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Source: http://www.doksinet 24.963 Linguistic Phonetics The acoustics of vowels 1 Source: http://www.doksinet • No class on Tuesday 10/13 (Tuesday is a Monday) Readings: • Johnson chapter 6 (for this week) • Liljencrants & Lindblom (1972) (for next week) Assignment: • Modeling lip-rounding, due 10/15 2 Source: http://www.doksinet Nelson Education. All rights reserved This content is excluded from our Creative Commons license For more information, see http:// ocw.mitedu/help/faq-fair-use/ 3 Source: http://www.doksinet F2 (Hz) 200 300 i 400 u I Ω F1 (Hz) 500 ε c 600 Q 700 800 2500 2000 A 1500 1000 Image by MIT OCW. Adapted from Peter Ladefoged. A Course in Phonetics 5th ed Berlin, Germany: Heinle, 2005 ISBN: 9781413006889. Available at: https://wwwphoneticsuclaedu/course/contentshtml 4 Source: http://www.doksinet The Acoustics of Vowels Source-Filter models: • Source: voicing (usually) • Filter
characteristics can be given a basic but useful analysis using simple tube models. • Tube models can be supplemented by perturbation theory for approximate analysis of the effects of wide constrictions. 5 Source: http://www.doksinet Low vowels [A, a, œ] • Pharyngeal constriction The shape of the vocal tract in the vowel [ ɑ] as in father schematized as two tubes. Image by MIT OCW. • • • Since the back tube is much narrower than the front tube, each can reasonably be approximated by a tube closed at one end and open at the other. The resonances of the combined tubes deviate from the values we would calculate for these configurations in isolation because the resonators are acoustically coupled. The degree of coupling depends on the difference in cross-sectional areas. 6 Source: http://www.doksinet Low vowels [A, a, œ] Ab (2n −1)c Fn = 4L Af lb lf Image by MIT OCW. Adapted from Johnson, Keith. Acoustic and Auditory Phonetics
Malden, MA: Blackwell Publishers, 1997. ISBN: 9780631188483 5 € nomogram Frequency (kHz) 4 F3 3 2 F2 Front cavity resonances 1 0 Back cavity resonances F1 0 2 4 6 8 10 12 14 16 Back cavity length (cm) Image by MIT OCW. Adapted from Johnson, Keith. Acoustic and Auditory Phonetics Malden, MA: Blackwell Publishers, 1997. ISBN: 9780631188483 7 Source: http://www.doksinet Non-low vowels (e.g [i, e]) • Short constriction in the mouth b c b c Ab Ac d Af d lb a a Image by MIT OCW. Adapted from Ladefoged, Peter. Elements of Acoustic Phonetics 2nd ed. Chicago, IL: University of Chicago Press, 1996 lc lf Image by MIT OCW. Adapted from Johnson, Keith. Acoustic and Auditory Phonetics Malden, MA: Blackwell Publishers, 1997. ISBN: 9780631188483 • The back cavity can be approximated by a tube closed at both ends. • The front cavity is approximated by a tube closed at one end. € • Neglects coupling. The degree of coupling depends on the
cross-sectional area of the constriction. € • How do we account for the F1 of high vowels? nc Fn = 2L (2n −1)c Fn = 4L 8 Source: http://www.doksinet Helmholtz resonators b c b c Ab Ac d Af d lb a a lc lf Image by MIT OCW. Adapted from Johnson, Keith. Acoustic and Auditory Phonetics Malden, MA: Blackwell Publishers, 1997. ISBN: 9780631188483 Image by MIT OCW. Adapted from Ladefoged, Peter. Elements of Acoustic Phonetics 2nd ed. Chicago, IL: University of Chicago Press, 1996 • The back cavity and the constriction together form a resonant system called a Helmholtz resonator. • If the length of the constriction is short, the air in it vibrates as a mass on the ‘spring’ formed by the air in the back cavity. c Ac c Ac • Resonant frequency, f = = 2π Vlc 2π Ab lb lc 9 Source: http://www.doksinet Non-low vowels - nomogram Ab lb 5 Frequency (kHz) lc Af lf Image by MIT OCW. Adapted from Johnson, Keith. Acoustic and
