View source for Diminished seventh chord

{{Short description|Musical chord}}
{{distinguish|text=[[diminished triad]] or [[half-diminished seventh chord]] (the name 'diminished seventh' conventionally refers only to the 'fully diminished' version of the chord)}}{{Infobox chord|chord_name=diminished seventh|first_interval=[[root (chord)|root]]|second_interval=[[minor third]]|third_interval=[[diminished fifth]] ([[tritone]])|fourth_interval=[[diminished seventh]]|tuning=[[just intonation|125:150:180:216]]<ref>Shirlaw, Matthew (1900). ''The Theory of Harmony'', p. 86. {{ISBN|978-1-4510-1534-8}}. "G{{music|#}}–B–D–F."</ref>|forte_number=4–28|complement=8–28}}

The '''diminished seventh chord''' is a four-note chord (a [[seventh chord]]) composed of a [[Root (chord)|root note]], together with a [[minor third]], a [[diminished fifth]], and a [[diminished seventh]] above the root: (1,&nbsp;{{music|flat}}3,&nbsp;{{music|flat}}5,&nbsp;{{music|doubleflat}}7). For example, the diminished seventh chord built on B, commonly [[Chord names and symbols (popular music)|written]] as B{{music|dim}}<sup>7</sup>, has pitches B-D-F-A{{music|flat}}:

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

The chord consists of a [[diminished triad]] plus the diminished seventh above the root. These four notes form a stack of three [[Interval (music)|interval]]s which are all [[minor third]]s. Since stacking yet another minor third returns to the root note, the four [[Inversion (music)|inversion]]s of a diminished seventh chord are symmetrical. The [[Pitch class#Integer notation|integer notation]] is {0,&nbsp;3,&nbsp;6,&nbsp;9}.

Since the diminished seventh interval is [[enharmonically equivalent]] to a [[major sixth]], the chord is enharmonically equivalent to (1,&nbsp;{{music|flat}}3,&nbsp;{{music|flat}}5,&nbsp;{{music|natural}}6).

The diminished seventh chord occurs as a [[leading-tone seventh chord]] in the [[harmonic minor scale]]. It typically has [[dominant function]] and contains two diminished fifths, which often resolve inwards.<ref>Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p. 219. Seventh Edition. {{ISBN|978-0-07-294262-0}}.</ref>

The [[Chord notation#Seventh chords|chord notation]] for the diminished seventh chord with C as the root is Cdim<sup>7</sup> or C{{music|dim}}<sup>7</sup> (or Cm<sup>6{{music|flat}}5</sup> for the enharmonic variant). The notation Cdim or C{{music|dim}} normally denotes a (three-note) diminished triad, but some jazz charts or other music literature may intend for these to denote the four-note diminished seventh chord instead.

[[François-Joseph Fétis]] tuned the chord 10:12:14:17 ([[17-limit tuning]]).<ref>[[François-Joseph Fétis|Fétis, François-Joseph]] and Arlin, Mary I. (1994). ''Esquisse de l'histoire de l'harmonie'', p. 139n9. {{ISBN|978-0-945193-51-7}}.</ref>

==Analysis==
Music theorists have struggled over the centuries to explain the meaning and function of diminished seventh chords. Currently, two approaches are generally used. 

The less complex method treats the leading tone as the [[Root (chord)|root]] of the chord and the other chord members as the [[Third (chord)|third]], [[Fifth (chord)|fifth]], and [[Seventh (chord)|seventh]] of the chord, the same way other [[seventh chord]]s are analyzed.

The other method is to analyze the chord as an "incomplete dominant ninth", that is a [[ninth chord]] with its root on the dominant, whose root is missing or implied. A vii{{music|dim}}<sup>7</sup> chord in the minor key (for example, in C minor, B{{music|natural}}–D–F–A{{music|b}}) occurs naturally in the [[Minor scale#Harmonic and melodic minor|harmonic minor scale]] and is equivalent to the dominant 7{{music|b}}9 chord (G–B–D–F–A{{music|b}}) without its root. 

