The Collaborative International Dictionary of English v.0.48:

Roundness \Round"ness\, n.
   1. The quality or state of being round in shape; as, the
      roundness of the globe, of the orb of the sun, of a ball,
      of a bowl, a column, etc.
      [1913 Webster]

   2. Fullness; smoothness of flow; as, the roundness of a
      period; the roundness of a note; roundness of tone.
      [1913 Webster]

   3. Openess; plainess; boldness; positiveness; as, the
      roundness of an assertion.
      [1913 Webster]

   Syn: Circularity; sphericity; globosity; globularity;
        globularness; orbicularness; cylindricity; fullness;
        plumpness; rotundity.
        [1913 Webster]

WordNet (r) 3.0 (2006):

roundness
    n 1: the fullness of a tone of voice; "there is a musky
         roundness to his wordiness" [syn: roundness, rotundity]
    2: the quality of being round numbers; "he gave us the results
       in round numbers, but their roundness didn't affect the point
       he was making"
    3: the property possessed by a line or surface that is curved
       and not angular [ant: angularity]
    4: the bodily property of being well rounded [syn: plumpness,
       embonpoint, roundness]

Moby Thesaurus II by Grady Ward, 1.0:

42 Moby Thesaurus words for "roundness":
   annularity, annulation, artlessness, belly, bluffness, bluntness,
   broadness, brusqueness, candidness, candor, circularity, convexity,
   cylindricality, directness, forthrightness, frankness, freedom,
   freeness, genuineness, globosity, globularity, ingenuousness,
   openheartedness, openness, orbicularity, outspokenness,
   plain dealing, plain speaking, plainness, plainspokenness,
   rotundity, rotundness, sincerity, sphericality, sphericalness,
   sphericity, spheroidicity, spheroidity, straightforwardness,
   unconstraint, unreserve, unrestraint