The Collaborative International Dictionary of English v.0.48:

Melodious \Me*lo"di*ous\, a. [Cf. F. m['e]lodieux. See
   Melody.]
   Containing, or producing, melody; musical; agreeable to the
   ear by a sweet succession of sounds; as, a melodious voice.
   "A melodious voice." "A melodious undertone." --Longfellow.
   -- Me*lo"di*ous*ly, adv. -- Me*lo"di*ous*ness, n.
   [1913 Webster]

WordNet (r) 3.0 (2006):

melodiousness
    n 1: the property of having a melody [syn: melodiousness,
         tunefulness]