Auditory Phonetics Malden, MA: Blackwell Publishers, 1997. ISBN: 9780631188483 4 F3 3 2 front cavity (2n −1)c Fn = 4L back cavity nc Fn = 2L F2 Front cavity resonances 1 0 Ac Back cavity resonances F1 0 2 4 6 8 10 12 14 16 Back cavity length (cm) € back cavity + constriction Ac c f = € 2π Ab lb lc • How would you model a mid vowel? Image by MIT OCW. Adapted from Johnson, Keith. Acoustic and Auditory Phonetics Malden, MA: Blackwell Publishers, 1997. ISBN: 9780631188483 10 Source: http://www.doksinet Perturbation Theory (Chiba and Kajiyama 1941) • Constriction near a point of maximum velocity (Vn) lowers the associated formant frequency. • Constriction near a point of maximum pressure raises the associated formant frequency. V1 V3' V3 F1 V3'' F3 V3' V1 V3 V3'' V2' V2 V4' V4 V4'' F2 V4''' F4 V4' V2 V2' V4 V4''
V4''' Image by MIT OCW. Adapted from Johnson, Keith. Acoustic and Auditory Phonetics Malden, MA: Blackwell Publishers, 1997. Based on Chiba and Kajiyama 1941 11 Source: http://www.doksinet Perturbation Theory (Chiba and Kajiyama 1941) • What is the effect of a pharyngeal constriction? • Does this correspond to the tube model above? • How do you raise F2 maximally? V1 V3' V3 F1 V3'' F3 V3' V1 V3 V3'' V2' V2 V4' V4 V4'' F2 V4''' F4 V4' V2 V2' V4 V4'' V4''' Image by MIT OCW. Adapted from Johnson, Keith. Acoustic and Auditory Phonetics Malden, MA: Blackwell Publishers, 1997. Based on Chiba and Kajiyama 1941 12 Source: http://www.doksinet Perturbation Theory vs. two-tube models • Our simple tube models ignore acoustic coupling and are therefore most valid where constrictions are narrow. • Perturbation theory accounts for
the effects of small perturbations of a uniform tube, and thus is most accurate for open constrictions. • Mrayati et al (1988): perturbation theory is generally valid for constrictions greater than 0.8 cm2, and two-tube models are valid for a constriction of 0.05 cm2 or less, with a transitional region in between. • Mrayati, Carré & Guérin (1988). Distinctive regions and modes Speech Communication 7, 257-286. 13 Source: http://www.doksinet American English [ɹ] • American English [ɹ] is characterized by an exceptionally low F3 (<2000 Hz). Reproduced from Espy-Wilson, Carol Y., Suzanne E Boyce, Michel Jackson, Shrikanth Narayanan, and Abeer Alwan "Acoustic modeling of American English/r." The Journal of the Acoustical Society of America 108, no 1 (2000): 343-356. doi: https://doiorg/101121/1429469, with the permission of the Acoustical Society of America 14 Source: http://www.doksinet • American English [ɹ] is produced in a variety
of ways across speakers and contexts (Alwan et al 1997 JASA, Westbury et al 1998, Speech Comm.) • A basic distinction that is often made: ‘bunched’ vs. ‘retroflex’ – But there appears to be a continuum of variants. Reproduced from Narayanan, Shrikanth S., Abeer A Alwan, and Katherine Haker "Toward articulatory-acoustic models for liquid approximants based on MRI and EPG data. Part I The laterals" The Journal of the Acoustical Society of America 101, no. 2 (1997): 1064-1077 doi: https://doiorg/101121/1418030, with the permission of the Acoustical Society of America. 15 Source: http://www.doksinet Perturbation Theory (Chiba and Kajiyama 1941) A nice story about Am. Eng [®] • Three constriction: labial (lip protrusion/rounding), palatal (bunching or retroflexion), and pharyngeal. • All 3 are near velocity maxima for F3, hence very low F3. • But Espy-Wilson et al (2000) argue actual constrictions are in the wrong place V1 V3'