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

This was already proposed by [[Arnold Schoenberg]],<ref>[[Arnold Schoenberg|Schoenberg, Arnold]]. ''Harmonielehre'', chapter IX, Wien, Universal Edition, 1911</ref> and [[Walter Piston]] championed this analysis.<ref>{{Cite book|url=https://archive.org/details/harmony3rdpist/page/191|title=Harmony|last=Piston|first=Walter|author-link=Walter Piston|publisher=W. W. Norton|year=1962|isbn=0393097374|edition=3rd|location=New York|page=[https://archive.org/details/harmony3rdpist/page/191 191]|oclc=2082824|url-access=registration}}</ref> Jazz guitarist [[Sal Salvador]], and other jazz theorists, also advocated this view, rewriting chord charts to reflect this and supplying the "missing" root as part of their bass lines.<ref>{{Cite book|title=Chordal Enrichment & Chord Substitution|last=Salvador|first=Sal|date=1985|publisher=Mel Bay Publications|isbn=0871665271|location=Pacific, Missouri|oclc=21109944|author-link=Sal Salvador}}</ref> The dominant ninth theory was questioned by [[Heinrich Schenker]]. He explained that although there is a kinship between all univalent chords rising out of the fifth degree, the dominant ninth chord is not a real chord formation.<ref>{{cite book |last=Schenker |first=Heinrich |author-link=Heinrich Schenker |editor=[[Oswald Jonas]]|translator=Elisabeth Mann Borgese |translator-link=Elisabeth Mann Borgese |title=Harmony |year=1954 |publisher=[[University of Chicago Press]] |location=Chicago |oclc=280916 |page=192}}</ref>

[[Jean-Philippe Rameau]] explained the diminished seventh chord as a [[dominant seventh chord]] whose [[supposition (music)|supposed]] [[bass note|fundamental bass]] is borrowed from the sixth degree in minor, raised a semitone producing a stack of minor thirds.<ref name="Christensen">Christensen, Thomas Street (2004). ''Rameau and Musical Thought in the Enlightenment'', p. 100. {{ISBN|978-0-521-61709-3}}.</ref> Thus, in C, the dominant seventh is G<sup>7</sup> (G–B–D–F) and the sixth degree borrowed from the minor scale produces A{{music|b}}–B–D–F.<ref name="Christensen" /> 

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

In his ''[[Treatise on Harmony]]'', he observed that three [[Minor third|minor thirds]] and an [[augmented second]] make up a chord where the augmented second is such that "the ear is not offended" by it. He may have been talking of the augmented second in [[quarter-comma meantone]], a tuning he favored, which is close to the just [[septimal minor third]] of 7:6.
==Function==

=== Most common functions ===
{{Image frame|content=<score sound="1">
   \new PianoStaff <<
      \new Staff <<
         \new Voice \relative c'' {
             \stemUp \key c \minor
             aes1 g 
             }
         \new Voice \relative c' {
             \stemDown
              d1 es
              }
            >>
     \new Staff <<
         \new Voice \relative c {
             \stemUp \clef F \key c \minor
             f1 es
             }
         \new Voice \relative c {
             \stemDown
             b1_\markup { \concat { "vii" \raise #1 \small "o7" \hspace #4.3 "i" } } c \bar "||"
             }
         >>
    >>
</score>|width=300|caption=Diminished seventh chord resolution: both [[diminished fifth]]s tend to [[resolution (music)|resolve]] inward, [[Voicing_(music)#Doubling|doubling]] the [[third (chord)|third]] of the tonic chord}}
The most common form of the diminished seventh chord is that rooted on the [[leading tone]] – for example, in the key of C, the chord (B–D–F–A{{music|flat}}) – so its other constituents are the {{music|scale|2}}, {{music|scale|4}}, and {{music|flat}}{{music|scale|6}} (flat [[submediant]]) [[degree (music)|scale degrees]]. These notes occur naturally in the harmonic minor scale. But this chord also appears in major keys, especially after the time of [[Johann Sebastian Bach|J.S. Bach]], where it is [[Borrowed chord|borrowed]] from the [[parallel minor]].

The chord possesses a [[dominant function]] when rooted on the leading tone (otherwise it doesn't, but can serve other functions - see [[#Functions when not rooted on leading-tone|below]]), and this is most straightforwardly shown when the root of a [[dominant seventh chord]] is omitted. The remaining third, fifth and seventh of that chord form a diminished triad (whose new root is the third of the former chord), to which a diminished seventh can be added. Thus, in C (major or minor), a dominant seventh chord consisting of G–B–D–F can be replaced by a diminished seventh chord B–D–F–A{{music|flat}}.

