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Human Hearing Time to read Chapter 6.1 and 6.2 of Berg & Stork. 3.2 mm 2. 55 mm 2. Ossicles. Pretty small …. Uncoiled cochlea (schematic). limber. stiffer. http://www.howstuffworks.com/hearing1.htm. Cross section of cochlea. Two theories for the vibrations inside the cochlea.

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Human Hearing

Time to read Chapter 6.1 and 6.2 of Berg & Stork


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3.2 mm2

55 mm2




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Uncoiled cochlea (schematic)

limber

stiffer

http://www.howstuffworks.com/hearing1.htm




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inner hair cell

outer hair cell




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An animation may help:

http://www.maxanim.com/physiology/Cochlear%20Structures/Cochlear%20Structures.htm



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Two frequencies f and 2f (one octave)

3.5 mm

“same” interval corresponds to the same frequency ratio

(fixed distance along the cochlea)


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Weber-Fletcher Law

feels like the same interval


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overlap for frequencies differing by less than about 15% (minor third)

sine wave excites about 1.2 mm of the basilar membrane


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excited hair cells (minor third)

distance along the basilar membrane

sharpening

The amount of sharpening determined the just noticeable difference in frequencies


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JND in pitch: (minor third)

0.5%

2%


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frequency up and down by 0.001 = 0.1% (minor third)

frequency up and down by 0.005 = 0.5%


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Periodicity pitch and fundamental tracking (minor third)

(This is not Physics, it’s psychology)

An overtone series like 2f, 3f, 4f, … which is missing the fundamental has a pitch equal to the f, 2f, 3f, 4f, … series (the brain “adds” the fundamental for the purpose of pitch determination

500 Hz + 750 Hz together, followed by the 250 Hz fundamental

900 Hz + 1200 Hz together, followed by the 300 Hz fundamental

700 Hz + 1050 Hz together, followed by the 350 Hz fundamental


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500 Hz + 750 Hz (minor third)has the same pitch as 250 Hz

an octave above (x 2)

BUT

750 Hz + 1000 Hz has the same pitch as 250 Hz

an octave and a fifth above (x 3)


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note D (minor third)

note D minus fundamental

note D minus fundamental and 2nd harmonic


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Aural harmonics (minor third)

sin(2p 50 t)

sin(2p 50 t)+ 0.2 sin(2p 100 t) +0.1 sin(2p 150 t) +…

extra frequencies

“aural harmonics”

400Hz, 400Hz+802Hz, 400Hz+1202Hz


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300Hz+400Hz, (minor third)

300Hz+400Hz=700Hz, 702Hz,

300Hz+2 400Hz=1100Hz, 1102Hz

rising

fixed

lowering


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Shepard tones (minor third)


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Sound localization (minor third)

How do we know where the sound is coming from ?

  • interaural level differences (ILD)

  • interaural time differences (ITD)

  • head-related transfer function (HRTF)

http://www.aip.org/pt/nov99/locsound.html


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Interaural level difference: (minor third)

one ear will be on the shadow cast by the head

we can detect even 0.5 dB in ILD

diffraction makes it ineffective at low frequencies


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300 Hz: (minor third)

2000 Hz:


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Interaural time difference: peaks and through will arrive at ears at different times

t ~ L/v ~ (0.15 m)/(340m/s) ~ 0.0005 s

difference in arrival time

distance between ears

much shorter than synaptic delays !


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Phase ambiguity: ears at different times

l/2=10 cm, f=340 m/s /0.2 m = 1700 Hz

distance between ears


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Artificial sounds and recording including ILD and ITD give a sense of localization but with the source inside the head


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Head-related transfer function: includes the reflection, refraction and diffraction from ears, chest, head, …




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Aside: since we are talking about auditory illusions outside the head

Tritone paradox:

Are the tones going up or down ?

What are they saying ?


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Precedence effect outside the head

The source appears to be entirely on the direction of the first (direct or reflected) sound to arrive

sound appears to come entirely from the blue speaker


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