1A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

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

2A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

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.

3A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

Physiological evidence for place coding

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

4A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

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.

5A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

Tuning curves for auditory nerve fibers

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

6A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

Psychophysical evidence for place coding

Auditory masking single frequency masking noise (several frequencies)

7A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

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

8A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

Result of masking experimentIn

crea

se in

test

-ton

e th

resh

old

Incr

ease

in te

st-t

one

thre

shol

d

9A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

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

10A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

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

11A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

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.

12A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

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

13A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

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.

14A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

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

15A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

Change of pitch with intensity

16A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

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±

17A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

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

18A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

Two pure tones of similar frequency adding together to produce beats

19A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

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.

20A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

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.

Summary of tone sensation evoked by superposition of two pure tones of equal

amplitude and of frequency f1 and f2 = f1 + f

21A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

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.

22A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

23A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

24A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

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.

25A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

26A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

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.

27A.Diederich– International University Bremen – Sensation and Perception – Fall 2004

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