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

In [[jazz]] harmony, a combination of the dominant seventh chord with its [[Chord substitution|substitute]] diminished seventh (with G in the bass and A{{music|b}} simultaneously in an upper voice) yields the seven flat-9 chord, which intensifies the dominant function of either a diminished seventh or dominant seventh chord. Other transformations of this kind facilitate a variety of substitutions and modulations: any of the four notes in a diminished seventh chord are ''raised'' by a [[semitone]], that raised note is then the flat-seventh of a [[half-diminished seventh chord]]. Similarly, if any of the four notes in the diminished seventh chord are ''lowered'' by a semitone, that lowered note is then the root of a dominant seventh chord.

{{Anchor|Functions when not rooted on leading-tone}}Diminished seventh chords may also be rooted on scale degrees other than the leading-tone, either as [[Secondary leading-tone|secondary function]] chords temporarily borrowed from other keys, or as [[appoggiatura]] chords: a chord rooted on the raised second scale degree (D{{music|#}}–F{{music|#}}–A–C in the key of C) acts as an appoggiatura to the tonic (C major) chord, and one rooted on the raised sixth scale degree (A{{music|#}}–C{{music|#}}–E–G in C major) acts as an appoggiatura to the dominant (G major) chord. Such chords however, having no leading tone in relation to the chords to which they resolve, cannot properly have a dominant function. They are therefore referred to commonly as ''non-dominant diminished seventh chords'' or ''common tone diminished seventh chords'' (see [[#Common-tone diminished seventh chord|below]]).

In jazz, the diminished seventh chord is often based on the {{music|flat}}{{music|scale|3}} scale degree (the flat [[mediant]]) and acts as a [[passing chord]] between the mediant triad (or [[First inversion|first-inversion]] tonic triad) and the [[supertonic]] triad: in C major, this would be the chord progression E minor – E{{music|b}} diminished – D minor. The chord, "plays no role in... jazz."<ref>[[Michael Tenzer|Tenzer, Michael]] and Roeder, John (2011). ''Analytical and Cross-Cultural Studies in World Music'', p. 157n10. {{ISBN|978-0-19-538458-1}}.</ref> The passing chord is used widely in [[Brazilian music]] such as [[choro]], [[samba]] and [[bossa nova]].

=== Other functions ===
{{Refimprove section|date=January 2019}}
{{Image frame|content=<score sound="1">
   \new PianoStaff <<
      \new Staff <<
         \new Voice \relative c'' {
             \stemUp
             f2 es d1 c
             }
         \new Voice \relative c'' {
             \stemDown
              <a c>1 <f b> <e g>
              }
            >>
     \new Staff <<
         \new Voice \relative c {
             \clef F
             f2 fis g1 c \bar "||"
             }
         >>
    >>
</score>|width=300|caption=A chord progression with a sharpened subdominant with diminished seventh chord}}

Another common use of the chord is as a ''sharpened subdominant with diminished seventh'' chord. This is represented by the Roman notation {{music|#}}iv{{music|dim}}<sup>7</sup>, but in classical music is more correctly represented as vii{{music|dim}}<sup>7</sup>/V, being a very common way for a composer to approach the dominant of any key. In the key of C, this is F{{music|#}}dim<sup>7</sup>. It is also a common chord in [[jazz]] and [[ragtime]] music. A common [[traditional jazz]] or [[Dixieland]] progression is IV–{{music|#}}iv{{music|dim}}<sup>7</sup>–V<sup>7</sup> (in C major: F–F{{music|#}}{{music|dim}}<sup>7</sup>–G<sup>7</sup>). Another common usage of {{music|#}}iv{{music|dim}}<sup>7</sup> is often found in [[Gospel music]] and jazz progressions such as in the song "[[I Got Rhythm]]":

:In C: |  C  C/E  |  F  F{{music|#}}dim<sup>7</sup>  |  C/G A<sup>7</sup>  |  Dm<sup>7</sup> G<sup>7</sup>  |

