-n't
This is the contraction of the negative particle not, and probably the most common in the English language. Phonetically, it behaves like any other word ending in -nt:
⦿ Before consonants, -n't is pronounced [nt̚]: You don't know. [yuɖòʊ̯nt̚ nóʊ̯]
⦿ Before vowels, -n't is pronounced [n]: You don't answer. [yuɖòʊ̯nǽnsʀ]
⦿ The combination -n't you(r) is pronounced [nt̚t̡yu] or [nt̚t̡yʀ]: Don't you know? [dòʊ̯nt̚t̡yunóʊ̯]
can't
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Due to the fact that -n't is commonly reduced to [n] before a vowel, the contraction can't is actually pronounced [khæːn] before words that start with a vowel, like always, even, answer, etc. For instance can't always [kʰæːnɑlwei̯z] can't even [kʰæːnivɛn] can't answer [kʰæːnænsʀ]. This may seem confusing since it looks and sounds more like the pronunciation of affirmative can. However, we rarely confuse can and can't before vowels because we use certain phonetic features to distinguish them:
(a)
Can is normally unstressed and reduced to [kʰɛn] or even [kʰɴ] before a vowel in neutral statements and questions. In this environment, you won't hear the vowel [æ] — you'll only hear a short [ɛ] or practically no vowel at all. This should be your first indication that it's the affirmative can:
He can understand.
[hì kʰɛ̣n/kʰɴǝ̣ndʀ̣stǽːnd]
(b)
Can't is pronounced [kʰæːn] in front of a vowel and usually has a secondary stress in a neutral context, and always a long vowel. Normally, words that end in -t are clipped and short, but when the t-sound is removed, the vowel reverts to long — even more so with the secondary stress.
He can't understand.
[hị kʰæ̀ːnǝ̣ndʀ̣stǽːnd]
Note that in some cases, the pronoun or noun in front of can't may have a secondary stress, in which case can't is unstressed, but still has the vowel [æ] which isn't as long as when it has the secondary stress, but is long enough to let you know that it's can't and not can, since affirmative can in the same context would be pronounced [kʰᵋn] or [kʰɴ] and never [kʰæːn].
He can't understand.
[hì kʰæːnǝ̣ndʀ̣stǽːnd]
So the only time [kʰæːn] actually means can, is when it has a primary stress, and the following verb is completely unstressed — like when someone is insisting:
(He says he can't understand, but) he can understand.
[hi kʰǽːnǝ̣ndʀ̣stæ̣ːnd]
The only ambiguity comes when stress is used to contrast an element other than the modal. In this example, the primary stresses are on angry and crying, since they're being contrasted, so the modals can and can't have secondary stress:
He càn understand why you're ángry, but he càn't understand why you're crýing.
Here, there's really no way to distinguish can and can't because they both have a secondary stress and are pronounced [kʰæːn]. When this happens, we normally bring out the -t in can't, which usually sounds like something between a [t] and a [d], and optionally use a glottal stop in front of the following vowel to separate the two words even more:
He càn understand why you're ángry, but he càn't understand why you're crýing.
[...kʰæ̀nt̬.ʔǝ̣ndʀ̣stæ̣ːnd wạɪ̯yʀ̣.kʰráyiŋ]
ain't
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The contraction ain't is pronounced [eɪ̯nt̚] before consonants, and [eɪ̯n] before vowels. It's a general contraction that can be used to negate all the forms of to be, regardless of person or number: I/you/he/she/it/we/they/who... ain't.
However, bear in mind that it's really the only contraction that actually is kind of incorrect and can be marginally vulgar, so use it in the right company because it can sound kind of uneducated.
Having said that, note that since am not doesn't really have a corresponding contraction (amn't isn't used in modern English), the form I ain't [ayéɪ̯nt̚] is extremely popular for the first person, as well as the inverted question form ain't I [éɪ̯naɪ̯]. When a more "correct" form is needed, you can just use I'm not and for the inverted forms, aren't I? [ɑ́rɛnaɪ̯] or am I not?
Another popular use of ain't, which I don't recommend, is as a substitute for haven't or hasn't, which goes beyond slang and just sounds wrong. Statements like I ain't seen her in two days. There's no reason for someone learning English to be speaking like this.
-ouldn't
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The contractions couldn't, shouldn't, and wouldn't are pronounced in several ways by different people.
The most common pronunciation in careful speech is with [-ʊ́ɾɛnt̚], however you'll also hear [-ʊd̚ɴt̚] and [-ʊ́t̚ɴt̚]. In normal speech, these differences are barely discernible and are all acceptable.
I shouldn't be here.
[ai̯.ʃʊ̀ɖɛnt̚ bíːhiǝr]
[ai̯.ʃʊ̀d̚ɴt̚ bíːhiǝr]
[ai̯.ʃʊ̀t̚ɴt̚ bíːhiǝr]
Before a vowel, only [-ʊ́ɾɛn] and [-ʊ́ʔɴ] are common. As is common in American English, the [t] is swallowed before the following vowel, and the [n] is either expanded to [ɛn] or vocalized to [ɴ]. :
I shouldn’t even go.
[ʃʊ́ɾɛnivɛn.góːʊ̯]
[ʃʊ́ʔɴ.ivɛn.góːʊ̯]