A.Diederich– International University Bremen – Sensation and Perception – Fall 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

A.Diederich– International University Bremen – Sensation and Perception – Fall  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 mm, no matter whether this frequency jump is from 220 to 440 Hz, or from 1760 to 3520 Hz.

A.Diederich– International University Bremen – Sensation and Perception – Fall Physiological evidence for place coding  Tonotopic maps on the chochlea  Hair cells and auditory nerve fiber tuning

A.Diederich– International University Bremen – Sensation and Perception – Fall Tuning curve of a single inner hair cell in the guinea pig's cochlea  The hair cell is most sensitive at 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.

A.Diederich– International University Bremen – Sensation and Perception – Fall Tuning curves for auditory nerve fibers Frequency tuning curves of cat auditory nerve fibers. They are similar to hair cell tuning curves.

A.Diederich– International University Bremen – Sensation and Perception – Fall Psychophysical evidence for place coding  Auditory masking  single frequency  masking noise (several frequencies)

A.Diederich– International University Bremen – Sensation and Perception – Fall Auditory masking (Experiment by Egan & Hake, 1950) 1.Experiments to determine thresholds for frequencies between 100 – 4000 Hz 2.Measure threshold again with narrow band of masking noise (combination of frequencies between 365 and 455Hz and 80 dB SPL) present 3.Masking signal constant, frequency of test tones varies between 100 – 4000 Hz

A.Diederich– International University Bremen – Sensation and Perception – Fall Result of masking experiment Increase in test-tone threshold

A.Diederich– International University Bremen – Sensation and Perception – Fall Explaining the asymmetry of the function in terms of basilar membrane vibration patterns

A.Diederich– International University Bremen – Sensation and Perception – Fall 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

A.Diederich– International University Bremen – Sensation and Perception – Fall  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.

A.Diederich– International University Bremen – Sensation and Perception – Fall 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

A.Diederich– International University Bremen – Sensation and Perception – Fall 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.

A.Diederich– International University Bremen – Sensation and Perception – Fall 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 < 2500 Hz: Perceived pitch decreases with increasing intensity

A.Diederich– International University Bremen – Sensation and Perception – Fall Change of pitch with intensity

A.Diederich– International University Bremen – Sensation and Perception – Fall 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 ±

A.Diederich– International University Bremen – Sensation and Perception – Fall  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. Superposition of two sinusoidal tones of equal amplitude perceived loudness

A.Diederich– International University Bremen – Sensation and Perception – Fall Two pure tones of similar frequency adding together to produce beats

A.Diederich– International University Bremen – Sensation and Perception – Fall  The frequency of the resulting vibration pattern of two tones of very similar frequencies f 1 and f 2 is equal to the average value:  The beat frequency (the number of amplitude changes per second) is given by  The closer together the frequencies f 1 and f 2 are, the "slower" the beats will result.  If f 2 = f 1 the beats disappear completely: both components sound in unison.

A.Diederich– International University Bremen – Sensation and Perception – Fall  At unison, we hear one single tone of pitch corresponding to f 1 and a loudness that will depend on the particular phase difference between the two tones.  When we slightly increase the frequency f 2, 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 f 2 moves away from f 1. Summary of tone sensation evoked by superposition of two pure tones of equal amplitude and of frequency f 1 and f 2 = f 1 +  f

A.Diederich– International University Bremen – Sensation and Perception – Fall 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 f 1 and f 2 (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.

A.Diederich– International University Bremen – Sensation and Perception – Fall

A.Diederich– International University Bremen – Sensation and Perception – Fall

A.Diederich– International University Bremen – Sensation and Perception – Fall 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.

A.Diederich– International University Bremen – Sensation and Perception – Fall

A.Diederich– International University Bremen – Sensation and Perception – Fall  The limit for pitch discrimination and the critical band depend strongly on the average frequency (f 1 + f 2 )/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.

A.Diederich– International University Bremen – Sensation and Perception – Fall 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