Editing Diminution (section)

== Diminution of intervals<span class="anchor" id="diminished_interval_anchor"></span> ==

A '''diminished interval''' is an interval obtained from a minor interval or perfect interval by narrowing it by a [[chromatic semitone]], meaning that the interval is narrowed by a semitone, but the staff positions are not changed (only an [[Accidental (music)|accidental]] is changed); the process may occasionally be referred to as diminution For example, a [[diminished sixth]] is a chromatic semitone narrower than the [[minor sixth]]: starting with the interval from B to G, which is a minor sixth, eight semitones wide, the interval from B to G{{music|flat}} is a diminished sixth, spanning seven semitones, but the same staff lines. By contrast, the interval from B to F{{music|sharp}} is not a diminished sixth (it is a perfect fifth): even though it is seven semitones wide, it spans five staff positions, and is thus a fifth, not a sixth; it is a [[diatonic semitone]] narrower than a minor sixth. The standard abbreviations for diminished intervals are dX, such that a diminished third = d3.<ref name="B&S"/> The diminished fifth ('''d5''') is the only diminished interval that appears in diatonic scales (in D{{music|flat}} major it occurs between C and G{{music|flat}}).

{| cellpadding="2" style="border: 1px solid darkgray; margin: 1em auto 1em auto;"
|+ '''Diminished intervals on C'''
|- align="center"
! width="140" | [[Diminished second]]
! width="140" | [[Diminished third]]
! width="140" | [[Diminished fourth]]
! width="140" | [[Diminished fifth]]
! width="140" | [[Diminished sixth]]
! width="140" | [[Diminished seventh]]
! width="140" | [[Diminished octave]]
|- border="0"
| [[Image:Diminished second on C.png|125px]]
| [[Image:Diminished third on C.png|125px]]
| [[Image:Diminished fourth on C.png|125px]]
| [[Image:Diminished fifth on C.png|125px]]
| [[Image:Diminished sixth on C.png|125px]]
| [[Image:Diminished seventh on C.png|125px]]
| [[Image:Diminished octave on C.png|125px]]
|- align="center"
|  {{Audio|Unison on C.mid|Play}}  ||  {{Audio|Major second on C.mid|Play}} ||  {{Audio|Major third on C.mid|Play}} || {{Audio|Tritone on C.mid|Play}} || {{Audio|Perfect fifth on C.mid|Play}} || {{Audio|Major sixth on C.mid|Play}} || {{Audio|Major seventh on C.mid|Play}}
|}

{{Quote|a diminished unison is unthinkable, and the diminished 2d{{sic}} and 9th are of no practical use:...|Foote<ref>Arthur Foote, Walter Raymond Spalding (1905). ''Modern Harmony in its Theory and Practice'', p.5. Arthur P. Schmidt.</ref>}}

{{Quote|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.<ref>Renold, Maria (2004). ''Intervals, scales, tones and the concert pitch'', p.15. {{ISBN|1-902636-46-5}}.</ref>}}

{{Quote|Augmented intervals have a rather over-tense quality, while diminished intervals are experienced as rather cramped. Therefore, one may call the former [[lucifer]]ic in tendency and the latter [[ahriman]]ic.|Renold (2004), p.16{{Clarify|date=August 2011}}}}

{{Quote|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.<ref name="B&S">Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.54. {{ISBN|978-0-07-294262-0}}.</ref>}}

{{Quote|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.<ref>Benward & Saker (2003), p.92. Benward & Saker (2009). ''Music: In Theory and Practice, Vol. II'', p.36. {{ISBN|978-0-07-310188-0}}.</ref>}}

===Diminished chords===
[[Image:Diminished triad on C.png|thumb|125px|right|Diminished triad on C {{Audio|Diminished triad on C.mid|play}}.]]
A [[diminished triad]] consists of two superposed [[minor third]]s, and thus contains a [[diminished fifth]]. In classical repertoire the usual symbol {{music|dim}} resembles the [[degree symbol]], as in vii{{music|dim}}. In lead sheets and popular music books it is usually written Cdim or C{{music|dim}}.

[[Image:Diminished seventh chord on C.png|thumb|125px|left|Diminished seventh chord on C {{audio|Diminished seventh chord on C.mid|Play}}.]]
A [[diminished seventh chord]] consists of three superposed minor thirds, and thus has all successive notes a minor third apart; it contains two diminished fifths. In jazz theory, a diminished seventh chord has four available tensions, each a major ninth above the chord tones, and thus forming a diminished seventh chord a whole tone (or major ninth) above the root chord. Because any chord tone of the diminished seventh can be heard as the root, the tensions are not numbered as ninth, eleventh and so on. The usual notation is Cdim<sup>7</sup> or C{{music|dim}}<sup>7</sup>, but some lead sheets or popular music books may omit the 7.

[[Image:Half-diminished seventh chord on C.png|thumb|125px|right|[[Half-diminished seventh chord]] on C ({{Audio|Half-diminished seventh chord on C.mid|Play}}).]]
A diminished triad with a minor seventh is a half-diminished chord, usually notated either Cm<sup>7({{Music|flat}}5)</sup> or C<sup>ø7</sup>. A diminished triad played over a root a major third away creates a Dominant 7th chord, notated C<sup>7</sup>, with a C Major triad on the bottom, and an E° from the chord third of C (<SPAN STYLE="text-decoration:overline">C <u>E G</u></span><u> B{{Music|flat}}</u>). A minor third below would give a fully diminished 7th chord which is made entirely of minor thirds that evenly divide an octave. This even division of the octave leaves us with only three unique diminished 7th chords: C E<sup>{{Music|flat}}</sup> G<sup>{{Music|flat}}</sup> B<sup>{{Music|doubleflat}}</sup>, C<sup>{{Music|sharp}}</sup> E G B<sup>{{Music|flat}}</sup>, and D F A<sup>{{Music|flat}}</sup> C<sup>{{Music|flat}}</sup>, as all other diminished 7th chords are inversions of one of those three.

[[File:Diminishedchords.png|thumb|Diminished chords with sheet music and tab.]]

===Diminished scales===
[[Image:Octatonic scales on C.png|thumb|right|Octatonic scales on C {{audio|Octatonic scales on C.mid|Play}}.]]
Several scales may be referred to as diminished. One of the more common is the [[Octatonic scale]] constructed from C{{music|dim}}<sup>7</sup> and its tensions (transposed into the same octave), which has alternating tone and semitone intervals.

[[Image:Half diminished scale C.png|thumb|right|[[Half diminished scale]] on C {{audio|Half diminished scale C.mid|Play}}.]]