Everything's relative

 Intervals come in many shapes and sizes, but in only five categories: major, minor, perfect, augmented and diminished.

 Here's how the categories are related:

 

A major interval lowered one half step equals a minor interval.

A major or perfect interval raised one half step equals an augmented interval.

A perfect interval lowered one half step equals a diminished interval.

  An interval's type is determined by the number of steps between the two notes.