什么 (shénme) sounds to my ears more like (shéme).
Assuming I'm hearing correctly, is this just a common contraction of this word, or is the sequence "-n" + "m-" generally contracted to "-m-"?
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Zhang and Yang (2007:157–165) classifies consonantal assimilation (輔音同化) in Mandarin into three types:
Examples of regressive assimilation
/n/ → [m] / _ [p pʰ m] (= all /n/ before [p], [pʰ], or [m] become [m]). All bilabial consonants in Mandarin exert an effect on an immediately preceding /n/.
什麼 naturally follows this rule.
|麵包||/mjɛn˥˩ paʊ˥˥/||[mjɛm˥˩ paʊ˥˥]||miàn bāo|
|亂跑||/lwan˥˩ pʰaʊ˨˩˦/||[lwam˥˩ pʰaʊ˨˩˦]||luàn pǎo|
|難免||/nan˧˥ mjɛn˨˩˦/||[nam˧˥ mjɛn˨˩˦]||nán miǎn|
/n/ → [ŋ̟] / _ [k kʰ x]. I added the advanced diacritic for [ŋ] because Zhang and Yang claims the inherent nature of /n/ is still stronger than assimilation, so the result is not exactly velar. Also, notice in the first and third examples how the final has not changed from [aŋ] to [ɑŋ], so the result of assimilation is also not exactly ang in pinyin, either.
|戰國||/ʈ͡ʂan˥˩ kuɔ˧˥/||[ʈ͡ʂaŋ̟˥˩ kuɔ˧˥]||Zhàn'guó|
|辛苦||/ɕɪn˥˥ kʰu˨˩˦/||[ɕɪŋ̟˥˥ kʰu˨˩˦]||xīn kǔ|
|山花||/ʂan˥˥ xwa˥˥/||[ʂaŋ̟˥˥ xwa˥˥]||shān huā|
/n/ → [ɲ] / _ [t͡ɕ t͡ɕʰ ɕ] (palatalisation before pinyin j q x), but /n/ → [ɳ] / _ [ʈ͡ʂ ʈ͡ʂʰ ʂ] (retroflexisation before pinyin zh ch sh). Personally I think these are less conspicuous.
|班級||/pan˥˥ t͡ɕi˧˥/||[paɲ˥˥ t͡ɕi˧˥]||bān jí|
|感情||/kan˨˩ t͡ɕʰɪŋ˧˥/||[kaɲ˨˩ t͡ɕʰɪŋ˧˥]||gǎn qíng|
|看戲||/kʰan˥˩ ɕi˥˩/||[kʰaɲ˥˩ ɕi˥˩]||kàn xì|
|班長||/pan˥˥ ʈ͡ʂɑŋ˨˩˦/||[paɳ˥˥ ʈ͡ʂɑŋ˨˩˦]||bān zhǎng|
|難吃||/nan˧˥ ʈ͡ʂʰɚ˥˥/||[naɳ˧˥ ʈ͡ʂʰɚ˥˥]||nán chī|
|天山||/tʰjɛn˥˥ ʂan˥˥/||[tʰjɛɳ˥˥ ʂan˥˥]||tiān shān|
Example of progressive assimilation
/∅/ → [ŋ] / [ŋ] _ (= all /∅/ after [ŋ] become [ŋ]).
|嫦娥||/ʈ͡ʂʰɑŋ˧˥ ɤ˧˥/||[ʈ͡ʂʰɑŋ˧˥ ŋɤ˧˥]||Cháng'é|
Example of bidirectional assimilation
/n ∅/ → [ŋ̟ ŋ̟]. It is as if the third and fifth rules are combined.
|專案||/ʈ͡ʂwan˥˥ an˥˩/||[ʈ͡ʂwaŋ̟˥˥ ŋ̟an˥˩]||zhuān àn|
|天鵝||/tʰjɛn˥˥ ɤ˧˥/||[tʰjɛŋ̟˥˥ ŋ̟ɤ˧˥]||tiān é|
Reference: Zhang Bennan & Yang Ruowei (2007). [普通話連讀音變]. Hong Kong: Commercial Press.