A type of diatonic interval which comes in two basic sizes, either major (big) or minor (small) -- as opposed to perfect, which is a type of interval with only one basic size.
In traditional diatonic music, the imperfect intervals are the 2nds, the 3rds, the 6ths, and the 7ths, and also the 9ths (8ve + 2nd), 10ths (8ve + 3rd), and 13ths (8ve + 6th).
If a major interval is widened by a chromatic semitone, it becomes augmented; if it is narrowed by a chromatic semitone, it becomes minor.
If a minor interval is narrowed by a chromatic semitone, it becomes diminished; if it is widened by a chromatic semitone, it becomes major.
If any imperfect interval is widened or narrowed by a diatonic semitone, the nominal changes and thus it becomes a different interval.