coarseness vs inelegance

coarseness and inelegance both are nouns.

Word	Noun	Adjective	Verb	Adverb
coarseness	Yes	No	No	No
inelegance	Yes	No	No	No

As nouns, inelegance is a hypernym of coarseness; that is, inelegance is a word with a broader meaning than coarseness:

coarseness (noun)	inelegance (noun)
looseness or roughness in texture (as of cloth)	the quality of lacking refinement and good taste
the quality of being composed of relatively large particles
the quality of lacking taste and refinement
language or humor that is down-to-earth