Frequency Analysis in the Cochlea and Auditory Nerve cont'd The Perception of Frequency

1. 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

2. 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.

3. Physiological evidence for place coding • Tonotopic maps on the chochlea • Hair cells and auditory nerve fiber tuning

4. 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.

5. Tuning curves for auditory nerve fibers Frequency tuning curves of cat auditory nerve fibers. They are similar to hair cell tuning curves.

6. Psychophysical evidence for place coding • Auditory masking • single frequency • masking noise (several frequencies)

7. 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

8. Result of masking experiment Increase in test-tone threshold Increase in test-tone threshold

9. Explaining the asymmetry of the function in terms of basilar membrane vibration patterns

10. 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

11. 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.

12. 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

13. 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.

14. 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

15. Change of pitch with intensity

16. 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±

17. 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.

18. Two pure tones of similar frequency adding together to produce beats

19. 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.

20. 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.

21. 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 frequencydiscrimination, 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.

24. 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.

26. 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.

27. 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