The interval between, say, C4 and D4 is a major 2nd.
What is the interval between B#3 and C4?
Is it still a 2nd?
For lack of a better term would it be something like a minor minor 2nd?
If I'm not mistaken, there are also double diminished and double augmented intervals, like Bb - Cx but rarely used
Generally the interval qualities are: Diminished, Minor, Major, Augmented or Diminished, Perfect, Augmented.