uɱ...

If the IPA were to admit a separate phonetic symbol for every subtlest nuance of sound that anyone can detect, chaos would ensue as symbols proliferated uncontrollably. So for at least the last hundred years we’ve followed the rule that we don’t have a special symbol unless there is some language that makes phonemic use of the corresponding sound: for any arbitrary pair of symbols there must be a language in which a phonological contrast between the corresponding sounds is attested. In the words of the 1949 Principles,

The current Handbook (p. 27-30) expresses the same general idea at greater length and with greater sophistication. It makes the point that if we have a phonemic contrast somewhere we generally ought to have a special symbol, though not the converse that if we don’t have a phonemic contrast then we ought not to have a special symbol.

Either way, the symbol for the labiodental nasal, ɱ, seems to be a striking exception to the principle. There is certainly no widely spoken or studied language in which ɱ contrasts with both m and n. If the sound occurs at all, it is virtually always a positional allophone of one or the other or both, found only adjacent to another labiodental (normally f or v).

If you say comfort as ˈkʌɱfə(r)t and emphasis as ˈeɱfəsɪs (as many textbooks assert), then English ɱ can be considered a realization of phonemic m.

There are two reasons why matters are not so simple, however.

• In practice many speakers do not use these pronunciations consistently. Between the nasal and the fricative, epenthesizers — those who make mince and mints homophonous — will have a voiceless plosive of some sort, usually labiodental and/or glottal, thus ˈkʌɱp̪fə(r)t ~ ˈkʌɱʔfə(r)t (where “p̪” in the first version stands for a voiceless labiodental plosive).

• Rather few people have such perfect dentition that they can effortlessly create a true labiodental stop. The smallest gap between any two upper front teeth is sufficient to preclude the complete closure needed for a plosive. Equally, any nasal at the same place will not be a true stop nasal, but will have some oral escape.

In practice what we get as the realization of the phonemic m here may typically range from a bilabial m in careful or overarticulated speech, through ɱ with the reservations just expressed, or perhaps a nasalized labiodental approximant, ʋ̃, down to mere vowel nasalization in rapid speech. I expect the same applies, mutandis mutatis, in other languages.

Be that as it may, the fact remains that as an IPA symbol the letter ɱ appears to be an anomalous exception. Certainly at the time of its adoption its distinctive use in a language had not been attested.

Are things different now, when so many more languages of the world have been phonetically investigated?

The only language that people mention as allegedly having a distinctive labiodental nasal phoneme is a language of the Republic of the Congo (Congo-Brazzaville) known as Kukuya or, more fully, as Teke-Kukuya.

In this language, it is claimed, there are various conclusive minimal pairs.
I have not been able to read the original in which this data was presented. I have, however, read a review of it by the Africanist Michael Mann (BSOAS, 1976, 39:725). He does not even mention Paulian’s striking claim about the labiodental nasal.

I also note that Kukuya is part of a continuum, Teke, containing eleven other languages (or perhaps dialects), for none of which the labiodental nasal phoneme is attested.

I can’t help wondering whether Paulian relied for her data mainly on a single informant who happened to have an unusual dental anatomy and who pronounced these words slightly differently from everyone else. Failing that, I wonder if this ɱ might alternatively be phonemicized as, say, /mv/ (compare the the ‘bv’ above).