An Etymological Dictionary of the German Language/Schmutz
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Schmutz, m., ‘dirt, filth,’ from the equiv. MidHG. smuz (-tzes), m., allied to MidHG. smotzen, ‘to be dirty’; also to Du. smet, ‘spot, dirt,’ smetten, ‘to get stained,’ smodderen, ‘to soil,’ E. smut, vb. and subst., MidE. bismitten, bismoteren, bismudden, ‘to stain, soil.’ It is uncertain whether these words are late graded forms of MidHG. smitzen, ‘to rub over.’