Re the symbol 'a' in IPA: I too find it strange that it's reserved for a phoneme which occurs so rarely in European languages (if it occurs at all). Whereas the common continental (and Northern English, methinks) 'a' has got to be transcribed 'ä'.I say no it isn’t, and no it doesn’t.
The vowel a occurs extremely commonly in European languages (and of course in non-European languages). The Northern English TRAP vowel, too, is very satisfactorily represented by the symbol a, with no diacritics. The contrary claims reveal a basic misunderstanding of how phonetic symbols are used when we represent the phonemes of a language or language variety. Let’s see why.
The symbol a is one of the set of symbols representing the ‘Cardinal Vowels’ i e ɛ a ɑ ɔ o u defined by Daniel Jones.
No language is actually spoken with cardinal vowels: they are idealized reference points not defined by what happens in any particular language. (They are, however, suspiciously similar to a subset of the vowels of standard French as spoken in Jones’s day — though the quality of French ɔ, at least, was and is considerably different from that of cardinal ɔ. In passing we may note that the articulatory-auditory theory behind Jones’s cardinal vowel scheme is no longer accepted.)
Rather, these symbols are used for vowels in the general area concerned. Like all IPA symbols, they allow some considerable leeway. A typical French e is not identical with a typical Italian e or a typical German e, although all share a general similarity and all can be characterized as unrounded, front, and close-mid (‘half-close’). Compare colour terms, where we happily refer to shades of crimson, scarlet, vermilion and so on all as ‘red’. We are dealing not with discrete entities but with points in a multidimensional continuum.
In those languages it so happens that the close-mid e is distinct from an open-mid (‘half-open’) ɛ. (This claim is subject to qualification: for many French speakers the choice of one or the other can be more or less predicted from the phonetic environment, although others distinguish e.g. les le from lait lɛ; not all Italians make the distinction between venti ‘twenty’ with e and venti ‘winds’ with ɛ; in German the vowel quality distinction is accompanied, in stressed syllables at least, by a length distinction.)
There are many other languages in which there is only one unrounded mid front vowel: they include Greek, Spanish, Serbian, and Japanese. Qualititatively this may lie anywhere between cardinal e and cardinal ɛ. In each case the appropriate symbol, though, is e. In the words of the 1949 IPA Principles booklet (§20),
When a vowel is situated in an area designated by a non-roman letter, it is recommended that the nearest appropriate roman letter be substituted for it in ordinary broad transcriptions if that letter is not needed for any other purpose. For instance, if a language contains an ɛ but no e, it is recommended that the letter e be used to represent it. This is the case, for instance, in Japanese…
Similarly, the symbol a, which as a cardinal vowel symbol denotes an unrounded front open (low) vowel, is also appropriate to denote an unrounded open vowel of any degree of advancement (anywhere from fully ‘front’ to fully ‘back’) if that is the only open vowel in the language. This is the case in Spanish, Italian, Greek, Serbian, German, and Polish, to mention only a handful of European languages. It is also the case in thousands of other languages around the world.
In RP I say ðə kæt sæt ɒn ðə mæt. If I switch into northern (I was bidialectal as a child), I say ðə kat sat ɒnt mat. That’s how I would transcribe it. I’ll leave someone else to measure the formant values of my northern a to determine just how central it might be.
This is a live issue. The Council of the IPA, having previously failed to agree, is again debating the issue of whether to recognize an additional vowel symbol, A, to represent a quality between cardinals a and ɑ. I shall vote against.