Using `interval` in a sentence

I Supposing a case of definition which is not mathematical, and which, although user Edwin Ashworth's comment would find it unidiomatic, I would find only rare, the following can be said as pertains to an interval of time.

"Interval between which" is very rare compared with two other options with the same meaning and it should be avoided in my opinion because it is not logical.
"Interval at which" is all right but "interval during which" is preferred. This and the rarity of "interval between which" can be verified in this ngram.
The preposition "in" will be used for time too but it is very probable that it is used less often than "in", as "in" is used a lot in mathematics. In mathematic "during" can also be used for intervals of time.

II Pertaining to a mathematical definition in which no unit is stipulated only the preposition "in" would be used. The following ngram shows that the overall frequence of "in" is greater than that of "during": in.