FANT'S MODEL OF THE VOCAL TRACT Model of the vocal ...
TOPIC 2 – FANT’S MODEL OF THE VOCAL TRACT Model of the vocal tract Source-Filter-Radiation Model o Source: Vocal chords o Filter: Vocal tract o Radiation: Lips and nostrils Standing Waves: It occurs when two progressive waves (the incident wave and the reflected wave) of the same frequency and amplitude travel through the same medium in opposite direction. They appear to be still rather than moving, although both waves are moving in opposite directions. Standing waves are the resultant wave (the sum), which is stationary. All tubes (vocal tract or trumpet) can have standing waves. Quarter Wavelength Resonator Only found in an unconstricted tube that is open at one end and closed at the other Wavelength: The distance between the same point on two successive cycles of a tone (from the beginning of one wave to the beginning of the next) Fundamental resonance (formant frequencies) o F = (2k-1)v/4L v = speed of sound (34,000cm/sec – almost constant) L = 17cm (length of vocal tract of a male adult) k = formant o Narrowing or constriction is irrelevant as it only depends on the speed of sound and the length of the tube o E.g. [ɑ], nasals (through the nasal cavity) [m, n, ŋ], straw closed at one end o E.g. tuba (long tube) and piccolo (short tube) therefore low frequency and high frequency o E.g. [ʃ] has a lower frequency than [s] due to the lengthened vocal tract by puckering up o F2 is F1*3, and F3 is F1*5, and so on (odd number of the F1) Helium o Higher formant frequency due to the higher speed (100,000cm/sec) Different vocal tract lengths o Male: 17.5cm, Female: 14.75cm, Infant: 8.75cm Volume Velocity (Pressure): the movement caused by a sound wave of a unit volume of a sound-transmitting medium through a unit area per unit of time. The lateral movement of a standing wave at any one location. All wavelength associated standing waves have a volume velocity which changes from location to location. o Analogous to air flow: particle movement o Volume velocity has a maximum at open end (quarter wavelength resonator) o Pressure has a minimum at open end (quarter wavelength resonator) Sound Pressure: measure of force divided by the area to which the force is applied; measured in dyne/cm2; an ear is a pressure receptor; interchangeable with sound intensity Half Wavelength Resonator Only found in tube when it is either open or closed at both ends
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Fundamental resonance (formant frequencies) o F = kv/2L o E.g. nasal consonants (through the oral cavity), flute, open straw Half wavelength anti-resonator o Anti-resonators of oral cavity resonance for nasals: where the loss of energy takes place [m] = 1000Hz [n] = 1700Hz [ŋ] = 3000Hz Half wavelength anti-resonances o Loss in energy E.g. nasals, nasalized vowels, bagpipes o Anti-resonances and anti-formants: The presence of anti-formants in the vocal tract transfer function. The opposite of formants, anti-formants arise from division of airflow in the vocal tract during production of nasal gestures and can be created when two tubs are in parallel and of difference acoustic conditions. o Wavelength Resonances (Transmission line): The series of resonances associated with standing waves that are generated in a tube. There can be phase changes brought about by the compressibility of air (an inherent physical condition for higher frequencies), which is why there can be high frequency wavelength formant resonances (F1-F4). Governed by the length (L) of a tube. E.g. molecules get out of sync with higher frequency (hitting each other side by side, as demonstrated in class) E.g. cars starting one by one after red to green light
Helmholtz Resonances Helmholtz Resonances (Lumped Element): A resonance brought about by the interplay between a volume of air and a constriction. There cannot be any phase changes which is why Helmholtz resonances or formants can only exist for the lower frequencies (F1, F2) No phase changes = lumped elements o E.g. all trains move together like a subway, unlike cars starting one by one Law of Tubes (e.g. vowels) 1. F2 proportional to back volume (the more front, the higher F2) 2. F1 proportional to constriction (the greater constriction, the lower F1) 3. No constrictions = wavelength 4. All higher frequency cues are not Helmholtz o F3 is proportional to rounding (the rounder, the lower the F3) o F3 and F4 only depend on length and have nothing to do with constriction o F1 and F2 can be Helmholtz or wavelength Formant Amplitudes 1. Cross sectional area of vocal tract o With larger cross sectional area, the greater are the formant amplitudes E.g. infant vs. adult 2. Shape of the vocal tract o A conical (flared) vocal tract
