Diminution, from Medieval Latin diminutio (alteration of Latin deminutio, decrease), is a musical term used to mean different things in the context of intervals, scales, chords or note values.
In the theory of harmony it is known that a diminished interval needs to be resolved inwards, and an augmented interval outwards."
—Maria Renold (2004), p.15
If a perfect or major interval is made one-half step larger (without changing its interval number) it becomes augmented. If a perfect or minor interval is made one-half step smaller (without changing its interval number) it becomes diminished.
—Benward & Saker (2003), p.54
Most nonharmonic tones are dissonant and create intervals of a second, fourth, or seventh. Diminished or augmented intervals are also considered dissonant.
—Benward & Saker (2003), p.92
An interval is diminished if a minor or perfect interval is narrowed by a chromatic semitone. Thus a diminished fifth interval, for example, is a chromatic semitone narrower than the perfect fifth. A diminished seventh interval is a chromatic semitone narrower than the minor seventh, and is enharmonic to a major sixth. Diminished intervals are often used is jazz, art and Heavy Metal music, but not as often in pop music.
An example of a diminished scale would be A Dim: A-B-C-D-D♯-F-F♯-G♯-A. Diminished scales are very easy to construct, you simply start at your required root note, and from there just move up a tone and then a semitone, continue this until you have your scale. This may be visualized:
Semitones: 2 1 2 1 2 1 2 1|=12
Note name: A B C D Eb F Gb Ab | A♮
From the diminished scale you can form a diminished triad chord by using the A, C, and E♭ (root, minor third, diminished fifth).
In a diminished seventh chord you have 4 notes which are each a successive minor third apart, leading to minimal transposition. In the latter So there are actually only 3 different diminished seventh chords (e.g. Cdim7 contains the notes C, E♭, G♭, A, as does the diminished seventh chords with the roots of E♭, G♭, and A)
In most sheet music books, Cdim or C° denotes a diminished seventh chord (a four note chord) with root C, and Cm-5 or Cm♭5 denotes a diminished triad with root C. However, in some modern jazz books and some music theory literature, Cdim or C° denotes a diminished triad, while Cdim7 or C°7 denotes a diminished seventh chord.
Diminished note values
A melody or series of notes is diminished if the lengths of the notes are shortened (this is opposed to augmentation, where the notes are lengthened). A melody originally consisting of four crotchets (quarter-notes) for example, is diminished if it later appears with four quavers (eighth-notes) instead. This technique is often used in contrapuntal music. It gives rise to the "canon in diminution", in which the notes in the following voice are shorter than those in the leading.
In Schenkerian analysis a diminution is a division, rather than a diminishing is a prolongation or expansion, "the process by which an interval formed by notes of longer value is expressed in notes of smaller value," see nonchord tone.
^ Sembos (2006). Principles of Music Theory, p.51. ISBN 1430309555. online.
^ Renold, Maria (2004). Intervals, scales, tones and the concert pitch, p.15. ISBN 1902636465.
^ Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.54. ISBN 978-0-07-294262-0.
^ Benward & Saker (2003), p.92. Benward & Saker (2009). Music: In Theory and Practice, Vol. II, p.36. ISBN 978-0-07-310188-0.