In American Accent Training, it shows that the "down" is pronounced as /dæon/, where /æo/ is a combination of /æ/ and /o/.
However, according to KK or DJ, this sound is a combination of /ɑ/ and /ʊ/. I know that different systems have different phonetic alphabet symbols, but I doubt the correctness of /æo/. Anyone can clarify this for me?
You might think your question is an easy one, but what you are asking is actually very complex. The problem is that what people (and dictionaries, courses, etc.) commonly call a "phonetic transcription" is actually a "phonemic transcription". See for example the difference between "broad" and "narrow" transcriptions on Wikipedia. So when a dictionary says that "now" is pronounced /naʊ/, it just means that it has the /aʊ/ phoneme, but that phoneme is not necessarily pronounced with [a] and [ʊ] sounds. The exact way a phoneme is pronounced depends on the region and dialect, and it also depends on the other phonemes that precede and follow it. Bed and bet appear to have the same vowel sound in transcriptions (/bɛd/ and /bɛt/), but the truth is that generally the vowel in bed is a bit longer, because it depends on the following consonant (/d/ is voiced, while /t/ is voiceless). That's not clear at all from the transcription, because it's a broad transcription. A much more noticeable example of this in American English is the pronunciation of /æ/ before certain consonants (especially nasal ones).
So I hope you now understand that the exact pronunciation of the /aʊ/ phoneme in American English can vary a lot of course. The article on the phonology of North American English on Wikipedia mentions several different pronunciations for /aʊ/: [ɑʊ~äʊ] in Eastern New England, [æɵ~æo] in Midland American English, [ɛɔ] in Mid-Atlantic dialects, etc. The article on General American on Wikipedia has [aʊ~æʊ].
