Quality
The name of any interval is further qualified using the terms perfect (P), major (M), minor (m), augmented (A), and diminished (d). This is called its interval quality. It is possible to have doubly-diminished and doubly-augmented intervals, but these are quite rare, as they occur only in chromatic contexts. The quality of a compound interval is the quality of the simple interval on which it is based (see here for details).
Major/minor
Major and minor intervals are so-called because certain diatonic intervals (seconds, thirds, sixths, sevenths, and their compounds) may occur in two sizes in the diatonic scale. The larger of the two versions is called major, the smaller one minor. For example, the third occurs both as three semitones away from Re, Mi, La, and Ti in the major scale (or in the C major diatonic scale, three semitones above D, E, A, and B), and four semitones away from Do, Fa, and Sol, (or C, F, and G). The smaller, three-semitone version is called the "minor third" and the larger, four-semitone one is called the "major third". Major intervals invert to minor ones, and vice-versa. For example, a major second inverts to a minor seventh, and the reverse.
Perfect
Perfect intervals are so-called because of their high levels of consonance, and because the inversion of a perfect interval is also perfect. Other kinds of intervals have an opposite quality with respect to their inversion. The inversion of a major interval is a minor interval, the inversion of an augmented interval is a diminished interval. Within the diatonic scale all fourths and fifths are perfect, with five and seven semitones respectively, except for one occurrence each of six semitones: the fourth between Fa and Ti (an augmented fourth), and its inversion, i.e. the fifth between Ti and Fa (a diminished fifth).
Augmented/diminished
Augmented and diminished intervals are so called because they exceed or fall short of either a perfect interval, or a major/minor pair by one semitone, while having the same interval number (i.e. encompassing the same number of staff positions). Except for the augmented fourth (Fa-Ti) and diminished fifth (Ti-Fa), they do not appear in the diatonic scale. For instance, there is no three-semitone interval in the diatonic scale that functions as a second, and the augmented second (e.g., Eâ–Fâ¯) is three semitones wide.
[edit] Example
Neither the number, nor the quality of an interval can be determined by counting semitones alone. As explained above, the number of staff positions must be taken into account as well.
For example, as shown in the table below, there are four semitones between A and Câ¯, between A and Dâ, between A⯠and D, and between Aâ and Bâ¯, but
* the interval A-C⯠is called a major third (as it spans 3 staff positions),
* the intervals A-Dâ and Aâ¯-D are called diminished fourths (as they span 4 staff positions),
* the interval Aâ-B⯠is called a doubly augmented second (as it spans 2 staff positions).