tripleness--prophetes.ai

tripleness rare.
  (ˈtrɪp(ə)lnɪs)
  [f. triple a. + -ness.]
  The quality or condition of being triple; triplicity.

c 1881 Hort in Expositor June (1907) 489 When there is tripleness and at the same time not mere co-ordination but progression.

Oxford English Dictionary