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Answer: •If you extend the lines of sight (shown with darker lines), you'll notice that this creates 2 new intersections (see red dots). • These intersections are 'false matches', and represent the correspondence-problem solution that your visual system arrived at. • In other words, there are 2 possible sets of matches, shown by the blue and red dots. While either is possible, the red (and incorrect) match was picked. (You can think about why that match might be preferred.) 2 nail illusion • You view a pair of nails, one in front of the other in depth. However, you perceive 2 nails, side-by-side, at the same depth. 3/23/2006 1 3/23/2006 2 Fletcher-Munson Curves 3/23/2006 3 3/23/2006 Characterizing simple and complex sounds The information that reaches the ear does not • The frequency composition of a sound is called its spectrum. • When sounds originate from multiple sources, the individual waveforms combine so that a single complex waveform reaches the ear. 4 separate sounds from different sources. • A pure tone contains only one frequency (sine wave). • Frequencies in a sound that are integer multiples of some fundamental frequency are called harmonics. 3/23/2006 5 3/23/2006 6 1 How do we analyze complex waveforms? Complex Sounds • Simple sounds – Sine waves are simple harmonic motion; pure tone • Complex sounds – Need Fourier analysis and Fourier synthesis 3/23/2006 7 3/23/2006 8 Harmonics: Fourier Analysis and Synthesis Fourier components of a complex tone are multiples of the fundamental frequency • Fourier transformation • Two pure tones whose frequencies are multiples of each other blend into one in our perception, producing a single tone at the fundamental (the lower) frequency – Allows a complex sound wave to be decomposed into constituent sinusoidal frequencies, each an integer multiple of the original’s (fundamental) frequency – Fundamental frequency (or first harmonic) determines the pitch of a complex sound (e.g., a 400 Hz tone and a 500 Hz tone would have a fundamental of 100 Hz) 3/23/2006 9 3/23/2006 10 3/23/2006 11 3/23/2006 12 2 Harmonics: Components of Complex Sound Harmonics (contd.) • Musical instruments hardly ever produce pure tones. – Instead, when you pluck a string on a guitar, it will produce a vibration at some fundamental frequency as well as several multiples (called harmonics). • Our perception of timbre is related to the harmonic composition of a tone. • This is also the basis of a capella singing. 3/23/2006 13 14 Musical Sounds Sound as a psychological experience • Hearing – Loudness is related to amplitude: sounds get louder with an increase in amplitude – Pitch is related to frequency: pitches get higher with an increase in frequency 3/23/2006 3/23/2006 15 • In addition to an increase of pitch with increase in frequency, tones are organized into octave. • Each octave contains seven notes (A, B, C, D, E, F, and G). • Two ‘A’ notes in different octaves sound similar (this similar-sounding quality is called tone chroma). • An ‘A’ note one octave above another note has a fundamental frequency twice that of the lower note (e.g., A4 = 220 Hz, A5 = 440 Hz, A6 = 880 Hz, etc.) 3/23/2006 16 Shepard Scale • One of the most widely used auditory illusions is Shepard's (1964) demonstration of pitch circularity, which has come to be known as the "Shepard Scale" demonstration. • The demonstration uses a cyclic set of discrete complex tones, each composed of 10 partials separated by octave intervals. 3/23/2006 17 3/23/2006 18 3 Shepard Scale Risset Scale • The tones are co-sinusoidally filtered to produce the sound level distribution shown below, and the frequencies of the partials are shifted upward in steps corresponding to a musical semitone (= ~ 6 %). • Another scale that illustrates circularity in pitch judgment is a continuous scale of JeanClaude Risset. 3/23/2006 3/23/2006 19 The Human Ear 3/23/2006 20 Overview of the parts of the ear 21 The ear is a receiver and transducer of 3/23/2006 22 The ear and auditory transduction pressure changes. • The outer ear: Directional collector and amplifier. • The middle ear: Impedance matching and protection. • The inner ear: Spectral (frequency) analysis and transduction. 3/23/2006 23 3/23/2006 24 4 Outer Ear The middle ear • Pinna: – The outer fleshy part of the ear helps focus sound waves • The middle ear cavity is filled with air. • Auditory canal (that part of the ear you're not supposed to put q-tips in): • The Eustachian tube links the middle ear with the nasopharyngeal cavity so that the middle ear can adjust to changes in atmospheric pressure. – Has wax to protect from insects and hairs to keep a constant temperature. also serves to amplify sounds around its resonant frequency (2,000-5,000 Hz). • Tympanic membrane (eardrum): – A taut membrane at the end of the auditory canal that vibrates with the changes in air pressure at the ear 3/23/2006 25 • Ossicles: – Three bones (the smallest bones in the body) that connect the tympanic membrane of the outer ear and the oval window of the inner ear. – The three bones in order are malleus, incus, and stapes. • The ossicles serve to amplify vibrations (about 22x) between the outer ear and inner ear. This is necessary since vibrations in the inner ear travel through fluid which is much more dense than air. 27 • Concentrate vibrations of the large tympanic membrane onto the small footplate of the stapes (an amplification of about 17 times). • Act as a fulcrum and so (because of the way they are hinged) benefit from the lever principle (another amplification of 1.3 times) 3/23/2006 The outer and middle ear are purely mechanical. 28 Inner Ear Transduction and analysis • Cochlea: a coiled liquid-filled structure. begin at the inner ear. – The liquid inside the cochlea vibrates because the stapes pushes on the oval window (at the base of the cochlea). – The cochlea has three layers: • The cochlea is the site at which vibrations of the stapes and inner ear fluid are transduced to neural responses in fibers of the auditory nerve. 3/23/2006 26 The ossicles amplify in two ways: Middle Ear 3/23/2006 3/23/2006 • scala vestibuli, • scala tympany, • and the cochlear partition. • Inside the cochlear partition is the organ of corti, which is the site of auditory transduction. 29 3/23/2006 30 5 The inner ear The cochlea is a coiled tube that resembles a snail shell • Part of the inner ear is concerned with balance (vestibular system). • The part of the inner ear that contains the receptor cells for hearing is the cochlea. 3/23/2006 31 • In humans, the cochlea coils about 2.5 times. • A cross-section through the coiled cochlear tube reveals that the inside is divided into three compartments. 3/23/2006 The organ of Corti • The receptor cells are located in the scala media, on the organ of Corti. • Composition of the fluids in the three compartments is different. 3/23/2006 33 32 3/23/2006 34 The organ of corti • • • • Contains inner hair cells and outer hair cells. Sits on top of the basilar membrane. Is covered by the tectorial membrane. Auditory transduction: – When the basilar membrane moves up and down, the cilia of the outer hair cells (small hair-like projection off of the hair cells) rub against the tectorial membrane. – The bending of the cilia produces and electrical response in the hair cells. • Inner hair cells help amplify vibrations of the basilar membrane. 3/23/2006 35 6