Editing Diminished triad

{{Short description|Two minor thirds above the root}}
{{redirect|Diminished chord|the seventh chord|Diminished seventh chord}}
{{Infobox chord|
chord_name=diminished triad|
first_interval=[[root (chord)|root]]|
second_interval=[[minor third]]|
third_interval=[[tritone|diminished fifth]] ([[tritone]])|
tuning=[[just intonation|45:54:64]];<ref name="Shirlaw">Shirlaw, Matthew (2012). ''The Theory of Harmony'', p. 304. Forgotten Books. {{ISBN|978-1-4510-1534-8}}.</ref> 54:45=[[just minor third|6:5]] & [[just tritone|64:45]]<ref>[[Harry Partch|Partch, Harry]] (1979). ''[[Genesis of a Music]]'', pp. 68–69. {{ISBN|978-0-306-80106-8}}.</ref>|
forte_number=3-10|
complement=9-10
}}In [[music theory]], a '''diminished triad''' is a [[triad (music)|triad]] consisting of two [[minor third]]s above the [[root (chord)|root]].<ref>{{cite book|last1=Benward|last2=Saker|date=2003|title=Music: In Theory and Practice, Vol. I|page=68|publisher=McGraw-Hill |edition=7th|isbn=978-0-07-294262-0}}</ref> It is a [[Minor chord|minor triad]] with a lowered ([[flat (music)|flattened]]) [[Fifth (chord)|fifth]].  When using [[Chord names and symbols (popular music)|chord symbols]], it may be indicated by the symbols "dim", "{{music|diminished}}", "m<sup>{{music|flat}}5</sup>", or "<small>MI</small><sup>({{music|b}}5)</sup>".<ref>Benward & Saker (2003), p.77.</ref> However, in most popular-music chord books, the symbol "dim" or "{{music|diminished}}" represents a [[diminished seventh chord]] (a four-tone chord), which in some modern jazz books and music theory books is represented by the "dim7" or "{{music|diminished}}<sup>7</sup>" symbols. 

For example, the diminished triad built on B, written as B{{music|diminished}}, has pitches B-D-F:

:<score sound="1">
{ \omit Score.TimeSignature \relative c' { <b d f>1 } }
</score>

The chord can be represented by the [[Pitch class#Integer notation|integer notation]] {0,&nbsp;3,&nbsp;6}.

In the [[common practice period]], the diminished triad is considered [[Consonance and dissonance|dissonant]] because of the [[Tritone|diminished fifth]] (or tritone).

==Harmonic function==
{{Image frame|content=<score sound="1" override_midi="Bach - WTC I, Prelude in G Major diminished chord.mid">
    {
      #(set-global-staff-size 14)
      \override Score.SpacingSpanner.strict-note-spacing = ##t
      \set Score.proportionalNotationDuration = #(ly:make-moment 1/2)
      \new PianoStaff <<
        \new Staff <<
            \relative c'' {
                \key g \major \time 24/16
                g16 b d g d b d b g b g d  
                e g c e c g c g e g e c  
                a c fis a fis c fis c a c a fis  
                g b d g d b d b g b g d
                }
            >>
        \new Staff <<
            \relative c' {
                \clef F \key g \major \time 24/16
                g8.[_\markup { \concat { "I" \hspace #20.5 "IV" \hspace #19.5 "vii" \raise #1 \small  "o" \hspace #19.5 "I" } }
                g,] r g' g[ g,] r g' g[ g,] r g' g[ g,] r g'
                }
            >>
    >> }
</score>|caption=A diminished triad substituting for dominant chord in [[Johann Sebastian Bach|J. S. Bach's]] ''[[Well-Tempered Clavier]]'' I, Prelude in G major.<ref>{{cite book|title=Das Wesen des musikalischen Kunstwerks: Eine Einführung in Die Lehre Heinrich Schenkers|last=Jonas|first=Oswald|date=1982|isbn=0-582-28227-6|page=[https://archive.org/details/introductiontoth0000jona/page/25 25]|publisher=Longman |translator-last=Rothgeb|translator-first=John|trans-title=Introduction to the Theory of [[Heinrich Schenker]]|author-link=Oswald Jonas|orig-year=1934|url=https://archive.org/details/introductiontoth0000jona/page/25}}</ref>}}

