1

Spring 2006 – Week 8 PHY 131 1

Concept of Critical Band

• Think of the basilar membrane as dividedinto 24 sections, the so-called critical bands

• As long as the frequencies of the complextone are within one critical band, the samegroup of hair cells is involved in “tickling”the nerve ends.

Spring 2006 – Week 8 PHY 131 2

Critical Bandwidth and Loudness

Frequency (Hz)

2

Spring 2006 – Week 8 PHY 131 3

Critical Band and Loudness

Spring 2006 – Week 8 PHY 131 4

Critical Band and Frequencyf < 1000 Hz

c.b. ≈ 90-150 Hz

f > 1000 Hz

c.b. ∝ f

3

Spring 2006 – Week 8 PHY 131 5

Loudness Summation and c.b.

• If the frequencies are within one c.b.Itot=I1+I2+…determine SILdetermine loudness level and loudness fromequal loudness curves

Spring 2006 – Week 8 PHY 131 6

Loudness Summation and c.b.

• If the frequencies are separated bymore than one c.b.The total loudness approaches (but remainsless) the sum of the individual loudnesses:

S ≤ S1 + S2 + S2…

4

Spring 2006 – Week 8 PHY 131 7

Loudness Summation and c.b.

• If frequency separation gets large a simpleloudness determination fails because mostlisteners focus on one tone and judgeloudness based on this tone.

• If the complex tone has many frequencycomponents, loudness determination mustbe done one c.b. at a time (filter banks).

Spring 2006 – Week 8 PHY 131 8

Masking• One tone “covers up” another• More effective when two frequencies are close. If the tones

differ by less than a c.b., the low-f tone will mask thehigher-f tone.

• A pure tone masks a tone of higher frequency more effectivethan a lower frequency

• More intense tones mask a greater frequency range• Masking also occurs by narrow bandwidth noise as long as

the bandwidth is equal or greater than the c.b.

5

Spring 2006 – Week 8 PHY 131 9

Frequency Response Curves

Spring 2006 – Week 8 PHY 131 10

Frequency Response Curves(Pairs of Pure Tones)

1046 Hz 523 Hz697 Hz 523 Hz588 Hz 523 Hz

6

Spring 2006 – Week 8 PHY 131 11

Response Curves and Masking

Spring 2006 – Week 8 PHY 131 12

Week 8

• Tone Quality (Timbre) and Spectrum

• Spectrum Analysis

• Spectrum Synthesis

• Pitch and its Perception

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Spring 2006 – Week 8 PHY 131 13

Timbre or Tone Quality

• Attack / Decay Transients– Tone envelope

• Spectrum of driving force– Reed, Lips, Bowing, Hammer, Plucking

• Harmonic response of each instrument– Depends on type and shape of instrument– Sounding box/board of String instruments– Formants (especially human voice)

• Inharmonicities:– Finite string size stretches Piano octaves.– Wind harmonics not necessarily pure integers

Spring 2006 – Week 8 PHY 131 14

62 cm-Long Pipe Open at Both Endswaveform

spectrum

-1.00

-0.50

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1.00

0 5 10 15

Sign

al

[V]

t [ms]

0.0

0.3

0.530.040.050.060.070.080.090.0

100.0

0 200 400 600 800 1000 1200 1400 1600 1800 2000

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er

Spec

trum

[a

rb.

unit

s]

f [Hz]

250 500 750 1000 1250 1500 Hz

T = 4 msf = 1/T = 250 Hz

8

Spring 2006 – Week 8 PHY 131 15

31 cm-Long Pipe Open at One Endwaveform

spectrum

-1.00

-0.50

0.00

0.50

1.00

0 5 10 15

Sign

al

[V]

t [ms]

0.0

0.3

0.530.040.050.060.070.080.090.0

100.0

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Pow

er

Spec

trum

[a

rb.

unit

s]

f [Hz]

250 500 750 1000 1250 1500 Hz

T = 4 msf = 1/T = 250 Hz