V3 F1 V3'' F3 V3' V1 V3 V3'' V2' V2 V4' V4 V4'' F2 V4''' F4 V4' V2 V2' V4 V4'' V4''' Image by MIT OCW. Adapted from Johnson, Keith. Acoustic and Auditory Phonetics Malden, MA: Blackwell Publishers, 1997. Based on Chiba and Kajiyama 1941 16 Source: http://www.doksinet Espy-Wilson et al (2000) argue from MRI data that: • Actual constrictions are in the wrong places, e.g pharyngeal constriction is too high. • Constrictions are too narrow to apply perturbation theory. • Argue that F3 is a front cavity resonance. • Low due to length (bunched) or sub-lingual cavity (retro) + lip constriction. (How long?) • Or: lip constriction is narrow enough for the front cavity to form a Helmholtz resonator. Reproduced from Narayanan, Shrikanth S., Abeer A Alwan, and Katherine Haker "Toward articulatory-acoustic models for liquid approximants based on
MRI and EPG data. Part I The laterals" The Journal of the Acoustical Society of America 101, no. 2 (1997): 1064-1077 doi: https://doiorg/101121/1418030, with the permission of the Acoustical Society of America. 17 Source: http://www.doksinet Constriction locations and area functions for [i] vowels Story et al (1998), MRI Journal of the Acoustical Society of America. All rights reserved This content is excluded from our Creative Commons license. For more information, see https://ocwmitedu/help/faq-fair-use/ Source: Story, Brad H., Ingo R Titze, and Eric A Hoffman "Vocal tract area functions for an adult female speaker . based on volumetric imaging." The Journal of the Acoustical Society of America 104, no 1 (1998): 471-487 Ladefoged & Maddieson (1996) – mean tongue positions MIT Press. All rights reserved This content is excluded from our Creative Commons license. For more information, see http://ocwmitedu/help/faq-fair-use/ Walter de Gruyter. All rights
reserved This content is excluded from our Creative Commons license. For more information, see http://ocwmitedu/help/faq-fair-use/ Fant (1960), Russian [i] F2 2250 Hz, F3 3200 Hz 18 Source: http://www.doksinet Hillenbrand et al (1995) – Michigan English vowel formants 3200 3000 i 2800 I O F3(Hz) 2600 2400 2200 2000 500 ø E a oU eI œ U u 1000 1500 F2 (Hz) 2000 2500 Courtesy of The Acoustical Society of America. Used with permission Source: Hillenbrand, James, Laura A. Getty, Michael J Clark, and Kimberlee Wheeler. "Acoustic characteristics of American English vowels" The Journal of the Acoustical society of America 97, no. 5(1995): 3099-3111 Source: http://www.doksinet Lip rounding • Lip-rounding also involves lip protrusion so it both lengthens the vocal tract and introduces a constriction at the lips. • Perturbation theory: All formants have a velocity maximum at the lips, so a constriction at
the lips should lower all formants. • Lengthening the vocal tract also lowers formants. • Tube models: The effect of a constriction at the lips is equivalent to lengthening the front cavity. Protrusion actually lengthens the front cavity. • This lowers the resonances of the front cavity - in front vowels the lowest front cavity resonance is usually F3, in back vowels it is F2. 20 Source: http://www.doksinet Lip rounding • Tube models 2: Fant (1960) suggests the front cavity plus lip constriction can form a helmholtz resonator. 21 Source: http://www.doksinet Fant’s (1960) nomograms • A more complex tube model for vowels: Area A cm2 14 12 A = Amin*cosh2 (X-Xmin)/h h = 4.75 / arcosh (8/Amin)1/2 l1/A1 = 1/4 10 8 6 Amin = 0.25 cm2 4 Xmin = 10.5 cm 2 0 X 16 14 12 10 8 6 4 2 0 X = Constriction coordinate in cm from glottis Image by MIT OCW. Based on Fant, Gunnar. Acoustic Theory of Speech Production The Netherlands: Mouton De Gruyter,