In [[Major scale|major scales]], a diminished triad occurs only on the seventh [[Degree (music)|scale degree]]. For instance, in the key of C, this is a B diminished triad (B, D, F). Since the triad is built on the seventh scale degree, it is also called the ''[[Leading-tone#Leading-tone triad|leading-tone triad]]''.  This chord has a [[dominant function]]. Unlike the [[dominant triad]] or [[Dominant seventh chord|dominant seventh]], the leading-tone triad functions as a [[prolongation]]al chord rather than a structural chord since the strong root motion by fifth is absent.{{sfn|Roig-Francolí|2011|page=248}}

On the other hand, in [[Natural minor scale|natural minor scales]], the diminished triad occurs on the second scale degree; in the key of C minor, this is the D diminished triad (D, F, A{{music|b}}). This triad is consequently called the ''[[supertonic]] diminished triad''. Like the supertonic minor triad found in a major key, the supertonic diminished triad has a [[Predominant chord|predominant function]], almost always resolving to a dominant functioning chord.{{sfn|Roig-Francolí|2011|page=174}}

If the music is in a minor key, diminished triads can also be found on the raised seventh note, {{music|#}}vii{{music|dim}}. This is because the [[ascending melodic minor scale]] has a raised sixth and seventh degree. For example, the chord progression {{music|#}}vii{{music|dim}}–i is common.

The leading-tone diminished triad and supertonic diminished triad are usually found in [[first inversion]] (vii{{music|dim}}<sup>6</sup>  and ii{{music|dim}}<sup>6</sup>, respectively) since the spelling of the chord forms a diminished fifth with the bass.{{sfn|Roig-Francolí|2011|page=248}} This differs from the [[fully diminished seventh chord]], which commonly occurs in [[root position]].<ref name="B&S2">{{cite book|title=Music in Theory and Practice: Volume II|last1=Benward|last2=Saker|date=2009|isbn=978-0-07-310188-0|edition=8th|page=76|publisher=McGraw-Hill }}</ref> In both cases, the bass resolves up and the upper voices move downwards in [[contrary motion]].<ref name="B&S2" />

==In popular music==

Walter Everett writes that "In [[Rock music|rock]] and [[Pop music|pop]] music, the diminished triad nearly always appears on the second scale degree, forming a generally maudlin and dejected ii{{music|dim}} with its members, 2–4–{{music|b}}6."<ref name="Everett">{{cite book|title=The Foundations of Rock|url=https://archive.org/details/foundationsrockf00ever_837|url-access=limited|last=Everett|first=Walter|date=2009|isbn=978-0-19-531023-8|page=[https://archive.org/details/foundationsrockf00ever_837/page/n211 195]|publisher=Oxford University Press, USA }}</ref> Songs that feature ii{{music|dim}} include [[Santo & Johnny]]'s "[[Sleep Walk]]", [[Jay and the Americans]]' "[[Cara Mia]]", and [[the Hollies]]' "[[The Air That I Breathe]]".<ref name="Everett" /> Not so rare but rare enough so as to imply knowledge of and conscious avoidance on the part of rock musicians, examples of its use include [[Oasis (band)|Oasis]]' "[[Don't Look Back in Anger]]", [[David Bowie]]'s "[[Space Oddity]]", and two in [[Daryl Hall]]'s "[[Everytime You Go Away]]".<ref name="Stephenson">{{cite book|title=What to Listen for in Rock: A Stylistic Analysis|last=Stephenson|first=Ken|date=2002|isbn=978-0-300-09239-4|page=[https://archive.org/details/whattolistenfori0000step/page/85 85]|publisher=Yale University Press |url=https://archive.org/details/whattolistenfori0000step/page/85}}</ref>

The vii{{music|dim}} in major keys is relatively less common than the ii{{music|dim}}, but still does happen. It is almost always used to [[Tonicization|tonicize]] the relative minor, in progressions such as vii{{music|dim}}–V<sup>7</sup>/vi–vi, which resembles ii{{music|dim}}–V<sup>7</sup>–i in the relative minor.

