natural body smell
sounds to me as "smells badly"
natural body odor
also smells badly - something "stinks"
natural body fragrance
a pleasant, sweet smell, also after using perfume.
Is there a neutral word that I can use?
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natural body odor is usually an unpleasant smell. While it is the proper scientific term, it is associated to sweating and bad hygiene in ads. So I wouldn't use it unless you are writing a scientific piece.
natural body smell is pleasant if and only if you add "pleasant". It's a neutral term, but that means you have to specify "good" or "bad" and without adjectives most people will assume "bad"
natural body fragrance definitely makes me think of something pleasant. But if you wear perfume or cologne, it's not natural any more :)
How about scent?
If your intention is to refer to a distinctive odor that is pleasant, use :
I think while 'smell' may represent 'bad' and 'good' both, 'odor', in almost all cases, is 'bad'. I've never encountered something with 'good odor'!
Said that, I'd prefer...
Body's natural smell
Note: When we talk about 'smell' it's either 'bad' or 'good'. In between comes 'smell-less' or 'odorless'. Hence, if the 'body' you are defining 'sweaty', it'd have 'odor', if the body is sprayed with 'deo', it'd have 'fragrance'. If it's neither of the cases, it's probably 'odor/smell less'.