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This 42 page Class Notes was uploaded by Petra Hansen on Friday September 18, 2015. The Class Notes belongs to SPA 3011 at University of Florida taught by James Harnsberger in Fall. Since its upload, it has received 16 views. For similar materials see /class/206798/spa-3011-university-of-florida in OTHER at University of Florida.
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Date Created: 09/18/15
SPA 3011 Tube Models for Consonants Introduction Consonant manner classes Fricatives Voiced V 6 Z 5 Voiceless s 9 S U Nasals III II 1 Stops VOIced b d g Voiceless p t k Affricates Voiced d3 Voiceless tj Approximants 1 J W U Introduction Vocal tracts for vowel production have been modeled as a tube that is closed at one end the glottis and open at the other lips Uniform crosssectional area for o Constriction at front or back or at lips for other vowels Vocal tracts for consonant production can be modeled as a tube with more significant constrictions Stop Affricate gt Fricative gt Approximant Nasal Fricatives Fricatives can be modeled as a I i e with a severe constriction that is narrow enough to accelerate airflow as a et resulting in eddies Eddies Rotating fluctuations in air pressure 0 Reynold s number The critical flow velocity at which turbulence takes place Jet Eddies gt 99 9y 7 gt I constriction I Fricatives Reynold s number Re v h 1 v velocity of air flow v coefficient of viscosity of air 015 cmZs h diameter of opening Critical Reynold s number for speech noise is gt 1800 Fricatives Reynold s number formula can also be expressed in terms of the volume velocity of the airflow volume of air traveling past a point at a certain moment in time cm3s U vA where U is volume velocity Thus Re UhAv U in turn depends on constriction size and subglottal pressure PS U kA VPs Volume velocities for fricatives typically range between 100 1000 cm3s Frequency Characteristics of Fricatives Noise generated by fricatives is not white noise some frequency bands have more energy than others Frequency Characteristics of Fricatives Length of front cavity determines the fre uenc characteristics of different fricatives C MW Ll WW e if Amplitude Characteristics of Fricatives The amplitude of the turbulence is a function of constriction area Solid line obstacle turbulence Dotted line glottal turbulence 2039 Ax02cmz Relative Level dB O 0 0 ll 2 03 04 03 Area of supraglottal constriction cmll Nasals Nasals possess Nasal formants Nasal quotantiformantsquot or zeros v I r t WM y hr 1 I l I quot quotHum 3954 391 4 I1 H w 10 NasalResonances Nasal N is the simplest to describe and can be modeled as a quarter wave resonator like 9 based on a uniform tube from the glottis closed to the nares Sizeshape of nares can result in nose a Helmholtz resonator Based on a tube length of 215 cm quchi Nasals Nasals in English m n 13 involve a sidebranch resonator Sidebranch resonators introduce zeros antiresonances due to impedance opposition to sound transmission Frequency components in the source signal at or near the natural frequencies of the closed oral cavity are absorbed The frequency of the zeros correspond to resonant frequencies of the oral cavity in a given configuration The longer the oral cavity eg bilabials the lower the frequency of the zeros Bilabial 750 1250 Hz Alveolar 1450 2200 Hz Vdan3000Hz 11086 I mouth l XIImud 12 Nasals Nasals with a side branch resonator formants have nasal formants based on cavity length from the uvula t0 the nares 11086 1250m N1 250 Hz I mouth N2 1000 Hz g N3 2000 Hz 3 N4 3000 Hz a Nasals The characteristic low amplitude of nasal murmur is due to Damping nasal sounds have greater surface area hence walls of vocal tract absorb more sound than for nonnasals Zeros absorb acoustic energy 39 I l j 39l I ll 39 392 quotI quotquot r u 39 i lquotl39l39l395lblttllllalllaih39l I w laml i lglfrfWquot Iquot quotH 3391 39J 1 ll39 391 l l 39quotu39uquot39t 39 14 Stops Involve total constriction of the vocal tract Air pressure builds up behind oostructlon and it abruptly released resulting in a short noise segment Called burst or transient khu Q 1llllllp39llj39 s llllllmllll Stops Stops are also characterized by a Iowifrequency Fl transition in a vowe stop vowe sequence Fl falls during the vowel to stop transition and rises during the stop to vowe transition ii i iii aw Y i ii Intensity Frequency Stop Voicing Voiced stops typicaHy have re ative to v01ce ess stops 1 w M WWW l lwlll lI VW NAH ntenswty Frequency T me Stop Voicing Stops can also be aspirated khu I Intensity Frequency WI 377quot it I i I 1 i ii um 1 Hi M Y 1 yiv iiquot uh1quot W M iquot iii W i I quot v I gmk ufll H 4 1ii M 1 Wit Affricates 39 Affricates are acoustically similar to a stop fricative sequence although the frication interval of affricates differs from that of fricatives in that The rise time time over which noise reaches its full amplitude is shorter in affricates Noise duration tends to be shorter in affricates Us r521 07 Time 3 Approximants Laterals 1 involve bifurcation ofthe