a. Forward limit of the vowel space: Butcher (1982) — ‘dorso-labial approximant’.
b. Upper limit: Problem of volume velocity of airflow; Butcher — it is perfectly possible to produce a fricative with tongue in the position of CV2.

2. What dimensions?

a. What is phonetician doing when putting dot in quadrilateral? Confusion due to mixing of tongue position and lip-rounding? Catford (1974) showed that trained phoneticians show a very high degree of agreement in their judgement of the articulatory placement of vowels on the quadrilateral, but that the ability to discriminate front rounded vowels from back unrounded vowels may be impaired if the phonetician cannot see the subject (and thus lacks visual information about lip- posture.) Three dimensional charts (as in Lass 1984) are technical improvements, but of little practical use.

b. Problem is that values for rounding only extreme for [i] and [u] — suggests other front vowels could be less rounded, back ones more. In fact, amount of effective lip rounding possible decreases as jaw is opened.

c. Other dimensions — How to represent nasality / retroflexion / tenseness. ?

d. Choice of major dimensions — height / front-back. Jones's view of vowel classification was informed by his study of a few X-rays (see Jones 1956, ¶ 134). However, the distance between vowel positions is not even invariant across speakers, and is certainly not equidistant.

3. Tense vs. Lax, [+ATR] vs. [–ATR], Narrow vs. Wide, etc.

a. Another dimension of classification — [i] vs. [ɪ], [u] vs. [ʊ], often [e] vs. [ɛ] — doesn't work well in terms of vowel height. What are the articulatory correlates: tongue width / pharynx width / general muscular tension?

b. Wood (1975, 1980) - [i, ɪ] have same degree of jaw opening (less than for [e] but [i] and [e] have similar degree of tongue bunching - more than for [ɪ] or [ɛ].

c. Fischer-Jørgensen: "It thus seems clear that tenseness (which is often, but not always, combined with length) is an independent vowel dimension. Height should therefore be indicated separately for tense and lax vowels." EF-J suggests that this saves height distinction ñ depends on wholesale acceptance of tense/lax distinction.
 

Bell, Sweet terms:	Narrow	Wide	Narrow	Wide
Jakobson, Halle terms:	Tense	Lax	Tense	Lax
Ladefoged terms:	[+ expanded pharynx]	[– expanded pharynx]	[+ expanded pharynx]	[– expanded pharynx]
Stewart, IPA terms:	[+ Advanced Tongue Root]	[– Advanced Tongue Root]	[+ Advanced Tongue Root]	[– Advanced Tongue Root]
High	i	ɪ	u	ʊ
Mid	e	ɛ	o	ɔ
Low	æ	a	ɑt(Am. balm)	ɒ, ɑ (Am. bomb)

4. Equidistance

Recall that the CVs are defined as separated by ʻauditorily equal steps.ʼ (Jones 1956 says that "vowels of the `front' series ... form an acoustic sequence between the vowels 1 and 5 such that the degrees of acoustic separation between each vowel and the next are equal, or, rather, as nearly equal as it is possible for a person with a well-trained ear to make them. Cardinal vowels 6, 7, and 8 ... continue this series of acoustically equidistant vowels."

5. Ventriloquism? Many-to-one articulatory-to-acoustic relationships

a. Russell (1928) was the first to seriously challenge the simple view that every different configuration of the vocal organs led to corresponding acoustic difference (and vice-versa). His work, based on X-ray photography, revealed considerable variation between different articulatory postures corresponding to similar auditory impressions.

b. The same criticism has been maintained by, e.g. Ladefoged, who pointed out that tongue height depends on both tongue raising and jaw closing, with many possible trade-offs between these two articulatory dimensions.

c. Research on the acoustics of resonating tubes has shown that similar sounds may be produced by different tube shapes. A practical example of this is ventriloquism.
 

Butcher, A. (1982) Cardinal Vowels and Other Problems. In D. Crystal (ed) Linguistic Controversies. Arnold.

Catford, J. C. (1974) Phonetic fieldwork. Current Trends in Linguistics vol. 12, pt. 4. 2489-2505.

Catford, J. C. (1977) Fundamental Problems in Phonetics. Edinburgh U. P. (Chap. 9)

Fischer-Jørgensen, E. (1985) Some Basic Vowel Features. In V. Fromkin (ed) Phonetic Linguistics. Academic Press.

Jones, D. (1956) An Outline of English Phonetics. (8th edition). Heffer. (Chapter VIII)

Ladefoged, P. (1967) The Nature of Vowel Quality. In Three Areas of Experimental Phonetics. OUP

Lass, R. (1984) Vowel system universals and typology: prologue to theory. Phonology Yearbook 1. 75-111.