An interval is defined as the distance between two different notes. The distance between C and G is referred to as an "interval of a fifth" (C d e f G). The distance between C and G is also a fifth, and so is that between C# and G, C and G#, Cb and Gb, etc. It is the alphabetical name that gives us the interval number. However, the interval is not completely explained until we describe its quality. This is shown by the number of semitones (or half-steps) included in the interval. The distance between C and E is a third. If this distance includes 4 semitones, we say that it is a major third. If it has only 3 semitones (C to Eb), we call it a minor third. A major interval always has one more semitone than its corresponding minor interval.
All 2nds, 3rds, 6ths and 7ths are either major or minor. We use the term perfect to describe intervals of the unison, octave, 4th and 5th values. If a major interval is chromatically increased by a semitone it becomes augmented. For example, C to A is a major sixth, but C to A# is referred as an augmented sixth. If a minor interval is reduced by one semitone it is said to be diminished. For example, G to Bb is a minor third, but G# to Bb is a diminished third. By adding or subtracting a semitone, perfect intervals can be made augmented or diminished.
Any interval of more than an octave is known as a compound interval - 9th, 10th, 11th, etc.
Intervals may also be referred as being concordant or discordant. Though the concept of which intervals are discordant or concordant have changed over time, and vary significantly from one culture to another, in Western music today it is usually considered that all perfect intervals and all major and minor thirds and sixths are concordant. All other intervals are discordant.
When two or more intervals are "stacked" on top of each other, the result is a chord.