airflow along the midline of the tongue 1 involves lowering of F3 w j can be modeled in much the same way as vowels quuchlel Laterals Laterals also involve a sideebranch resonator formed by the tongue blade Zero Laterals have highereamplitude acoustic energy in the lower frequencies than in the higher frequencies ala on ll 3 lllllll lllllllllm lll 5 n men quuumYle Approximants F2 frequency High Mid LOW High 1 F3 frequency J W Low r 22 Central Approximants W MM mu awa era aj a 13 w example r example J exam ple MW SPA 3011 SourceFilter Theory of Speech Production Introduction Neutral vocal tracts 9 can be modeled as a tube with uniform cross sectional areas that is closed at one end the glottis and open at the other lips Other vocal tract shapes involve constrictions along their length and can be approximated by connecting together two or more uniform tubes with different crosssectional areas Openclosed tube f c4I 3c4l 5c4l Closedclosed or openopen tube f cZI 3c2l 5c 2 Closednarrow opening tube Helmholtz resonator Low Vowel Example Vocal tract configurations with pharyngeal constriction eg 0 Since the back tube is much narrower than the front tube each can be approximated as a tube closed at one end and open at the other Note that the two tubes are actually acoustically coupled Low Vowel Example GLOTTIS LIPS Low Vowel Example l a lT 39 ll b Recallf c4l 3c4I which holds for and back cavities The front cavity is slightly longer than the back cavity If gt lb so the lowest resonance 1 quot l 39 a F2 is affiliated with the back cavity F1 and F2 are relativel close in fre uenc F1 is higher and F2 lower than those of a Nonlow Vowel Example Vocal tract configurations with a constriction in the middle Tube closed at both ends back cavity Tube closed at one end open at the other front cavity Helmholtz resonator high from wide pharynx tongue cm39ny LIPS GLOTTIS l l open at closed m both one end Helmholz resonator Nonlow Vowel Example Helmholz resonator an arrangement in which a small body of air acts as a F1 E fAg piston oscillating against a 27 Allll2 larger enclosed body of air back tube constriction The natural resonant A frequency of the Helmholz t2 resonator depends on the A relative volumes of air in the 1 back cavity and in the I1 2 constriction produces an extralow resonance low F1 Nonlow Vowel Example 4 Ib gt LN i back cavity r Helmholtz resonator f c2l 3c2l F12 Ag 27 A112 So the resonances of i come from three different parts of the vocal tract one very low resonance F1 from the Helmholz resonator two high resonances one from the back tube closed at both ends F2 one from the front tube closed at one end open at the other F3 8 Perturbation Theory The relation between the configurations and resonances of the vocal tract can also be examined in terms of formantfrequency changes due to perturbations local constrictions along the length of the tract Consider a singletube model but instead ofa tube with a uniform cross sectional area as for 9 consider the acoustic consequences of introducing a perturbation The effect of the perturbation on formant frequency F depends on whether the constriction is near a velocity node or antinode Node volume velocity maximum pressure minimum Antinode volume velocity minimum pressure maximum Perturbation Theory i I F1 Chm F2 300 Fain41 F2 F3 Uquot3 U3 U Node Constrict a node lower a N Node A and C corresponding formant frequency A Antlnode B and D 0 Constrict an antinode raise a 1392 Formants corresponding formant frequency Perturbation Theory Labial constriction rounded vowels lowers F1 and F2 bc tube is constricted at volume velocity maximum node A Pharyngeal constriction 2 low vowel lowers F2 bc tube is constricted at volume velocity maximum for F2 node C Palatal constriction 2 front vowel raises F2 bc tube is constricted at volume velocity minimum for F2 antinode B Perturbation Theory Other Locations for constriction Fraction of Length of vocal tract glottis O pharynx 14 uvula 12 velum 23 palate 34 alveOIum 78 lips 44 ALVEOLAR VNASAL CAVITY RIDGE I HARD PALATE FT PALATE LIP I 39ifuvu LA LPHAHYNX TONGUE EPIGLOTTS Tip LARYNX 839 OESOPHAGUS Front Typical Formants for Monopthongal Vowels Male 4000 3000 2000 1000 H2 MwinMInwmirmmwmm i I 8 351 9 aw mm Wu n M I 4 w mum me u I r w I I x I v I I w I I x ms Typical Formants for Monopthongal Vowels Female 4000 1000 ll w W gt alllWlllllll ml WW l x I l x Typical Formant Values for Monopthongal Vowels Men Women Children Vowel F1 F2 F3 F1 F2 F3 F1 F2 F3 1 270 2300 3000 300 2800 3300 370 3200 3700 1 400 2550 430 2500 3100 530 2750 3600 E 530 1850 00 2350 00 3550 a 660 1700 2400 850 2050 2850 1000 2300 3300 a 730 1100 2450 850 1200 2800 1030 1350 3200 570 850 2400 590 900 2700 680 050 3200 11 MO 1000 7750 A70 1150 7 nn 56 1 00 33910 U 300 850 2250 370 950 2650 430 l 150 3250 A 6110 1 00 760 1400 2800 850 1600 3350 3 A90 1350 1700 500 1650 1950 560 1650 2150 Mean 500 1420 2400 575 1 700 2800 670 1 900 3250 F2F1 284 296 284 F3F2 169 1 65 1 71 From Peterson and Barney 1952
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