1960 22 Source: http://www.doksinet Nomogram showing variation in constriction location and lip-rounding narrow constriction (Amin = 0.65 cm2) Curve L1 cm A1 cm2 c/s 5000 1 2 3 4 5 Amin = 0.65cm2 4500 4000 F5 3500 F4 3000 2500 2000 1500 1000 750 500 8.0 6.0 2.0 0.65 0.16 0 1 1 1 1 F3 F2 F1 0 cm from lip unrounded -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 opening rounded -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 18 16 14 12 10 8 6 4 2 0 -2 cm from glottis 20 Axial coordinate of the tongue constriction center. 1 2 3 4 5< Image by MIT OCW. Based on Fant, Gunnar. Acoustic Theory of Speech Production The Netherlands: Mouton De Gruyter, 1960 23 Source: http://www.doksinet Nomogram showing variation in constriction location and lip-rounding wider constriction (Amin = 2.5 cm2) Curve L1 cm A1 cm2 c/s 5000 4500 4000 F5 3500 F4 3000 2500 2000 1500 1000 750 500 1 2 3 4 5 Amin = 2.6 cm2 8.0 6.0 2.0 0.65 0.16 0 1 1 1 1 F3 F2
F1 0 cm from lip unrounded -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 opening rounded -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 18 16 14 12 10 8 6 4 2 0 -2 cm from glottis 20 Axial coordinate of the tongue constriction center. 1 2 3 4 5 Image by MIT OCW. Based on Fant, Gunnar. Acoustic Theory of Speech Production The Netherlands: Mouton De Gruyter, 1960 24 Source: http://www.doksinet Nomogram showing variation in constriction location and degree. Amin = 0.32 cm2 Amin = 1.3 cm2 c/s Amin = 5.0 cm2 5000 4500 4000 F5 3500 F4 3000 2500 2000 1500 1000 750 500 Curve L1 cm A1 cm Amin cm2 1 2 3 0 0 0 8.0 6.0 2.0 0.32 1.3 5.0 F3 F2 F1 0 cm from lip unrounded -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 opening state 18 16 14 12 10 8 6 4 2 0 -2 cm from glottis 20 Axial coordinate of the tongue constriction center. 1 2 3 Image by MIT OCW. 25 Source: http://www.doksinet MIT OpenCourseWare https://ocw.mitedu 24.915 /
24963 Linguistic Phonetics Fall 2015 For information about citing these materials or our Terms of Use, visit: https://ocw.mitedu/terms
characteristics can be given a basic but useful analysis using simple tube models. • Tube models can be supplemented by perturbation theory for approximate analysis of the effects of wide constrictions. 5 Source: http://www.doksinet Low vowels [A, a, œ] • Pharyngeal constriction The shape of the vocal tract in the vowel [ ɑ] as in father schematized as two tubes. Image by MIT OCW. • • • Since the back tube is much narrower than the front tube, each can reasonably be approximated by a tube closed at one end and open at the other. The resonances of the combined tubes deviate from the values we would calculate for these configurations in isolation because the resonators are acoustically coupled. The degree of coupling depends on the difference in cross-sectional areas. 6 Source: http://www.doksinet Low vowels [A, a, œ] Ab (2n −1)c Fn = 4L Af lb lf Image by MIT OCW. Adapted from Johnson, Keith. Acoustic and Auditory Phonetics
