There are two audio recordings that I am listening to both have different pronunciations of the pinyin “kun”.
Which pronunciation should I be following or which is more standard for stuff like HSK?
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In my opinion, the Chinese pinyin "kun" sounds like "kwen".
If you like to take a further look at the the pronunciation, you can see Zhuyin(Bopomofo), which we often use it in Taiwan: ㄎㄨㄣ
ㄎ / ㄨ / ㄣ
k / wu / en
BTW, I think those two audio sounds familiar.