One variant of the [[supertonic]] seventh chord is the ''supertonic diminished seventh''<ref>Kitson, C. H. (2006). ''Elementary Harmony'', p. 43. {{ISBN|1-4067-9372-8}}.</ref> with the raised supertonic, which is [[enharmonic equivalence|enharmonically equivalent]] to the lowered third (in C: D{{music|#}} = E{{music|b}}). It may be used as a dominant [[chord substitution|substitute]].<ref name="Coker">[[Jerry Coker|Coker, Jerry]] (1997). ''Elements of the Jazz Language for the Developing Improvisor'', p. 82. {{ISBN|1-57623-875-X}}.</ref>
{{Image frame|content=<score sound="1" override_midi="Common-tone diminished seventh chord in 'In the Good Old Summertime', Strictly Barbershop.mid">
    {
      \new StaffGroup <<
        \new Staff <<
            \new Voice \relative c' {
                \stemUp \clef "G_8" \key bes \major \time 3/4
                es4 es2 cis2 cis4 d2 d4 es2 r4
                }
            \new Voice \relative c' {
                \stemDown
                bes4 c2 bes2 g4 f2._~ f2 s4
                }
           \addlyrics { good old sum mer time __ }
            >>
        \new Staff <<
            \new Voice \relative c' {
                \stemUp \clef F \key bes \major \time 3/4
                g4 g2 g2 bes4 bes2 aes4 a!2 r4
                }
            \new Voice \relative c {
                \stemDown
                es4 es2 es2 es4 bes2 b4 c2 s4 \bar "||"
                }
           \addlyrics { good old sum mer, sum mer time __ }
            >>
    >> }
</score>|width=380|caption=According to Benward and Saker, "The...<!--"raised supertonic and raised submediant diminished seventh chords"--> [{{music|#}}ii{{music|dim}}{{music|7}} and {{music|#}}vi{{music|dim}}{{music|7}}] chords are very common in 20th-century<!--twentieth-century--> [[Barbershop quartet|'barbershop' quartet]] music."<ref name="B&S">Benward, Bruce & Saker, Marilyn (2009). ''Music: In Theory and Practice, Vol. II'', pp. 220-222. Eighth Edition. {{ISBN|978-0-07-310188-0}}.</ref> The music shows the chord progression IV–vi<sup>6</sup>–Ger<sup>+6</sup>–I {{music|sharp}}vi{{music|dim}}{{music|65}}–V{{music|43 chord}}.<!--Example from "[[In the Good Old Summer Time|In the Good Old Summertime]]"-->}}
{{Image frame|content=<score sound="1" override_midi="Common-tone diminished seventh chord in Tchaikovsky's Nutcracker Suite, op. 71a, III, Valse des Fleurs.mid">
    {
      \new PianoStaff <<
        \new Staff <<
            \relative c' {
                \tempo "Tempo di Valse"
                \key d \major \time 3/4
                \override DynamicText.X-offset = #-4
                \once \override DynamicLineSpanner.staff-padding = #3
                <e a>4--\f <e a cis>-- <e a cis e>-- <fis a bis fis'>2->\sf <e a cis e>4-- <e a cis e>2.~ <e a cis e>8 r r4 r
                }
            >>
        \new Staff <<
            \new Voice \relative c {
                \clef F \key d \major \time 3/4
                <a e' a cis>4--_\markup { \concat { "V" \hspace #10 "♯vi" \raise #1 \small "o" \combine \raise #1 \small 4 \lower #1 \small 2 \hspace #1 "V" } } <a e' a cis>-- <a e' a cis>-- <a dis a' bis>2-> <a e' a cis>4-- <a e' a cis>2.~ <a e' a cis>8 r r4 r
                }
            >>
    >> }
</score>|caption=Example (B{{music|#}}{{music|dim}}{{music|42 chord}}) in the ''[[The Nutcracker|Waltz of the Flowers]]'' (1892)<ref name="K&P">Kostka, Stefan and Payne, Dorothy (1995). ''Tonal Harmony'', p. 435. Third edition. McGraw-Hill. {{ISBN|0-07-300056-6}} "The ct{{music|dim}}{{music|7}} chords... embellish [the] dominant chord. While the ct{{music|dim}}{{music|7}} chords are clearly ornamental, their flavor is crucial to this passage and to the waltz that follows."</ref><ref name="B&S"/>}}