== Tuning ==
[[File:Comparison of diminished triads (0,3,6).png|thumb|Comparison, in cents, of diminished triad tunings]]

In a [[twelve-tone equal temperament]], a diminished triad has three [[semitone]]s between the third and fifth, three semitones between the root and third, and six semitones between the root and fifth. 

In [[5-limit]] [[just intonation]], the diminished chord on VII (in C: B–D–F) is 15:8, 9:8, and 4:3, while on II (in C: D–F–A{{music|b}}) it is 9:8, 4:3, and 8:5 (135:160:192). According to [[Georg Andreas Sorge]], the [[trumpet#Fingering|trumpet]], in its overtone series on C, gives the diminished triad E–G–B{{music|b}} = 5:6:7 ("perfect diminished chord"<ref>{{cite book|last1=Fétis|first1=François-Joseph|author1-link=François-Joseph Fétis|last2=Arlin|first2=Mary I.|date=1994|title=Esquisse de l'histoire de l'harmonie|page=[https://archive.org/details/esquissedelhisto0000feti/page/139 139n9]|isbn=978-0-945193-51-7|url=https://archive.org/details/esquissedelhisto0000feti/page/139}}</ref>), but the [[harmonic seventh|7]] is too flat and 45:54:64 is preferred.<ref name="Shirlaw" /> [[Hermann von Helmholtz|Helmholtz]] describes the diminished triad as  <sub>1</sub>&nbsp;−&nbsp;D&nbsp;|&nbsp;F, giving a just minor third and Pythagorean minor third (45:54:64) in the notation system used in ''[[On the Sensations of Tone as a Physiological Basis for the Theory of Music]]''.<ref>{{cite book|first=Hermann|last=Helmholtz|author-link=Hermann von Helmholtz|date=1885|title=On the Sensations of Tone as a Physiological Basis for the Theory of Music|page=344|location=Longmans, Green}}</ref> 

Play {{audio|Perfect diminished chord on C.mid|Perfect}}, {{audio|Preferred diminished chord on C.mid|Preferred}} (5-limit major), or {{audio|Five-limit minor diminished chord on C.mid|5-limit minor}} on C.

