Two classes of vowel theories
Tongue Constriction Theories
Historically older, traditional view
(at least as old as early Indian grammarians, 7th century).
Vowels come in three distinct types:
Each type is categorically distinct.
Within each type, jaw height may be used to distinguish vowels
By the 19th century, further differentiation of constriction types was acknowledged, by allowing the lip and tongue actions to "mix."
Continuous Vowel Space Theories
developed a system for teaching speech to deaf children
Bell was haunted by inability to categorize the vowel in "Sir" within the tongue constriction theories.
Bell invented central ("mixed') vowels (around 1867), and characterized vowels as points in a 2-dimensional space (e.g., high vs. low, front vs. back).
"Mixed" vowels were both front and back.
Here are the vocal tract shapes he imagined corresponding to his descriptive system:
Cardinal vowels of Daniel Jones
Vowels repesented as points in a quadrilateral that represent the positions of the highest point of the tongue during the production of the vowel.
Reference (cardinal) vowels on the periphery of the vowel quadrilateral were learned by rote from Jones.
Vowels were assumed to be spaced at auditorily equal intervals of tongue position.
System could be used reliably.
System gained popularity because it allowed the qualities of vowels newly discovered (by British colonials) to be communicated.
Even during Jones's time (1930-1950), however, it was known that the highest point of the tongue description did not reflect actual tongue positions, as measured by X-rays:
position of highest point of the tongue during cardinal vowels (after S. Jones, 1929)
Position within vowel quadrilateral and vowel resonances
Sir Isaac Newton recognized the relation between vowel qualities and resonances.
He noted that he could hear a progression of different vowels as he poured beer into a flaggon.
Striking resemblance between position of vowels in CV quadrilateral (based on auditory judgements) whose axis are high-low and front-back, and position in a formant frequency graph (F1 vs. F2-F1)
measured formant frequencies averages
American English Vowels
Auditory judgments (phonetician) formant frequencies
Untrained listeners from similarity judgments
Systematic Vowel differences between languages in Cardinal Vowel diagrams also captured in formant frequency measurements:
Danish (Uldall, 1933) English (Jones, 1956)
Formant frequency comparison
Problem with equating vowel quality with resonances: head size
Individuals differ in range of formant frequencies.
Ranges of F1 and F2 associated with a single (even cardinal) vowel, differ across speakers, and even overlap:
Formants of cardinal vowels in a group of phoneticians trained by Daniel Jones:
Formants values of American English speakers (after Peterson & Barney, 1952):
How do we normalize formants of speakers with different head sizes?
- relative normalization
- absolute normalization
- dynamic normalization
Since no normalization scheme is generally accepted, how can we compare formants for two different languages:
- use bilinguals
- select a group of speakers in each language and take means.
Rounding is a 3rd dimension of traditional vowel space, independent of high-low and front-back, which characterize position of the tongue:
primary slice Secondary slice
But, rounding effects formant frequencies. So position within the formant graph is not independent of rounding.
Note that formant frequency difference between front and back vowels is maximized when back vowels are rounded and front vowels are unrounded.
Lindblom: Theory of Adaptive Dispersion
Vowels are dispersed in the phonetic space (tongue position, rounding) in such a way as to maximize auditory differences among the vowels.
Same tongue shape, same position on cardinal vowel chart are associated with different formant frequencies.
Conclusion: relation between position in vowel quadrilateral and formant frequencies holds only for a given lip configuration (single "slice" through 3-dimensional vowel space).
When phoneticians listen to a audio recording of a vowel in an unknown language that is not found on the primary cardinal vowel "slice", they may not be able to tell whether the the vowel is a front rounded or a back unrounded vowel--they cannot separate position in the space from rounding.
Phoneticians' judgments of Gaelic vowels (Ladefoged, 1967):
vowels on primary plane (14/15 judgments) high vowel not on primary plane
Since front-rounded and back-unrounded vowels are so auditorily similar that skilled phoneticians confuse them, we would expect that, if goals for vowels were acoustic, or auditory, there would be languages in which individual speakers vary as to which of these types they produce.
This doesnt appear to be the case.
But front-back judgments seem to be dependent of state of lips.
Audio-visual experiment with phoneticians would probably yield different quality judgment depending on lips display.
but then in what sense is front-back strictly an auditory (or acoustic) property?
This suggests that goals for vowel gestures are defined in terms of constrictor action, not the resulting sound.
back to cardinal vowels
A problem for the continuous vowel space theory
Individual differences among talkers of a given language include "reversals" of vowel height, measured either by tongue height or by F1 frequency:
If vowel height is the relevant parameter on which vowel gestures contrast, how can different speakers order the same two vowels differently along this parameter?
The speakers are mutually intelligible; they do not confuse the vowels.
Quantal theory of vowels (Wood, Stevens)
Return to more traditional theory, that vowels come in qualiatively distinct types.
Each type is defined by:
Measured area functions from a variety of languages show constrictions limited to these four locations:
With only four constriction locations, how are full range of vowels produced?
Other parameters along which vowels can contrast:
Resulting formant space:
Analysis of palatal vowels: /i I e E/
lax tongue shape
Position of tongue with respect to palate, and therefore F1, will be similar for [e] and [I].
Modeling of palatal vowels using these parameters:
German palatal vowels
X-ray data from American English:
Problem with this theory of palatal vowels: tongue may compensate for jaw height, at least in case of mechanical pertubation (bite-block)
Muscles employed for four vowel types
Tongue as complex structure
Muscles shape bag and position it with respect to fixed surfaces.
Two types of muscles for positioning and shaping tongue:
Muscle function in shaping tongue
Contraction of muscle shortens length of bag along the dimension along which muscle runs.
Tongue will expand out in other dimensions to conserve volume.
Intrinsic muscles (primary for consonants)
Extrinsic muscles (primary for vowels)
Palatoglossus, pharyngeal constrictors