diminished interval, chords, and scales
Fig 1. Diminished seventh.
Fig 2. C diminished scale.
Diminished means lowered or reduced. A diminished interval is a perfect or minor interval that has been reduced in pitch by a half-tone (semitone). For example, a perfect fifth is an interval of seven semitones; therefore, a diminished fifth is an interval of six half-tones.
A diminished triad is a triad which contains a root, a minor third, and a diminished fifth – in other words, a root with two minor thirds stacked on top (or a minor chord with a flattened 5th). For example, B dim = B D F (there being 3 half-tones between the B and the D, and another 3 half-tones between the D and the F). Likewise, F♯ dim = F♯ A C.
In practise, the diminished triad is considered dissonant (see dissonance) and unstable because the diminished fifth splits the octave right down the middle. In a major scale, a diminished triad always starts on the seventh degree of the scale because of the way intervals are laid out in a major scale.
Diminished triads are not the most attractive-sounding of chords and are not used very often.
More commonly used than the diminished triad is the diminished seventh (d7), also called the full diminished, which adds a double flattened seventh (equivalent to a sixth) to the basic triad (Fig 1). In other words, it's an interval produced by reducing a minor seventh by a semitone. It spans nine semitones and is enharmonically equivalent to a major sixth. The result is a chord in which each note is separated from the next by the interval of a minor third. The chord can resolve in any number of directions, and was prized by Romantic composers for its versatility, its ambiguity, and, in dramatic contexts, its somewhat dark, threatening sound.
For instance, the interval from A to G is a minor seventh (10 semitones wide), and both the intervals from A♯ to G, and from A to G♭ are diminished sevenths (9 semitones wide).
The diminished seventh occurs naturally in every diatonic harmonic minor scale, between the leading note (7th degree or VII) and the submediant (6th degree or VI).
The diminished seventh forms part of the chord of the diminished seventh (in the key of C consisting of the notes B-D-F-A flat). The theoretical explanation of the chord is that it is the chord of the minor ninth (G-B-D-F-A flat) with the root omitted. This chord is particularly serviceable as a pivot for neat and easy modulation on account of its protean versatility (e.g. the B-D-F-A flat mentioned above may be enharmonically changed into B-D-F-G sharp, or B-D-E sharp-G sharp, etc., thus turning it into an inversion of the chord of the diminished seventh in some other key, in which it may be quitted).
The other diminished chord of note is the half diminished, or minor 7 flat 5. This is the same chord type as the ordinary minor seventh but with the fifth scale degree flattened.
A diminished scale (Fig 2), also known as a symmetric scale, is a scale in which the octave is divided symmetrically into eight intervals with the step pattern:
For example, the scale of C diminished is C D E♭F G♭A♭A B C.
Each diminished scale has four potential key-centers – the first, third, fifth, and seventh notes in the scale. This means that only three diminished scales are needed in order to cover all twelve keys. One starts from C, the second starts from C♯/D♭, and the third starts from D. The scale that starts from C contains the same notes as the E♯, G♯, and A scales. C♯ is the same as E, G, and B♭, and D is the same as F, A♭, and B.
The diminished scale is like the augmented scale in its potential to occupy or suggest more than one key-center. Melodies and chords built on diminished scales are very unlike the familiar melodies built on diatonic harmony, and tend to have a disorienting effect on a key-center.