The chromatic scale
The chromatic scale splits an octave in 12 semitones. The twelve notes on this scale are the familiar C, C#/Db, D, D#/Eb, E, F, F#/Gb, G, G#/Ab, A, A#/Bb, B. The scales that arise from them are the most commonly used scales in Western music.
Since the chromatic scale and scales that use the notes of the chromatic scales are common, during the historical development of music theory based on these scales various names have appeared to describe the intervals between notes on these scales. For example, the interval of two semitones (such as between C and D) is sometimes called a major second. This interval is called "second", if it is occurring between the first note of a scale and the second note of the scale. For example, the C major scale starts with C and its second note is D. Hence, this scale starts with a major second. The interval is called "major" as theorists noted that this interval was larger than the other commonly occurring interval – the minor second (one semitone).
Major, minor, and perfect intervals
The most commonly used scales based on the chromatic scales are the modes of the primary heptatonic scale (also known as "diatonic scale"). The major scale and the natural minor scale are two examples of these scales. Such scales use only intervals of one semitone or two semitones between adjacent notes (two one-semitone intervals and five two-semitone intervals for a total of twelve semitones) and have the one-semitone intervals most evenly spaced. For example, the major scale uses the following intervals between adjacent notes: 1, 1, ½, 1, 1, 1, ½.
If you write out all modes of the primary heptatonic scale, you will note the following. The difference between the root of the scale and the second note on the scale is either one semitone or two semitones giving rise to the names minor second and major second for these intervals respectively. The difference between the root of the scale and the third note on the scale is either three or four semitones giving rise to the names minor third and major third for these intervals respectively. The difference between the root of the scale and the fourth note of the scale is almost always five semitones (except for the Lydian scale) and hence this interval was called a perfect fourth (the term "perfect" is used when there is no need to denote minor or major intervals). Similarly, the terms perfect fifth, and major and minor sixth and seventh are also used.
Augmented intervals and diminished intervals
While these are the most common intervals between notes on the primary heptatonic scales, other intervals exist as well. For example, the interval between the root and the fourth of the Lydian scale is six semitones, which is one semitone larger than the perfect fourth. This interval is called an augmented fourth. The interval between the root and the fifth of the Locrian scale is also six semitones, one semitone smaller than the perfect fifth. This interval is called a diminished fifth. While an augmented fourth and a diminished fifth are both six semitones, they actually denote the interval between the root and two different degrees of the scale (the fourth and the fifth).
Thus, the term "augmented" is used to describe intervals that are larger by one semitone than a "major" or a "perfect" interval as the case may be. The term "diminished" is used to describe intervals that are smaller by one semitone than a "minor" or a "perfect" interval as the case may be. Obviously, an "augmented seventh" is not really a useful term as it would produce twelve semitones (the same note an octave higher). Similarly, "diminished second" is not useful as it would produce the interval of zero semitones (unison).
A listing of topics related to the intervals of the chromatic scale is provided in the topic Intervals on the chromatic scale (index).