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I have come accross "per each" several times when editing scientific papers, but it sounds unnatural and even redundant.

Doesn't "per" mean "for each" already, thus making "per each" redundant or incorrect?

Example: "The video sample has three audio channels per each section."

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    Yes, it is completely redundant. "three audio channels per section" would be correct. – Hellion Oct 4 '16 at 18:59
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    In this context, I agree. However "per" is not exactly equivalent to "for each". It must be followed by a unit of measure. For example, you can say "$10 per piece" and you can say "$10 for each" but you can't say "$10 per". You can even say "$10 per each" and be understood because "each" can be understood as a unit of measure. – MetaEd Oct 4 '16 at 21:19
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I agree that "for each" or "per" are more fluent terms than "per each" and that "each" is likely redundant to the meaning.

However, it is not entirely clear in your example sentence what definition of "per" is desired. If it simply means "for each section" then the phrase is indeed poorly worded. However, the author may have intended to say:

The video sample has three audio channels through each section

Regardless of the intended meaning, "per each" is both irregular and unclear; so the alternate phrasing mentioned above should be encouraged in its stead.

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In the given example, yes, "per each" is redundant, and the sentence should just be "... channels per section". However, "per" should be connected to something, so there are cases where it needs each attached. For example, a table listing item names, quantities, price per item, and total price. The third column might be titled "cost per", but this doesn't work. I have seen "cost per each" written, although I would prefer "cost per item" if possible.

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You either use per or each. You cannot use both at the same time

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    While this answer might be correct, it would be better with references to back it up. Please find and edit some into the answer. – CJ Dennis Jan 31 at 3:27

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