Two classes of vowel theories

continuous vowel space

tongue constriction

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


A.M. Bell

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)


Danish vowels

auditory judgment

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


Whose resonances?

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?


Since no normalization scheme is generally accepted, how can we compare formants for two different languages:


Problem with equating vowel quality with acoustic

resonances: rounding

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 doesn’t 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:

Speaker 1

Speaker 2


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:




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:

sagittal view

coronal view

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)



Styloglossus, hyoglossus

Palatoglossus, pharyngeal constrictors

Other contrasts