Its full specification is (n-)APSp: (n pitches of an) arithmetic pitch sequence adding by irrational interval p. The n is optional. If not provided, the sequence is open-ended.
The pitch of the kth step of an APSp is quite simply k⋅p.
Relationship to other tunings
vs. rank-1 temperaments & equal multiplications
If specified, an APS will be equivalent to some EPD, or equal pitch division. Specifically, n-EPDx = n-APS(x/n), for example 12-EPD1200¢ = 12-APS(1200¢/12=100¢).
The only difference between an APS and an AS (ambitonal sequence) is that the p for an APS is irrational.