:{| class="wikitable"
|-
! rowspan="1" |
! colspan="3" | Sorge (perfect)/<br/>7-limit
! colspan="3" style="background: silver;" | Sorge (preferred)/<br/>5-limit major
! colspan="3" | 5-limit minor<br/>(D,F,A{{music|b}})
|-
| colspan="10" style="text-align: center;" | Harmonics
|-
! Root
| E
| 5
| 386.31
| style="background: #e8e8e8;" | F{{music|#}}{{music|plus}}
| style="background: #e8e8e8;" | 45
| style="background: #e8e8e8;" | 590.22
| C{{music|#}}
| 135
| 92.18
|-
! Third
| G
| 6
| 701.96
| style="background: #e8e8e8;" | A{{music|+}}
| style="background: #e8e8e8;" | 54
| style="background: #e8e8e8;" | 905.87
| E
| 160
| 386.31
|-
! Fifth
| {{nowrap|B{{music|7}}{{music|b}}}}
| 7
| 968.83
| style="background: #e8e8e8;" | C
| style="background: #e8e8e8;" | 64
| style="background: #e8e8e8;" | 1200
| G
| 192
| 701.96
|-
| colspan="10" style="text-align: center;" | On B
|-
! Root
| B
| 15:8
| 1088.27
| style="background: #e8e8e8;" | B
| style="background: #e8e8e8;" | 15:8
| style="background: #e8e8e8;" | 1088.27
| B
| 15:8
| 1088.27
|-
! Third
| D
| 9:8
| 203.91
| style="background: #e8e8e8;" | D
| style="background: #e8e8e8;" | 9:8
| style="background: #e8e8e8;" | 203.91
| D-
| 10:9
| 182.40
|-
! Fifth
| F{{music|7}}{{music|+}}
| 21:16
| 470.78
| style="background: #e8e8e8;" | F
| style="background: #e8e8e8;" | 4:3
| style="background: #e8e8e8;" | 498.04
| F
| 4:3
| 498.04
|-
| colspan="10" style="text-align: center;" | On C
|-
! Root
| C
| 1:1
| 0
| style="background: #e8e8e8;" | C
| style="background: #e8e8e8;" | 1:1
| style="background: #e8e8e8;" | 0
| C
| 1:1
| 0
|-
! Third
| E{{music|b}}
| 6:5
| 315.64
| style="background: #e8e8e8;" | E{{music|b}}
| style="background: #e8e8e8;" | 6:5
| style="background: #e8e8e8;" | 315.64
| E{{music|b}}{{music|-}}
| 32:27
| 294.13
|-
! Fifth
| G{{music|7}}{{music|b}}
| 7:5
| 582.51
| style="background: #e8e8e8;" | G{{music|b}}{{music|-}}
| style="background: #e8e8e8;" | 64:45
| style="background: #e8e8e8;" | 609.78
| G{{music|b}}{{music|-}}
| 64:45
| 609.78
|}

==Diminished chord table==
:{| class="wikitable"
!Chord
!Root
!Minor third
!Diminished fifth
|-
!Cdim
|C
|E{{music|b}}
|G{{music|b}}
|-
!C{{music|#}}dim
|C{{music|#}}
|E
|G
|-
!D{{music|b}}dim
|D{{music|b}}
|F{{music|b}} (E)
|A{{music|bb}} (G)
|-
!Ddim
|D
|F
|A{{music|b}}
|-
!D{{music|#}}dim
|D{{music|#}}
|F{{music|#}}
|A
|-
!E{{music|b}}dim
|E{{music|b}}
|G{{music|b}}
|B{{music|bb}} (A)
|-
!Edim
|E
|G
|B{{music|b}}
|-
!Fdim
|F
|A{{music|b}}
|C{{music|b}} (B)
|-
!F{{music|#}}dim
|F{{music|#}}
|A
|C
|-
!G{{music|b}}dim
|G{{music|b}}
|B{{music|bb}} (A)
|D{{music|bb}} (C)
|-
!Gdim
|G
|B{{music|b}}
|D{{music|b}}
|-
!G{{music|#}}dim
|G{{music|#}}
|B
|D
|-
!A{{music|b}}dim
|A{{music|b}}
|C{{music|b}} (B)
|E{{music|bb}} (D)
|-
!Adim
|A
|C
|E{{music|b}}
|-
!A{{music|#}}dim
|A{{music|#}}
|C{{music|#}}
|E
|-
!B{{music|b}}dim
|B{{music|b}}
|D{{music|b}}
|F{{music|b}} (E)
|-
!Bdim
|B
|D
|F
|}

==See also==
* [[Half-diminished seventh chord]]
* [[Secondary leading-tone chord]]
* [[Augmented triad]]
* [[Diminished seventh chord]]

==References==
{{Reflist}}
'''Sources'''
* {{cite book|last=Roig-Francolí|first=Miguel|author-link=Miguel Roig-Francolí|title=Harmony in Context|year=2011|publisher=McGraw-Hill|location=New York|isbn=9780073137940}}

{{Degrees}}
{{Chords}}

{{DEFAULTSORT:Diminished Triad Chord}}
[[Category:Chords]]