the perceived position of a sound on a scale from low to high and its formal definition by the American National Standards Institute is couched in these terms as: 'pitch is that attribute of auditory sensation in terms of which sounds are ordered on a scale extending from low to high'.
  • The measurement of pitch is therefore 'subjective' because it requires a human listener (the 'subject') to make a perceptual judgement. This in contrast to the measurement in the laboratory of for example, the fundamental frequency (f₀) of a note, which is an objective measurement.
  • In general, sounds which have a periodic acoustic pressure variation with time are perceived as having a pitch associated with them, and sounds whose acoustic pressure waveform is non periodic are perceived as having no pitch.
• Place theory of pitch perception
  • The place theory of pitch perception relates directly to the frequency analysis carried out by the basilar membrane in which different frequency components of the input sound stimulate different positions, or places, on the membrane.
  • One of the earliest versions of the place theory suggests that the pitch of a sound corresponds to the place stimulated by the lowest frequency component in the sound which is f_0.
  • Schouten (1940) demonstrated that the pitch of a pulse wave remained the same when the fundamental component was removed, thus demonstrating: (i) that f₀ did not have to be present for pitch perception, and (m that the lowest component present is not the basis for pitch perception because the pitch does not jump up by one octave.
• Problems with the place theory
  • the fine degree of accuracy observed in human pitch perception,
  • pitch perception of sounds whose frequency components are not resolved by the place mechanism,
  • the pitch perceived for some sounds which have continuous (non-harmonic) spectra, or
  • pitch perception for sounds with an f₀ less than 50 Hz
  • The place mechanism will resolve a given harmonic of an input sound provided that the critical bandwidth of the filter concerned is sufficiently narrow to exclude adjacent harmonics. It turns out that, no matter what the f₀ of the sound is, only the first 5 to 7 harmonics are resolved by the place analysis mechanism.
• Temporal theory of pitch perception
  • based on the fact that the waveform of a sound with a strong musical pitch repeats or is periodic
  • relies on the timing of neural firings generated in the organ of Corti which occur in response to vibrations of the basilar membrane
  • There are nerve fibres available to fire at all places along the basilar membrane, and they do so in such a manner that a given nerve fibre may only fire at one phase or instant in each cycle of the stimulating waveform, a process known as 'phase-locking'. Although the nerve firing is phase locked to one instant in each cycle of the stimulating waveform, it has been observed that no single nerve fibre is able to fire continuously at frequencies above approximately 300 Hz.
  • A 'volley firing' principle has also been suggested by Wever (1949) in which groups of nerves work together, each firing in different cycles to enable frequencies higher than 300 Hz to be coded.
  • For places which respond to frequencies below about the sixth harmonic, the minimum time between firings is at the period of the harmonic itself, and for places above, the minimum time between firings is the period of the input waveform itself (i.e. 1/ f₀).
• Problems with the temporal theory
  • not all observed pitch perception abilities can be explained by the temporal theory alone, the most important being the pitch perceived for sounds whose to is greater than 5 kHz.This cannot be explained by the temporal theory because phase locking breaks down above 5 kHz.
  • In practice it has been established that human pitch perception for sounds whose f₀ is greater than 5 kHz is rather poor with many musicians finding it difficult to judge accurately musical intervals in this frequency range.
• Contemporary theory of pitch perception
  • Neural firings occur stimulated by the detailed vibration of the membrane at places equivalent to frequency components of the input sound based on phase locking but not always once per cycle, the latter is illustrated on the right-hand side of the figure. The fact that firing is occurring from particular places provides the basis for the place theory of pitch perception.
  • The intervals between neural firings (spikes) are analysed and the results are combined to allow common intervals to be found which will tend to be at the fundamental period and its multiples, but predominantly at (1/ f₀). This is the basis of the temporal theory of pitch perception. The pitch of the sound is based on the results
• Secondary aspects of pitch perception
  • If the intensity of a sine wave is varied between 40 dBSPL and 90 dBSPL while keeping its to constant, a change in pitch is perceived for all to values other than those around 1-2 kHz.
  • For f₀ values greater than 2 kHz the pitch becomes sharper as the intensity is raised, and for to values below 1 kHz the pitch becomes flatter as the intensity is raised.
• The doppler effect
  • It is important to note that although pitch and frequency are related they are not necessarily the same. The a sound source is moving the waves are compressed in front of it and the apparent pitch rises. This is called the Dopper effect.