The mod of an oscillator or spaceship is the smallest number of generations that it takes for it to reappear in its original form, possibily subject to some rotation or reflection.
The mod of a pattern may be equal to its period, but it may also be a quarter of the period (for oscillators that rotate 90 degrees every quarter period) or half the period (for other oscillators that rotate 180 degrees every half period, oscillators with 180 degree rotational symmetry that rotate 90 degrees every half period, and also for flippers).
The toad is an example of an oscillator with a mod identical to its period, as its two phases are completely distinct and one cannot be mapped to the other purely through rotation and translation. (click above to open LifeViewer) RLE:herePlaintext:here
The clock is an example of an oscillator with a mod which is half its period, as both of its phases are a three-cell-long line and one can clearly be turned into the other by a 90-degree rotation. (click above to open LifeViewer) RLE:herePlaintext:here
The phoenix 1 is another example of an oscillator with a mod which is half its period, as both of its phases are interchangeable through orthogonal mirroring. (click above to open LifeViewer) RLE:herePlaintext:here
Sixty-nine is an example of an oscillator with a mod which is a quarter its period, as all four of its phases are identical and differ only by 90 degree rotation. (click above to open LifeViewer) RLE:herePlaintext:here