Invertible counterpoint
Counterpoint whose voices can be swapped.
What it means
Invertible counterpoint refers to a two-part passage constructed so that the upper and lower voices can exchange places without producing faulty part-writing such as forbidden parallel fifths or octaves. Usually one of the two voices is displaced by a fixed interval, such as an octave, a tenth, or a twelfth, which is why one speaks of invertible counterpoint at the octave, the tenth, or the twelfth.
Musical use
Invertible counterpoint is a central tool of contrapuntal part-writing, especially in fugues, where a two-part passage invented once returns later with the voices swapped, yielding a new sonic variant of the same musical material without composing new substance. It requires the composer to anticipate, already in the original draft, all the interval relationships that the later inversion will create.
It should be distinguished from a simple voice exchange made without such precautions, where swapping the parts would create parallels or other undesirable successions. With more than two exchangeable voices, one speaks of triple or multiple counterpoint.
Performance practice
When listening to a passage in invertible counterpoint, notice whether a passage recalls an earlier one with the voices simply swapped: this often reveals the composer's contrapuntal craftsmanship. If you write counterpoint yourself, check every planned voice inversion at the piano beforehand to catch forbidden parallels early.