We class "unison, octave, perfect fifth, perfect foruth, major and minor third, and major and minor sixth" intervals as "consonant" intervals. All others ("seconds, sevenths, ninths, elevenths, and thirteenths, and all augmented and diminished intervals - are dissonant"(Prout, p. 10). We have as subclasses of the consonant intervals the perfect and imperfect consonances.
Perfect consonances - these consist of the "unison, octave, perfect fourth, and perfect fifth"(Prout, p. 10). Any alteration of either note by an accidental (which will raise or lower it a chromatic semitone) causes the perfect consonance to become dissonant. However, we can change a major 3rd into a minor 6th or a minor 6th into a major third and preserve its consonance.
Imperfect consonances - These consist of "the major and minor thirds and major and minor sixths"(Prout, p. 10).
Prout, Ebenezer. (1889). Harmony, its Theory and Practice. London: Augener, LTD.