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I have never heard the T of "lunatic" become flap in American English. You can also listen to the data from Youglish. Compare "janitor" /ˈdʒænəɾɚ/ (Cambridge Dictionary gives /ˈdʒæn.ə.t̬ɚ/). The T in "janitor" is between two unstressed vowels and it is flap. The T of "lunatic" is also between two unstressed vowels: /ˈluː.nə.tɪk/ but it is never flap (as the data from Youglish show, and Cambridge Dictionary also gives /t/, not flap).

I also found another word in which the T is not flap in AmE, "heretic": /ˈher.ə.tɪk/

Why is the T never flap in "lunatic" (and "heretic") in American English? Is it an exception or is there some kind of explanation for it?

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    peripatetic? hectic? apathetic? Or am I missing the point. – Xanne Mar 17 at 7:38
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    @Xanne I think you missed the point. "Peripatetic" and "apathetic" both can have flapped T. "Hectic" can't because there's a consonant before the T; flap T usually occurs between vowels. My question is, if all those words can have flapped T, why not "lunatic" (or "heretic"). – Sphinx Mar 17 at 10:29
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    Secondary stress; we don't flap the /t/ in politic or heretic, either. And we flap the /t/ in arithmetic when we pronounce it as a mathematical adjective /er.ɪθˈmet̬.ɪk/ (e.g. arithmetic geometry) but not when it's a noun /əˈrɪθ.mə.tɪk/. – Peter Shor Mar 17 at 13:02
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    How observant! Why anyone would downvote this is beyond me. I believe this has to do with the phenomenon known as the Withgott effect, which I haven't been able to fully wrap my head around... But in essence, it's because English has the tendency to group every sequence of two (or sometimes three) syllables into what are known as feet, stressing one syllable and reducing the other(s), hence the unreduced [t] in lunatic. – Nardog Mar 17 at 13:07
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    This still doesn't explain why positive, interpreting, etc. are flapped but lunatic, heretic, etc. aren't, even though -ic can clearly be preceded by a flap when immediately following stress, as in attic, critic, etc. Presumably this is where the Withgott effect provides explanation, which seems to involve synchronic morphological analysis. – Nardog Mar 17 at 13:28
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American English flap is regulated predominantly by stress. In order for "t" to get flapped, the syllable immediately before "t" must be stressed as strongly, or more strongly than, the following syllable where "t" is in the onset.

For example:
atom [ˈæ.t̬əm] --> the syllable [ˈæ] is stressed, the syllable [t̬əm] is unstressed, so there is a flap.
vs.
atomic [ə.ˈtɑ:.mɪk] --> the syllable [ə] is unstressed, the syllable [ˈtɑ:] is stressed, so there is no flap.

The words lunatic and heretic have a very weak, one might say "secondary", stress on the syllable tic. As a consequence, the preceeding syllable is NOT stronger than the syllable with "t", and therefore there is no flap.

heretic [ˈhe.rə.ˌtɪk] --> the syllable [rə] is extremely weak, the syllable [ˌtɪk] is also weak, but slightly stronger with some stress, so there is no flap.
lunatic [ˈlu:.nə.ˌtɪk] --> the syllable [nə] is completely unstressed, whereas the syllable [ˌtɪk] has some weak stress, so there is no flap.

We can compare these words to, say, erratic or clarity, where there is a flap.

erratic [e.ˈræ.t̬ɪk] -> the syllable [ræ] is stressed, and stronger than the weak syllable [tɪk], so there is a flap.
clarity [ˈkle.rə.t̬i] -> the syllable [rə] is unstressed, but the syllable [t̬i] is also unstressed, so both are equally strong, and there is a flap.

A great reference that should answer you question in greater detail is Eddington and Elzinga (2008), referenced below. Here is the table with their empirical corpus evidence they collected that summarises the relevant stress pattern and how likely it is to find a flap in them. The relevant row for this question has been highlighted.

enter image description here

References

Eddington, David and Dirk Elzinga (2008) The Phonetic Context of American English Flapping: Quantitative Evidence. Language and Speech 51.3, 245-266.

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    If flapping was blocked by secondary stress, then how was the secondary stress posited there in the first place? This doesn't explain why [ɪk] in lunatic induces secondary stress and [i] in clarity doesn't, as [ɪk] too can occur after a flap, as in erratic. It may as well be encoded in the grammar of English that /ˈV.V.tɪk/ may not be realized with [ɾ] (while /ˈV.tɪk/ may be), but to assign secondary stress to it and then attribute the lack of flapping to that stress is circular reasoning, absent other evidence for the presence of stress independent of the lack of flapping. – Nardog Mar 17 at 19:59
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    In addition to what Nardog said, [ˈæ.t̬əm] is phonotactically ill-formed (and no one syllabifies 'atom' that way). Does English permit /æ/ syllable-finally? [e.ˈræ.t̬ɪk] and [ˈkle.rə.t̬i] are also ill-formed. – Decapitated Soul Mar 17 at 20:09
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    @DecapitatedSoul There is no universally accepted method of syllabification for English. The syllable is only useful insofar as one makes it. The English flap has been argued to be syllable-final, ambisyllabic, and syllable-initial, but I don't think people really have that debate anymore because they realized how futile it is given what an elusive concept the syllable is in the first place. – Nardog Mar 17 at 20:29
  • @Nardog I used "secondary" stress here because this is a popular science site and not an academic publication. It can be shown that the phonetics of "tik" are stronger than those of "ne" in "lunatic" in terms of pitch, duration and loudness. The CMU Pronouncing Dictionary, the source for the paper I cited, transcribes words including their stress pattern based on such criteria. The stress pattern is therefore independently established and not circular. speech.cs.cmu.edu/cgi-bin/cmudict#about – Richard Z Mar 17 at 20:33
  • @DecapitatedSoul Well, I suppose you can have your favourite theory of syllabification, following popular ideas like the MOP or ambisyllabicity, but that does not make my syllabification objectively "ill-formed". I can simply say that lax vowels must occur in closed or non-final syllables, and that rule will do just fine. – Richard Z Mar 17 at 20:35
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My suspicion—based on my own (American English) pronunciation—is that the presence of flap/no-flap is conditioned by the following consonant. In brief, if the 't' is followed by an 'r', an 'l', or 'ng' (flyswatter, capital, ferreting), it will have a flap; if not, no flap (e.g. decapitate, ferreted, Caratunk)

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    I don't use ferret as a verb very often, but when I do I flap the /t/ in both the past and the present participle forms. Except that with the flap before a final /d/, there's the tendency to drop one simply to keep from trilling. The aspiration before final syllables prevents flapping; it's occasioned by the secondary stress on the final syllable (you can usually tell because the vowels aren't reduced). – John Lawler Mar 17 at 14:11

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