Parity means even or odd, particularly as applied to the phase of an oscillator or spaceship. For example, in slow salvo constructions, the intermediate targets are frequently period 2, most often because they contain blinkers or traffic lights. A glider striking a P2 constellation will generally produce a different result depending on its parity. Period-4 intermediate targets are rare (or not used), so it doesn't matter if an incoming glider is in phase 1 or phase 3. Only the even/odd parity is important.