Primary, "first order" or "first harmonic" balance is supposed to indicate the balancing of items that could shake an engine once in every rotation of the crankshaft, i.e. having the frequency equal to one crank rotation.
A cylinder in 4 cycle engines fires once in two crank rotations, generating forces with the frequency of a half the crankshaft speed, so the concept of "half order" vibrations, is sometimes used when the discussion is on the balances on torque generation and compression.