{{Anchor|Common-tone diminished seventh chord}}A diminished seventh chord may function as a ''common-tone diminished seventh chord''. In this role, a diminished seventh chord resolves to a [[Major seventh chord|major]] or [[Major minor seventh chord|dominant seventh chord]] whose root is one of the notes of the diminished seventh chord ([[common tone (chord)|common tone]]), the most common being the raised supertonic seventh, which resolves to the tonic in major keys ({{nowrap|{{music|#}}ii{{music|dim}}<sup>7</sup>}}–I, shown below) and the raised submediant, which resolves to dominant triad or seventh in major keys ({{nowrap|{{music|#}}vi{{music|dim}}<sup>7</sup>}}–V, shown right), with the altered tones resolving upward by half step in both cases.<ref name="B&S">Benward, Bruce & Saker, Marilyn (2009). ''Music: In Theory and Practice, Vol. II'', pp. 220-222. Eighth Edition. {{ISBN|978-0-07-310188-0}}.</ref>
:<score sound="1">
{
\omit Score.TimeSignature
\relative c' { 
      <dis a' c fis>1_\markup { \concat { "♯ii" \raise #1 \small "o7" \hspace #4 "I" \raise #1 \small "6" } } <e g c g'> \bar "||"
   }
}
</score>

The ct{{music|dim}}<sup>7</sup> chord, whose function, "is simply one of embellishment," most often spelled {{nowrap|{{music|#}}ii{{music|dim}}<sup>7</sup>}} when embellishing I or {{nowrap|{{music|#}}vi{{music|dim}}<sup>7</sup>}} when embellishing V, is distinguished from the vii{{music|dim}}<sup>7</sup>/V chord by common tone chords resolving to I or I{{sup|6}} while vii{{music|dim}}<sup>7</sup>/V resolves to V or I{{music|64}}.<ref name="K&P" /> They may be confused, due to enharmonic equivalency, but resolution is a better indicator of function than spelling. In C:

:ct{{music|dim}}<sup>7</sup>/I = d{{music|#}}{{music|dim}}<sup>7</sup> = D{{music|#}}–F{{music|#}}–A–C
:vii{{music|dim}}<sup>7</sup>/V = f{{music|#}}{{music|dim}}<sup>7</sup> = F{{music|#}}–A–C–E{{music|b}} (= D{{music|#}})

The diminished chord may also resolve through lowering two of the chord tones producing a supertonic seventh chord (ii<sup>7</sup>) that may lead to a conventional cadence:<ref>Alchin, Carrie Adelaide (1917). ''[https://books.google.com/books?id=fgQtAAAAYAAJ&q=%22diminished+seventh+chord%22&pg=PA6 Applied Harmony]'', p. 99. Los Angeles: C. A. Alchin. {{pre-ISBN}} [https://archive.org/details/appliedharmonyte00alchrich].</ref>

:<score sound="1">
{
  \set Score.proportionalNotationDuration = #(ly:make-moment 1/4)
\omit Score.TimeSignature
\key d \major
\relative c'' { 
      <b d f aes>2_\markup { \concat { "vii" \raise #1 \small "o7" \hspace #1.2 "ii" \raise #1 \small "7"  \hspace #4.7 "V" \raise #1 \small "7" \hspace #4 "I" } } <b d e g> <a cis e g> <a d fis> \bar "||"
   }
}
</score>

==Expressive potential==
During the [[Baroque music|Baroque]] era (1600–1750), European composers became aware of the expressive potential of the diminished seventh chord.  In operas and other dramatic works, the chord was frequently used to heighten the sense of passion, anger, danger or mystery. One famous example can be found in [[Johann Sebastian Bach|J. S. Bach]]'s ''[[St. Matthew Passion]]'' (1737), in which he sets verses from the [[Gospel of Matthew]], chapter 27, verses 20–21: "But the chief priests and elders persuaded the multitude that they should ask Barabbas, and destroy Jesus. The governor [Pilate] answered and said unto them, 'Whether of the twain will ye that I release unto you?' They said, 'Barabbas'." Bach sets the text so that the angry multitude's harsh reply on the word ''Barabbam'' is a diminished seventh chord:

:<score sound="1">
    { \new StaffGroup <<
        \new Staff <<
            \set Staff.midiInstrument = #"voice oohs"
            \key d \minor
            \relative c' {
                \set Score.tempoHideNote = ##t \tempo 8 = 120
                \time 2/4
                <fis a c fis>8.^"Choir" <fis a c fis>16 <fis a c fis>4
                }
            \addlyrics { Ba -- rab -- bam! }
            >>
        \new Staff <<
            \set Staff.midiInstrument = #"church organ"
            \clef F \key d \minor \time 2/4
            \new Voice \relative c {
                <dis dis'>8. <dis dis'>16 <dis dis'>4
                }
            >>
    >> }
</score>