Malden, MA: Blackwell Publishers, 1997. ISBN: 9780631188483 5 € nomogram Frequency (kHz) 4 F3 3 2 F2 Front cavity resonances 1 0 Back cavity resonances F1 0 2 4 6 8 10 12 14 16 Back cavity length (cm) Image by MIT OCW. Adapted from Johnson, Keith. Acoustic and Auditory Phonetics Malden, MA: Blackwell Publishers, 1997. ISBN: 9780631188483 7 Source: http://www.doksinet Non-low vowels (e.g [i, e]) • Short constriction in the mouth b c b c Ab Ac d Af d lb a a Image by MIT OCW. Adapted from Ladefoged, Peter. Elements of Acoustic Phonetics 2nd ed. Chicago, IL: University of Chicago Press, 1996 lc lf Image by MIT OCW. Adapted from Johnson, Keith. Acoustic and Auditory Phonetics Malden, MA: Blackwell Publishers, 1997. ISBN: 9780631188483 • The back cavity can be approximated by a tube closed at both ends. • The front cavity is approximated by a tube closed at one end. € • Neglects coupling. The degree of coupling depends on the
cross-sectional area of the constriction. € • How do we account for the F1 of high vowels? nc Fn = 2L (2n −1)c Fn = 4L 8 Source: http://www.doksinet Helmholtz resonators b c b c Ab Ac d Af d lb a a lc lf Image by MIT OCW. Adapted from Johnson, Keith. Acoustic and Auditory Phonetics Malden, MA: Blackwell Publishers, 1997. ISBN: 9780631188483 Image by MIT OCW. Adapted from Ladefoged, Peter. Elements of Acoustic Phonetics 2nd ed. Chicago, IL: University of Chicago Press, 1996 • The back cavity and the constriction together form a resonant system called a Helmholtz resonator. • If the length of the constriction is short, the air in it vibrates as a mass on the ‘spring’ formed by the air in the back cavity. c Ac c Ac • Resonant frequency, f = = 2π Vlc 2π Ab lb lc 9 Source: http://www.doksinet Non-low vowels - nomogram Ab lb 5 Frequency (kHz) lc Af lf Image by MIT OCW. Adapted from Johnson, Keith. Acoustic and
Auditory Phonetics Malden, MA: Blackwell Publishers, 1997. ISBN: 9780631188483 4 F3 3 2 front cavity (2n −1)c Fn = 4L back cavity nc Fn = 2L F2 Front cavity resonances 1 0 Ac Back cavity resonances F1 0 2 4 6 8 10 12 14 16 Back cavity length (cm) € back cavity + constriction Ac c f = € 2π Ab lb lc • How would you model a mid vowel? Image by MIT OCW. Adapted from Johnson, Keith. Acoustic and Auditory Phonetics Malden, MA: Blackwell Publishers, 1997. ISBN: 9780631188483 10 Source: http://www.doksinet Perturbation Theory (Chiba and Kajiyama 1941) • Constriction near a point of maximum velocity (Vn) lowers the associated formant frequency. • Constriction near a point of maximum pressure raises the associated formant frequency. V1 V3' V3 F1 V3'' F3 V3' V1 V3 V3'' V2' V2 V4' V4 V4'' F2 V4''' F4 V4' V2 V2' V4 V4''
V4''' Image by MIT OCW. Adapted from Johnson, Keith. Acoustic and Auditory Phonetics Malden, MA: Blackwell Publishers, 1997. Based on Chiba and Kajiyama 1941 11 Source: http://www.doksinet Perturbation Theory (Chiba and Kajiyama 1941) • What is the effect of a pharyngeal constriction? • Does this correspond to the tube model above? • How do you raise F2 maximally? V1 V3' V3 F1 V3'' F3 V3' V1 V3 V3'' V2' V2 V4' V4 V4'' F2 V4''' F4 V4' V2 V2' V4 V4'' V4''' Image by MIT OCW. Adapted from Johnson, Keith. Acoustic and Auditory Phonetics Malden, MA: Blackwell Publishers, 1997. Based on Chiba and Kajiyama 1941 12 Source: http://www.doksinet Perturbation Theory vs. two-tube models • Our simple tube models ignore acoustic coupling and are therefore most valid where constrictions are narrow. • Perturbation theory accounts for
