‘An A-Z of English Grammar and Usage’ by Leech and others suggests the following:

With be, use the contraction + not (e.g. That’s not right).

With have and modal auxiliaries, use the verb + n’t option, e.g. hasn’t, can’t.

The authors go on to say that forms such as She isn’t hungry, as opposed to She’s not hungry, are less common, and that forms such as I’ve not met him, as opposed to I haven’t met him, are much less common.

The authors don’t say on what basis they make their recommendations, but they are likely to be based on frequency of use. There doesn’t seem to be any difference of meaning or emphasis. I would just add myself that a contraction such as I’ve not met him sounds more formal, perhaps because of its lower frequency.

Answer from Barrie England on Stack Exchange
Discussions

negation - How to choose a proper contraction "it's not" versus "it isn't"? - English Language Learners Stack Exchange
With be, use the contraction + not (e.g. That’s not right). With have and modal auxiliaries, use the verb + n’t option, e.g. hasn’t, can’t. More on ell.stackexchange.com
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What is the proper contraction of "it has"?
"It's" can be a contract of either "it is" or "it has," when "has" is helping the tense of the main verb, as in "It's been a good time." You should not contract "it has" when "has" is your main verb, as in "It has four legs and a tail." More on reddit.com
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2
March 23, 2012
What is the best way to use contractions in the phrase "I have not"?
Both are equally acceptable and I use both, even in the same sentence: "I haven't done it yet: I've not had chance." I was trying to think if one or the other might be preferred based on what you are stressing but I can't see that that is even necessarily true. More on reddit.com
🌐 r/grammar
4
4
September 11, 2019
Is "it's" an acceptable contraction for "it has"?
Yes, but only when the "has" is working as part of a verb phrase, not standing on its own. So: "It has been a been long day." -> "It's been a long day." : Okay. "It has broken part." -> "It's broken apart." : Okay. "It has three parts." -> "It's three parts." : Not okay. "Has it opened yet?" "It has." -> "Has it opened yet?" "It's." : Not okay. More on reddit.com
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7
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October 19, 2017
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WordReference
forum.wordreference.com › english only › english only
haven't / hasn't [contraction 'Have'] | WordReference Forums
October 23, 2014 - You are not contracting 'have' in any of these. To contract have / has you can do it in these ways: they've not got a house yet they've not finished yet she's not got a job yet she's not had breakfast he's not worked since yesterday.
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Wikipedia
en.wikipedia.org › wiki › Wikipedia:List_of_English_contractions
Wikipedia:List of English contractions - Wikipedia
This list is part of the internal Wikipedia Manual of Style. For encyclopedic information see English auxiliaries and contractions. This is a list of contractions used in the Wikipedia:Manual of Style/Abbreviations; these are to be avoided anywhere other than in direct quotations in encyclopedic ...
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Lawless English
lawlessenglish.com › home › contractions with the verb have
Contractions with the verb HAVE - Lawless English
April 18, 2014 - Has can never be contracted with its subject (he, she, or it) when it is the main verb in the sentence and is in the present tense.
Top answer
1 of 2
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‘An A-Z of English Grammar and Usage’ by Leech and others suggests the following:

With be, use the contraction + not (e.g. That’s not right).

With have and modal auxiliaries, use the verb + n’t option, e.g. hasn’t, can’t.

The authors go on to say that forms such as She isn’t hungry, as opposed to She’s not hungry, are less common, and that forms such as I’ve not met him, as opposed to I haven’t met him, are much less common.

The authors don’t say on what basis they make their recommendations, but they are likely to be based on frequency of use. There doesn’t seem to be any difference of meaning or emphasis. I would just add myself that a contraction such as I’ve not met him sounds more formal, perhaps because of its lower frequency.

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As you've said, placing emphasis on a word is a matter of desired emphasis which is a matter of personal style rather than rules. I think you could make exactly the same point by putting stress on isn't (It ISN'T my fault!)

In the Python sketch, the emphasised word is 'it' not, 'not'. Part of the humour in the sketch is the repetition of it - 'It is.' 'No, it isn't.' 'Yes it is.'. This wouldn't have carried the same impact if the humour was based on, perhaps, the back and forth of 'It's not', 'Yes, it is.' 'No, it's not.'

