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→All Intervals
The other numbered intervals come in pairs of major and minor, with the minor nearer the root and major further. Think minor = smaller and major = larger in terms of the distance between the component pitches.
Sometimes you may see interval names not listed above, like {{Mn7|A6]] }} (augmented 6th) or {{M6|d7}} (diminished 7th). Augmented simply means raised a half-step above a major or perfect interval and diminished means lowered a half-step below a minor or perfect interval. So an {{Mn7|A6}} is really the same interval as a {{Mn7|m7}}, and a {{M6|d7}} is the same as a {{M6|M6}}. The reason the alternate names are occasionally used is that the interval names are sometimes required to fulfill the practice of naming the intervals in a scale while using 2-7 once each, for more exotic scales. Also, interval names imply harmonic function - the alternate names suggest a different function from how such intervals usually act.
Let's play all of the different intervals: