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I recognize one vowel in every syllable except "ん" when speaking Japanese. It may be helpful to compare English words with loanwords. When I run across a word "count" in an English text, I only feel one vowel, but when I see the corresponding loanword カウント in a Japanese text, I feel it has four syllables, three of which have vowels: カ(ka), ウ(u), ン(n), and ト(to).
If you say "count" in English, it sounds to monolingual Japanese something like か + unknown foreign sound (kind of mixture of "oo" and "n" following か smoothly) + noise (consonant "t"). Note that the brains of monolingual Japanese don't recognize the consonant "t" as part of language because it isn't followed by a vowel, and they either ignore it or think your tongue made a noise with saliva. It's no more a phoneme than grinding of the teeth.
Also, the smoothness between kah-oo-nn makes your pronunciation quite foreign.
That said, I think it'd be better to just mimic native speakers and not to analyze phonetics. Well, I should've said this first, but whatever.