Also, they can do this with a number of forms of the sentences in the sketch, for example 'It can be.' 'No, it can't ...' The humour wouldn't carry through these sentences if the emphasis had been used on the 'Is/Not' structure.

Find elsewhere
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Espresso English
espressoenglish.net › home › english tips blog › 50+ contractions in english: list & examples
50+ Contractions in English: List & Examples - Espresso English
July 16, 2024 - Contractions with “not” are often used in tag questions: ... Remember: its without an apostrophe is a possessive pronoun, ex. The car crashed because its brakes failed. It’s with an apostrophe is the short form of “it is” or “it has” (which you’ll see in the next section).
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University of Sussex
sussex.ac.uk › informatics › punctuation › apostrophe › contractions
Contractions : The Apostrophe
The apostrophe is used in writing contractions — that is, shortened forms of words from which one or more letters have been omitted. In standard English, this generally happens only with a small number of conventional items, mostly involving verbs. Here are some of the commonest examples, with their uncontracted equivalents: ... Note in each case that the apostrophe appears precisely in the position of the omitted letters: we write can't, not *ca'nt, and aren't, not *are'nt.
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Wikihow
wikihow.com › education and communications › studying › english › english grammar › how to use contractions: 12 steps (with pictures) - wikihow
How to Use Contractions: 12 Steps (with Pictures) - wikiHow
August 14, 2025 - As well, the contraction “‘s”, the contracted form of “is” or “has” can be used with pronouns and it can be used with nouns, names, question words, and words like “here” and “there”. For example: “The plane’s late.” ...
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Southern Living
southernliving.com › news › why-is-will-not-conjunction-wont
The Reason The Contraction For Will Not Isn't "Willn't"
December 15, 2023 - A consensus wasn't reached until the 16th century when wil ultimately became will, and wold became our would. As RD points out, however, the most popular negative verb form remained woll not. This contracted to wonnot, which modern English later turned into won't.
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GCFGlobal
edu.gcfglobal.org › en › grammar › contractions › 1
Grammar: Contractions
For instance, the contraction couldn't means could not. As you can see, the o in not isn't in the word couldn't.
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Cambridge Dictionary
dictionary.cambridge.org › grammar › british-grammar › contractions
Contractions - Grammar - Cambridge Dictionary
The following are the most common contractions. ... She is not is contracted to she isn’t or she’s not. I am not is only contracted to I’m not. Not: I’m n’t or I am n’t. They are not is contracted to they aren’t or they’re not. The isn’t / aren’t contractions are more common after nouns.
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San Jose State University
sjsu.edu › writingcenter › docs › handouts › Contractions.pdf pdf
Contractions [pdf]
Here are some common contractions and the groups of words that they represent. aren’t  are not · there’s  there is; there has · can’t  can not · they’d  they had; they would · couldn’t  could not · they’ll  they will; they shall ·
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Grammarly
grammarly.com › blog › grammar › contractions
What Are Contractions in Writing? Definition and Examples | Grammarly
August 10, 2022 - There’s another rule about contractions, again particular to American English, related to subject contractions in the present perfect tense (used for past actions that are related to or continue into the present). When the present perfect tense is used in the negative, it’s incorrect to use a subject contraction like she’s or I’ve. Instead you should use the subject followed by the contractions haven’t or hasn’t. I’ve not even gotten dressed yet!
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University of Nevada, Reno
unr.edu › university › writing & speaking center › writing & speaking resources › contractions
Contractions | University Writing & Speaking Center | University of Nevada, Reno
Contractions that take out the second letter of the second word: Note: Contractions that use the word “not” will replace the “o” with an apostrophe (‘).
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University of Hull Library
libguides.hull.ac.uk › writing › contractions
Contractions - Writing academically - Library at University of Hull
This page gives examples of common contractions and what to use instead. * It is a common misconception that the non-abbreviated form of could've and should've is 'could of' and 'should of'. Please note this is not the case and the full form uses the word 'have'.
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Learn English
learnenglish.ecenglish.com › lessons › contractions
Contractions | Learn English
Has not → Hasn't → "She hasn't left." Is not → Isn't → "This isn't difficult." Must not → Mustn't → "I musn't make a noise." Need not → Needn't → "You needn't come." Should not → Shouldn't → "We shouldn't eat sweets." Was not → Wasn't → "It wasn't bad."