The most common use of Interval is in the construal Time↝Interval: the time of an event is described via a temporal offset from some other time.
(This category is unusual in primarily marking a construal for a different scene role. But this seems justified given the restrictive set of English temporal prepositions that can appear with a temporal offset, and the distinct ambiguity of in. Interval is designed as the temporal counterpart of Direction, which can construe static distance measures; in fact, TimeDirection was considered as a possible name, but Interval seemed more straightforward for the most frequent class of usages.)
Other adpositions can also take an amount of intervening time as their complement (object):
Some adpositions license a temporal difference measure in modifier position, which does not qualify:
The prepositions in and within are ambiguous between Interval and Duration.4 The distinction can be subtle and context-dependent. The key test is whether the phrase answers a When? question. If so, its scene role is Time; otherwise, it is a Duration.
With a negated event, we use Duration:
While a while back and a few generations back are generally accepted, the use of back rather than ago for nearer and more precise temporal references, e.g. 10 minutes back, appears to be especially associated with Indian English (Yadurajan, 2001, p. 7). ↩
This usage of in, as well as ago #001 and back #002, #003, are deictic, i.e., they are inherently relative to the speech time or deictic center. (See also (Klein, 1994, pp. 154–157).) This was taken to be a criterion for the v1 category DeicticTime, but that was never well-defined in v1 and was broadened for this version. ↩
By contrast, after seems to strongly favor Time↝Interval. After a week, I had climbed all the way to the summit is possible, but the conclusion that the climbing took a week may be an inference rather than something that is directly expressed. ↩
A marker that points retrospectively or prospectively in time, and if transitive, marks the time elapsed between two points in time.