the effects of small perturbations of a uniform tube, and thus is most accurate for open constrictions. • Mrayati et al (1988): perturbation theory is generally valid for constrictions greater than 0.8 cm2, and two-tube models are valid for a constriction of 0.05 cm2 or less, with a transitional region in between. • Mrayati, Carré & Guérin (1988). Distinctive regions and modes Speech Communication 7, 257-286. 13 Source: http://www.doksinet American English [ɹ] • American English [ɹ] is characterized by an exceptionally low F3 (<2000 Hz). Reproduced from Espy-Wilson, Carol Y., Suzanne E Boyce, Michel Jackson, Shrikanth Narayanan, and Abeer Alwan "Acoustic modeling of American English/r." The Journal of the Acoustical Society of America 108, no 1 (2000): 343-356. doi: https://doiorg/101121/1429469, with the permission of the Acoustical Society of America 14 Source: http://www.doksinet • American English [ɹ] is produced in a variety
of ways across speakers and contexts (Alwan et al 1997 JASA, Westbury et al 1998, Speech Comm.) • A basic distinction that is often made: ‘bunched’ vs. ‘retroflex’ – But there appears to be a continuum of variants. Reproduced from Narayanan, Shrikanth S., Abeer A Alwan, and Katherine Haker "Toward articulatory-acoustic models for liquid approximants based on MRI and EPG data. Part I The laterals" The Journal of the Acoustical Society of America 101, no. 2 (1997): 1064-1077 doi: https://doiorg/101121/1418030, with the permission of the Acoustical Society of America. 15 Source: http://www.doksinet Perturbation Theory (Chiba and Kajiyama 1941) A nice story about Am. Eng [®] • Three constriction: labial (lip protrusion/rounding), palatal (bunching or retroflexion), and pharyngeal. • All 3 are near velocity maxima for F3, hence very low F3. • But Espy-Wilson et al (2000) argue actual constrictions are in the wrong place V1 V3'
V3 F1 V3'' F3 V3' V1 V3 V3'' V2' V2 V4' V4 V4'' F2 V4''' F4 V4' V2 V2' V4 V4'' V4''' Image by MIT OCW. Adapted from Johnson, Keith. Acoustic and Auditory Phonetics Malden, MA: Blackwell Publishers, 1997. Based on Chiba and Kajiyama 1941 16 Source: http://www.doksinet Espy-Wilson et al (2000) argue from MRI data that: • Actual constrictions are in the wrong places, e.g pharyngeal constriction is too high. • Constrictions are too narrow to apply perturbation theory. • Argue that F3 is a front cavity resonance. • Low due to length (bunched) or sub-lingual cavity (retro) + lip constriction. (How long?) • Or: lip constriction is narrow enough for the front cavity to form a Helmholtz resonator. Reproduced from Narayanan, Shrikanth S., Abeer A Alwan, and Katherine Haker "Toward articulatory-acoustic models for liquid approximants based on
MRI and EPG data. Part I The laterals" The Journal of the Acoustical Society of America 101, no. 2 (1997): 1064-1077 doi: https://doiorg/101121/1418030, with the permission of the Acoustical Society of America. 17 Source: http://www.doksinet Constriction locations and area functions for [i] vowels Story et al (1998), MRI Journal of the Acoustical Society of America. All rights reserved This content is excluded from our Creative Commons license. For more information, see https://ocwmitedu/help/faq-fair-use/ Source: Story, Brad H., Ingo R Titze, and Eric A Hoffman "Vocal tract area functions for an adult female speaker . based on volumetric imaging." The Journal of the Acoustical Society of America 104, no 1 (1998): 471-487 Ladefoged & Maddieson (1996) – mean tongue positions MIT Press. All rights reserved This content is excluded from our Creative Commons license. For more information, see http://ocwmitedu/help/faq-fair-use/ Walter de Gruyter. All rights
