Chase F. answered 7d
Music Theory Tutor – Harmony, Rhythm, Scales & Applied Skills
Hi Jax,
I think it's important we first get our terminology straight. A "minor interval" isn't a common term, but you might be referring to all the minor intervals (minor 2nd, minor 7th, minor 13th, etc.). Same thing with diminished (diminished 5th or 7th). When talking about intervals, major, minor, diminished, augmented and perfect are modifiers of the interval. For 2nds, 3rds, 6ths and 7ths, we use minor and major, with major always being one half step above the respective minor interval. So a minor 6th (m6) is 8 half steps while a major 6ths (M6) is nine half steps. For 4ths, 5ths and unisons (or octaves), we use perfect to describe how that interval is in the major scale. If it's a half step below that perfect interval, we use diminished and if a half step above, we use augmented. For example, an augmented 5th is enharmonically equivalent is a m6. This diminished/augmented system can be applied to 2nds, 3rds, 6ths and 7ths as well. Commonly, in jazz harmony we will have an augmented 2nd (or 9th) which is equal to a m3. We can even have double diminished or double augmented intervals, although these are rarely used in real music.
For determining whether an interval is a m6 or an augmented 5th, it depends on context. If we already have a 5th, it's safe to say we have a m6. The same thing can be said if it's a minor chord without a 5th. An augmented 5th is generally part of a major chord, thus having a major third. These sound quite different despite being the "same interval."
For chords, the same words (minor, major, diminished, augmented) are used to refer to related triads. An augmented chord has a major third and augmented 5th while a diminished chord has a minor third and diminished 5th. For diminished chords, we also have half diminished and fully diminished seventh chords which add a minor 7th (10 half steps from root) or diminished 7th (9 half steps from root) respectively.
Hope this helps and please let me know if you have other questions :)