The Collaborative International Dictionary of English v.0.48:

Instrumentally \In`stru*men"tal*ly\, adv.
   1. By means of an instrument or agency; as means to an end.
      --South.
      [1913 Webster]

            They will argue that the end being essentially
            beneficial, the means become instrumentally so.
                                                  --Burke.
      [1913 Webster]

   2. With instruments of music; as, a song instrumentally
      accompanied. --Mason.
      [1913 Webster]