reserved This content is excluded from our Creative Commons license. For more information, see http://ocwmitedu/help/faq-fair-use/ Fant (1960), Russian [i] F2 2250 Hz, F3 3200 Hz 18 Source: http://www.doksinet Hillenbrand et al (1995) – Michigan English vowel formants 3200 3000 i 2800 I O F3(Hz) 2600 2400 2200 2000 500 ø E a oU eI œ U u 1000 1500 F2 (Hz) 2000 2500 Courtesy of The Acoustical Society of America. Used with permission Source: Hillenbrand, James, Laura A. Getty, Michael J Clark, and Kimberlee Wheeler. "Acoustic characteristics of American English vowels" The Journal of the Acoustical society of America 97, no. 5(1995): 3099-3111 Source: http://www.doksinet Lip rounding • Lip-rounding also involves lip protrusion so it both lengthens the vocal tract and introduces a constriction at the lips. • Perturbation theory: All formants have a velocity maximum at the lips, so a constriction at
the lips should lower all formants. • Lengthening the vocal tract also lowers formants. • Tube models: The effect of a constriction at the lips is equivalent to lengthening the front cavity. Protrusion actually lengthens the front cavity. • This lowers the resonances of the front cavity - in front vowels the lowest front cavity resonance is usually F3, in back vowels it is F2. 20 Source: http://www.doksinet Lip rounding • Tube models 2: Fant (1960) suggests the front cavity plus lip constriction can form a helmholtz resonator. 21 Source: http://www.doksinet Fant’s (1960) nomograms • A more complex tube model for vowels: Area A cm2 14 12 A = Amin*cosh2 (X-Xmin)/h h = 4.75 / arcosh (8/Amin)1/2 l1/A1 = 1/4 10 8 6 Amin = 0.25 cm2 4 Xmin = 10.5 cm 2 0 X 16 14 12 10 8 6 4 2 0 X = Constriction coordinate in cm from glottis Image by MIT OCW. Based on Fant, Gunnar. Acoustic Theory of Speech Production The Netherlands: Mouton De Gruyter,
1960 22 Source: http://www.doksinet Nomogram showing variation in constriction location and lip-rounding narrow constriction (Amin = 0.65 cm2) Curve L1 cm A1 cm2 c/s 5000 1 2 3 4 5 Amin = 0.65cm2 4500 4000 F5 3500 F4 3000 2500 2000 1500 1000 750 500 8.0 6.0 2.0 0.65 0.16 0 1 1 1 1 F3 F2 F1 0 cm from lip unrounded -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 opening rounded -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 18 16 14 12 10 8 6 4 2 0 -2 cm from glottis 20 Axial coordinate of the tongue constriction center. 1 2 3 4 5< Image by MIT OCW. Based on Fant, Gunnar. Acoustic Theory of Speech Production The Netherlands: Mouton De Gruyter, 1960 23 Source: http://www.doksinet Nomogram showing variation in constriction location and lip-rounding wider constriction (Amin = 2.5 cm2) Curve L1 cm A1 cm2 c/s 5000 4500 4000 F5 3500 F4 3000 2500 2000 1500 1000 750 500 1 2 3 4 5 Amin = 2.6 cm2 8.0 6.0 2.0 0.65 0.16 0 1 1 1 1 F3 F2
F1 0 cm from lip unrounded -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 opening rounded -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 18 16 14 12 10 8 6 4 2 0 -2 cm from glottis 20 Axial coordinate of the tongue constriction center. 1 2 3 4 5 Image by MIT OCW. Based on Fant, Gunnar. Acoustic Theory of Speech Production The Netherlands: Mouton De Gruyter, 1960 24 Source: http://www.doksinet Nomogram showing variation in constriction location and degree. Amin = 0.32 cm2 Amin = 1.3 cm2 c/s Amin = 5.0 cm2 5000 4500 4000 F5 3500 F4 3000 2500 2000 1500 1000 750 500 Curve L1 cm A1 cm Amin cm2 1 2 3 0 0 0 8.0 6.0 2.0 0.32 1.3 5.0 F3 F2 F1 0 cm from lip unrounded -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 opening state 18 16 14 12 10 8 6 4 2 0 -2 cm from glottis 20 Axial coordinate of the tongue constriction center. 1 2 3 Image by MIT OCW. 25 Source: http://www.doksinet MIT OpenCourseWare https://ocw.mitedu 24.915 /
24963 Linguistic Phonetics Fall 2015 For information about citing these materials or our Terms of Use, visit: https://ocw.mitedu/terms
