1. Classification of vowels (vocoids)
a) Vowels are produced in a relatively small area of the mouth - earlier writers talked of palatal vowels (the frontmost ones) and velar vowels (the furthest back). The tongue may be further to the front or to the back and higher or lower in the mouth (as shown in this video clip) and the lips may be more or less rounded. The shape of the area in which the tongue moves is usually idealised to form a quadrilateral, (sometimes a triangle, as in the graphic above), on which the position of each different vowel sound can be marked by a dot. (Refer to IPA vowel chart.) What the points marked on the vowel quadrilateral actually represent is open to dispute. As a first, working hypothesis, we will take the view espoused in many textbooks.
b) The tongue arching model. Vowels can be classified according to, (and so points on the quadrilateral represent,) the position of the highest point of the tongue in forming the vowel. The first things one needs to know, therefore when categorising vowels are:
(i) How high is the highest point of the tongue? (the height of the vowel.) Is it close to the roof of the mouth, as for [i], i.e. with the tongue as near the roof of the mouth as it can get without causing friction - or open as for , with the tongue as low in the mouth and the jaws as wide open as possible; or is it intermediate between these two - either close-mid, like [e] as in French "donner"; or open-mid like  as in French "père"? Of course the majority of sounds do not correspond exactly to any of these, but using these categories allows us to describe them accurately.
(ii) How far forward or back is the highest point of the tongue? Is it front - corresponding to a palatal consonant - such as [i], [e],  and [a], or back - corresponding to a velar consonant - such as [u], [o],  and ; or central, like the  sound in English "bird" or "hurt".
c) To help identify vowels in different languages, phoneticians use a series of reference vowels, called cardinal vowels with which to compare them. These consist of four vowels produced at each extremity of the vowel producing area: [i], [a],  and [u], plus four in intermediate positions which sound equidistant between [i] and [a] at the front, and [u] and  at the back. (Refer to IPA chart.) [e] and  are intermediate at the front, and [o] and are intermediate at the back. These eight cardinal vowels are numbered as follows: 1[i], 2 [e], 3 , 4 [a], 5 , 6 , 7 [o], and 8 [u]. In addition, equidistant between [i] and [u] is the central, close vowel .
d) The above are the primary cardinal vowels. There are
secondary cardinals, which differ from the related primary ones in lip
|Primary Cardinal Vowels||Secondary Cardinal Vowels|
The vowel quadrilateral and the cardinal vowels are the work of Daniel Jones. His definitions of the primary cardinals may be found in An Outline of English Phonetics, paragraphs 131-133.
e) In short: (i) The CV's are an arbitrary set of reference vowels - arbitrary in the sense that there is no apparent reason why there should be eight rather than ten, twelve or any other number. (ii) They are peripheral vowels - they define the boundary of the space within which vowels can be produced. For this reason they hardly ever occur in real speech, or as the vowels of any language.
2. Problem areas
(i) Only cardinal vowels 1 and 5 have strictly articulatory definitions. It is not clear how far Jones intended that the "equal acoustic difference" between intermediate vowels is supposed to reflect articulatorily equal steps. Starting from X-ray photos of his own mouth he talks of "approximate tongue positions" and approximately equal intervals. We now know that the resemblance of tongue positions to the vowel quadrilateral is only very approximate; neither Jones's X-rays, nor those Ladefoged discusses in his Course really bear out the tongue arching model.
(ii) So what does the quadrilateral represent? Catford (Fundamental Problems...p. 169) considers that phoneticians have been making proprioceptive judgements based not just on the height of the tongue, but on its overall shape and configuration in the mouth.
3. Using the Cardinal Vowels
The idea is that in identifying the quality of each vowel in
a particular language, one will compare it to the cardinal vowels, note
its relationship to them, and then use the symbol of the nearest
vowel as a basis from which to transcribe it. The relationship of the
vowel to the nearest cardinal vowel is recorded by using the four
diacritics , ,
example: [i] means
more open (lower) than [i]", [o+] means
more advanced (fronter) than [o]", and [e] means
more retracted (backer) than [e]". These diacritics can be combined or
multiplied e.g. [a],
etc. This impressionistic use of the cardinal vowels plus
is rarely seen in phonetics textbooks. Once a body of impressionistic
has been made, it becomes convenient to dispense with diacritics
whenever possible, especially in print. But you cannot proceed straight
to a simplified transcription at once: it is necessary to record each
quality precisely before deciding on appropriate simple symbols to use
in a simplified, systematic transcription.
As well as the peripheral cardinal vowels, the IPA also provides
for less peripheral sounds: [I], , 
and , and
diacritics [ ¨ ] (centralized: makes a front vowel symbol backer
and a back vowel symbol fronter) and [x]
(mid-centralized: means, "nearer to the mid-centre of the vowel
These symbols are not as precisely defined as the cardinal vowels, but
are very useful additional symbols.