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From Citizendium, the Citizens' Compendium
A vowel is a unit of language, defined in phonetics as a speech sound that lacks any 'closure' of a part of the oral tract (such as the mouth), permitting fairly free airflow, and in phonology as a segment that occupies the nucleus or 'peak' of a syllable. Vowels, then, are not just speech sounds, but abstract entities used to build up larger structures, e.g. syllables, within an utterance; they can therefore appear in written language (e.g. <A>, <B>, etc.) as well. Vowels are similar to consonants in this regard, but different terminology is used to describe their articulation. Their production primarily involves the tongue and vocal folds, but the lips, hard and soft palate and the nasal cavity may also be involved.
Because vowels are produced in a much smaller region then consonants, mostly being around the velum area towards the back of the mouth, it is inappropriate to use the same descriptive terms applied to consonants. The basic features of vowels used by phoneticians include height (of the tongue), backness (of the tongue, again) and rounding (of the lips); these are supplemented by length, nasalisation, palatalization, voicing (by the vocal folds) and a contrast between monophthongs and diphthongs (the latter involving tongue movement throughout the articulation). For example, the vowel [i:] can be described as a 'high front unrounded vowel', and additionally as a long, voiced, oral monophthong. Criteria other than length are collectively labelled vowel 'quality', as opposed to 'quantity', i.e. vowel length.
The vowel quadrilateral
Phoneticians and phonologists represent vowels on a diagram called the 'vowel quadrilateral', a shape which simplifies the actual physical positions of the vowel articulations in the mouth. The diagram shows the rough positions of the vowels relative to each other and at their maximally extreme position according to height, backness and rounding: for example, [i] is placed at the same level as the back vowel [u] because the distinctive feature 'height' treats them as identical in that they are both high vowels. Typically, [i] is in fact higher than [u] in the world's languages and the mouths of their speakers, but this difference is not significant in capturing the behaviour of these units. Nevertheless, phoneticians and phonologists use the quadrilateral to identify a set of vowels based on the criteria of 'height', 'backness' and so on, and refer to these as 'cardinal vowels'.
While cardinal vowels are positioned at the most extreme edges of the quadrilateral, actual vowels in the world's languages may or may not be pronounced exactly like these; for example, for ease of discussion English apparently includes the cardinal vowel [u], but in fact the English [u:] is rather longer, lower and further forward than the cardinal vowel, and a more detailed transcription might well use [ʉ:] instead. 'Cardinal vowels' are useful for discussing actual cases such as these; another example is that the German high front long vowel [i:] can be described as closer to 'cardinal vowel 1', i.e. [i], than its English equivalent. The 'Cardinal Vowel' chart was proposed by the phonetician Daniel Jones in the 1920s, and has remained fundamental to phonetics and phonology ever since.
Vowels are divided into high, mid and low, with high-mid and low-mid also possible. These correspond to the alternative terminology close, close-mid, open-mid and open. [e] can be described as a close-mid or mid vowel, depending on the detail necessary; [i] is an open or high vowel. Most languages have two or three groups of vowels distinguished by height: e.g. English [i:], [ɛ] and [ɑ:] in see, bed and (British English) car are high, mid and low vowels. Some languages make a four-way distinction: Danish, for example, has [i e ɛ a] as front vowels.
Front, central and back comprise the description of how far back in the mouth a vowel is articulated. Languages make up to a three-way distinction in this regard, though in many, central vowels are absent. Languages with only three or five vowels, for instance, typically lack central vowels such as the schwa [ə]. English preserves a three-way distinction as in [i:], [ə] and [u:].
The presence or absence of lip-rounding permits a further vocalic distinction, such as between the French vowels [i] and [y], which are basically identical high front vowels except for rounding on [y]. Most unrounded vowels have a possible rounded counterpart, and the vowel quadrilateral shows this by placing unrounded vowels to the left of vertical lines, with the rounded versions on the right. English has both rounded and unrounded vowels - [i:] and [u:], for example - but no pairs that contrast only in rounding, unlike French.
'Length' or 'quantity' refers to how long the vowel production lasts; this is shown by the use dots immediately after the vowel symbol in phonetic transcription: [i] versus [i:], for instance, with [i:] being a long vowel. More detailed transcription may include 'half-long' vowels by using a single dot, e.g. [iˑ]. A minority of languages make a three-way distinction of this kind, but otherwise this is used in very detailed transcription to indicate slight differences in vowel length. For example, the vowels in the English words bead and beat may appear identical, and indeed may both be transcibed as [i:] in a 'broad' or less-detailed transcription. A 'narrow' transcription might incorporate the half-long diacritic to show that the vowel in beat is actually shorter (and that the consonant [t] is longer): [bi:d] and [biˑtˑ].
The velum is a flap of muscle at the back of the mouth which raises or lowers to allow air to escape through the nasal cavity. This allows speech sounds to be distinguished by nasality: oral and nasal. Vowels such as [ɛ], when nasalised, are shown with a diacritic ~ above the symbol. French makes use of nasalisation to contrast words such as [lɛ] lait 'milk' with lin 'flax', which has a nasalised vowel.
Vowels are usually voiced, i.e. the vocal folds vibrate as the vowel is produced. A few languages do use voicing to distinguish different words, but in most cases a voiceless vowel does not contrast with its voiced equivalent. English vowels are voiceless in some environments, such as when aspiration are other voiceless sounds are involved: the first vowel in particular, for example, is voiceless for many speakers, seemingly 'whispered'. A small circle underneath the vowel symbol represents voicelessness.
Monophthongs versus diphthongs
The tongue may move throughout the articulation of a vowel, moving from the rough position of one vowel in the direction of another - this is a diphthong, such as [aɪ] in buy. A 'pure' vowel such as [i:], in which the tongue does not move towards the position of another vowel, is a monophthong. It is important to note that diphthongs are not simply the production of one vowel followed by another: the vowel in [ɪə] ear is not the same as the two vowels in [sɪtɪ ətæk] city attack, for example. Rather, the tongue begins moving from close to but not exactly the same position as the English monophthong [ɪ], towards the position of the central vowel [ə], often not quite reaching it. Diphthongs involve a single tongue movement and articulation, rather than comprising two separate sounds.