Yes, but you haven't stated, even yet, that the /æ/ phoneme is usually pronounced the same in 'back' and 'man', or 'that' and 'than'.
Since it is a phonemic symbol, it has allophonic variations and, as far as I know, there are no English accents that pronounce the 'ash' phoneme the same in 'bat' and 'man'; and no one has denied that. That's all I'm saying.
Some speakers may have a longer /
æ/ in certain words (so there can be a difference) but most speakers have the same vowel quality. There is nothing like an /
æ/ - /e/ difference in the vowels of 'back' and 'man' in any one speaker.
[h=2]Bad–lad split[/h] The
bad–lad split is a
phonemic split of the Early Modern English short
vowel phoneme /æ/ into a short /æ/ and a long /æː/. This split is found in some varieties of
English English and
Australian English in which
bad (with long [æː]) and
lad (with short [æ]) do not rhyme. (Wells 1982: 288–89, 596; Horvath and Horvath 2001; Leitner 2004).
The phoneme /æ/ is usually lengthened to /æː/ when it comes before an /m/ or /n/, within the same syllable. It is furthermore lengthened in the adjectives
bad,
glad and
mad;
family also sometimes has a long vowel, regardless of whether it is pronounced as two or three syllables. Some speakers and regional varieties also use /æː/ before /ɡ/, /ŋ/, /l/ and/or /dʒ/; such lengthening may be more irregular than others. Lengthening is prohibited in the past tense of irregular verbs and function words and in modern contractions of polysyllabic words where the /æ/ was before a consonant followed by a vowel. Lengthening is not stopped by the addition of word-level suffixes.
Note that British dialects with the bad–lad split have instead
broad /ɑː/ in some words where an /m/ or /n/ follows the vowel. In this circumstance, Australian speakers usually (but not universally) use /æː/, except in the words
aunt,
can't and
shan't, which have broad /aː/.
Daniel Jones noted for RP that some speakers had a phonemic contrast between a long and a short /æ/ which he wrote as /æː/ and /æ/, respectively. Thus, in
An outline of English phonetics (1962, ninth edition, Cambridge: W. Heffer & Sons) he noted that
sad,
bad generally had /æː/ but
lad,
pad had /æ/. In his pronouncing dictionary, he recorded several minimal pairs, for example
bad /ˈbæːd/,
bade /ˈbæd/ (also pronounced /ˈbeɪd/). He noted that for some speakers,
jam actually represented two different pronunciations, one pronounced /ˈdʒæːm/ meaning 'fruit conserve', the other /ˈdʒæm/ meaning 'crush, wedging'. Later editions of this dictionary edited by
Alfred C. Gimson, dropped this distinction.
Phonological history of English short A - Wikipedia, the free encyclopedia