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E.g. [ɑ] will have enhanced high frequency amplitudes compared to [u] Degree of damping o The greater the damping, the lower will be the formant amplitudes o Damping: Any means of dissipating vibration energy within a vibrating system. The action of frictional or dissipative forces on a dynamic system causing the system to lose energy and reduce the amplitude of movement. A highly damped system (such as formants in our nasal cavities) has lower amplitudes than less damped locations such as our oral cavity. Reduction in sound level is independent of frequency. Nature of glottal pulse o Because of the lack of higher frequency energy in the glottal sources, the higher frequency formants are of lower amplitude o Glottal Pulse: A term used in the study of linguistics to describe the variances in voice quality affected by the manipulation of the folds of the vocal cords when speaking. This is shown in the time domain. It defines the harmonic structure in the frequency domain. Formant frequency location o If F1 is lowered, then the higher frequency formants are lower in amplitude Location of constriction in vocal tract o If a constriction coincides with an anti-node in the standing wave pattern, there will be greater damping and therefore a lower amplitude for the formant corresponding to that standing wave pattern E.g. mouse wire demonstration in class – if there is constriction, the wire cannot spin properly
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Fundamental resonance (formant frequencies) o F = kv/2L o E.g. nasal consonants (through the oral cavity), flute, open straw Half wavelength anti-resonator o Anti-resonators of oral cavity resonance for nasals: where the loss of energy takes place [m] = 1000Hz [n] = 1700Hz [ŋ] = 3000Hz Half wavelength anti-resonances o Loss in energy E.g. nasals, nasalized vowels, bagpipes o Anti-resonances and anti-formants: The presence of anti-formants in the vocal tract transfer function. The opposite of formants, anti-formants arise from division of airflow in the vocal tract during production of nasal gestures and can be created when two tubs are in parallel and of difference acoustic conditions. o Wavelength Resonances (Transmission line): The series of resonances associated with standing waves that are generated in a tube. There can be phase changes brought about by the compressibility of air (an inherent physical condition for higher frequencies), which is why there can be high frequency wavelength formant resonances (F1-F4). Governed by the length (L) of a tube. E.g. molecules get out of sync with higher frequency (hitting each other side by side, as demonstrated in class) E.g. cars starting one by one after red to green light
Helmholtz Resonances Helmholtz Resonances (Lumped Element): A resonance brought about by the interplay between a volume of air and a constriction. There cannot be any phase changes which is why Helmholtz resonances or formants can only exist for the lower frequencies (F1, F2) No phase changes = lumped elements o E.g. all trains move together like a subway, unlike cars starting one by one Law of Tubes (e.g. vowels) 1. F2 proportional to back volume (the more front, the higher F2) 2. F1 proportional to constriction (the greater constriction, the lower F1) 3. No constrictions = wavelength 4. All higher frequency cues are not Helmholtz o F3 is proportional to rounding (the rounder, the lower the F3) o F3 and F4 only depend on length and have nothing to do with constriction o F1 and F2 can be Helmholtz or wavelength Formant Amplitudes 1. Cross sectional area of vocal tract o With larger cross sectional area, the greater are the formant amplitudes E.g. infant vs. adult 2. Shape of the vocal tract o A conical (flared) vocal tract
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E.g. [ɑ] will have enhanced high frequency amplitudes compared to [u] Degree of damping o The greater the damping, the lower will be the formant amplitudes o Damping: Any means of dissipating vibration energy within a vibrating system. The action of frictional or dissipative forces on a dynamic system causing the system to lose energy and reduce the amplitude of movement. A highly damped system (such as formants in our nasal cavities) has lower amplitudes than less damped locations such as our oral cavity. Reduction in sound level is independent of frequency. Nature of glottal pulse o Because of the lack of higher frequency energy in the glottal sources, the higher frequency formants are of lower amplitude o Glottal Pulse: A term used in the study of linguistics to describe the variances in voice quality affected by the manipulation of the folds of the vocal cords when speaking. This is shown in the time domain. It defines the harmonic structure in the frequency domain. Formant frequency location o If F1 is lowered, then the higher frequency formants are lower in amplitude Location of constriction in vocal tract o If a constriction coincides with an anti-node in the standing wave pattern, there will be greater damping and therefore a lower amplitude for the formant corresponding to that standing wave pattern E.g. mouse wire demonstration in class – if there is constriction, the wire cannot spin properly
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