24.910 Laboratory Phonology The Theory of Adaptive DispersionLindblom’s Theory of Adaptive DispersionLindblom’s Theory of Adaptive DispersionLindblom’s Theory of Adaptive DispersionLiljencrants & Lindblom (1972)Liljencrants and Lindblom (1972)The vowel spaceWhy do the perceptual dimensions of vowel quality correspond to formant frequencies?Why do the perceptual dimensions of vowel quality correspond to formant frequencies?Why do the perceptual dimensions of vowel quality correspond to F1, F2 (&F3)?The vowel spaceLiljencrants and Lindblom (1972)Liljencrants and Lindblom (1972)Minimizing E - stochastic searchToo many high non-peripheral vowels Too many high non-peripheral vowels Too many high non-peripheral vowels Too many high non-peripheral vowels The ‘corner’ vowels [i, a, u] Too few interior vowelsAlternative measures of distinctivenessAlternative measures of distinctivenessProblems with Adaptive DispersionExtending Adaptive DispersionMIT OpenCourseWare http://ocw.mit.edu24.910 Topics in Linguistic Theory: Laboratory PhonologySpring 2007 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.24.910Laboratory PhonologyThe Theory of Adaptive DispersionImage by MIT OpenCourseWare. Adapted from Liljencrants, Johan, and Bjorn Lindblom. "Numerical Simulation of Vowel Quality Systems: The Role of Perceptual Contrast." Language 48, no. 4 (December 1972): 839-862.Readings for next week: • Steriade (1999), pp. 1-21• Wright (2004).Assignment:• Waveform editing• Common vowel inventories: i u i u i u Lindblom’s Theory of Adaptive Dispersion e o e  o a a a Arabic, Nyangumata, Aleut, etc. Spanish, Swahili, Cherokee, etc. Italian, Yoruba, Tunica, etc. • Unattested vowel inventories: i i  i u e e    a a ɔ• Try to explain why vowel systems are the way they are.• Observation: vowels in an inventory tend to be evenly dispersed through the vowel space (cf. Disner 1984).• Hypothesis: this facilitates efficient communication by minimizing the likelihood of confusing vowels.Lindblom’s Theory of Adaptive Dispersion i u i u i u e o e o a a a Figure by MIT OpenCourseWare. Adapted from Liljencrants, Johan, and Bjorn Lindblom. "Numerical Simulation of Vowel Quality Systems: TheRole of Perceptual Contrast." Language 48, no. 4 (December 1972): 839-862. ɔMELMELkHz500100015007505002502.52.5.51.01.5 .5Second Formant (M2)First Formant (F1)First Formant (F1).75• Try to explain why vowel systems are the way they are.• Observation: vowels in an inventory tend to be evenly dispersed through the vowel space (cf. Disner 1984).• Hypothesis: this facilitates efficient communication by minimizing the likelihood of confusing vowels.• Vowels that are closer in the perceptual space are more easily confused.• Confusions between contrasting sounds impair communication.• So contrasting vowels should be as far apart as possible (dispersion).Lindblom’s Theory of Adaptive DispersionApproach to exploring dispersion hypothesis:• Modeling• Simulation• Comparison of simulation results to impressionistic descriptions of a large sample of vowel inventories.Liljencrants & Lindblom (1972)Liljencrants and Lindblom (1972)• The role of perceptual contrast in predicting vowel inventories.• The perceptual space of articulatorily possible vowels:Figures by MIT OpenCourseWare. Adapted from Liljencrants, Johan, and Bjorn Lindblom. "Numerical Simulation of Vowel Quality Systems: The Role of Perceptual Contrast." Language 48, no. 4 (December 1972): 839-862. MELMELkHz50010001500150020004.03.02.01.52.5 1.01.5 .5Second Formant (M2)Third Formant (F )Third Formant (F3)3MELMELkHz500100015007505002502.52.5.51.01.5 .5Second Formant (M2)First Formant (F1)First Formant (F1).75• Why does the vowel space look like this?¾Why do the dimensions correspond to formant frequencies?¾Why just the first 2-3 formant frequencies?¾Why does the F1-F2 space have this shape?The vowel spaceFigures by MIT OpenCourseWare. Adapted from Liljencrants, Johan, and Bjorn Lindblom. "Numerical Simulation of Vowel Quality Systems: The Role of Perceptual Contrast." Language 48, no. 4 (December 1972): 839-862. MELMELkHz50010001500150020004.03.02.01.52.5 1.01.5 .5Second Formant (M2)Third Formant (F3)Third Formant (F3)MELMELkHz500100015007505002502.52.5.51.01.5 .5Second Formant (M2)First Formant (F1)First Formant (F1).75(cf. Pierrehumbert 2000)Production - we can control formant frequencies.• Given that vowels are produced with a relatively open vocal tract, the properties of these sounds that we can manipulate most easily are:– f0 (pitch) - a source property. The basis for tone contrasts.– formants - filter property - the resonant frequencies of the vocal tract.• Bandwidths and formant intensities generally covary with formant frequencies (Fant 1956).• Varying bandwiths independently would involve changing the stiffness of the vocal tract walls, or the mode of vocal fold vibration. (NB nasalization affects formant bandwidths).Why do the perceptual dimensions of vowel quality correspond to formant frequencies?Perception - we can perceive formant peaks.• f0 is (usually) much lower than formant frequencies.– Resonant frequencies are well represented as peaks in the ouput spectrum.– Exception: soprano singing.• Formant peaks are more robustly perceptible than ‘valleys’because they can rise above background noise.Why do the perceptual dimensions of vowel quality correspond to formant frequencies?Higher formants are not important in vowel quality because they are insufficiently perceptible (especially in noise).• There is less energy in the voice source at higher frequencies.• Our ears are less sensitive to higher frequencies.Why do the perceptual dimensions of vowel quality correspond to F1, F2 (&F3)?0.0050.01 sFrequency in HzIntensity Level in dBLower limit of audibilityUpper limit of hearing-20-10010203040506070809010011012013014015020 100 1K 10K 20KFigure by MIT OpenCourseWare.Figure by MIT OpenCourseWare.Figure by MIT OpenCourseWare.0-10-20-30-40dBHz0 1000 2000 3000 Hz• Why does the range of possible F2 values taper as F1 increases?• How do you achieve maximum and minimum F1?• How do you achieve maximum and minimum F2?The vowel spaceFigures by MIT OpenCourseWare. Adapted from Liljencrants, Johan, and Bjorn Lindblom. "Numerical