After Bach, diminished sevenths featured regularly in music to evoke the uncanny or a sense of impending danger. A powerful diminished seventh chord heralds the resurrection of the murdered Commendatore in the final scene of [[Wolfgang Amadeus Mozart|Mozart]]'s ''[[Don Giovanni]]'' (1787). The dead man's statue comes to life and takes the Don down to Hell in one of the most chilling episodes in the entire operatic repertoire ([https://www.youtube.com/watch?v=7cb1QmTkOAI Listen]):

:<score sound="1">
{
      <<
        \new Staff <<
            \tempo Andante
            \relative c' {
                \set Score.tempoHideNote = ##t \tempo 4 = 86
                \set Staff.midiInstrument = #"trombone"
                \clef F \key d \minor
                R1 R1 R1 r2 a4.^"COMMENDATORE" a8 d2 d, r4 d f d a'2 a
                }
                \addlyrics { Don Gio -- van -- ni! A ce -- nar te -- co }
            >>
      \new PianoStaff <<
        \new Staff <<
           \set Staff.midiInstrument = #"string ensemble 1"
           \key d \minor
           \relative c'' {
                \override DynamicLineSpanner.staff-padding = #3
                <d f gis d'>4\ff <d f gis d'>2 <d f gis d'>4~ <d f gis d'>4 r4 r2 <a e' g! a>4 <a e' g a>2 <a e' g a>4~ <a e' g a>4 r4 r2 <a, f'>4.\p <a f'>8 <a f'>4. <a f'>8 <a f'>4. <a f'>8 <a f'>4. <a f'>8 <a e'>4. <a e'>8 <a e'>4. <a e'>8
                }
            >>
        \new Staff <<
           \clef F \key d \minor
           \relative c, {
                <b b'>2 <b b'> <b b'> r <cis cis'> <cis cis'> <cis cis'> r d'4. d8 d4. d8 d4. d8 d4. d8 c4. c8 c4. c8
                }
            >>
    >>  >> }
</score>

In the early years of the 19th century, composers used the diminished seventh with increasing frequency. In "Die Stadt", one of his darkest and most melancholy songs from ''[[Schwanengesang]]'' (1828), [[Franz Schubert]] conjures "the pianistic elaboration of a diminished seventh over an octave [[tremolo]]"<ref name=":0">{{Cite book|title=Hearing and Knowing Music|last=Cone|first=Edward T.|author-link=Edward T. Cone|date=2009|publisher=Princeton University Press|isbn=9781400830466|location=Princeton|page=109|oclc=670430565}}</ref> to convey the sinister rippling of the oars as the protagonist is rowed across a lake towards the town where his lost beloved once lived. According to [[Edward T. Cone]], "This famous [[arpeggiation]] seems to arise from nowhere to create an atmospheric prelude... and it dies away to nothing in a postlude."<ref name=":0" />  The song ends on the diminished seventh chord; there is no [[Resolution (music)|resolution]], "the [[Dissonance (music)|dissonance]] is terminal":<ref name=":0" /> 

:<score override_ogg="Schubert, 'Die Stadt' from Schwanengesang.wav">
{
      #(set-global-staff-size 17)
      <<
      \new PianoStaff <<
        \new Staff <<
           \tempo "Mässig geschwind"
           \key c \minor \time 3/4
            \set Score.currentBarNumber = #35
            \bar ""
           \relative c'' {
                R2.
                R
                \tuplet 9/8 { a32([ c es fis a fis es c a)] } <c, es fis a>8->([ a16)] r \clef bass <c, es fis a>8->([ a16)] r \clef G
                \tuplet 9/8 { a''32([ c es fis a fis es c a)] } <c, es fis a>8->([ a16)] r \clef F <c, es fis a>8->([ a16)] r \clef G
                \tuplet 9/8 { a''32([ c es fis a fis es c a)] } <c, es fis a>8->([ a16)] r \clef F <c, es fis a>8->([ a16)] r
                R2.\fermata
                }
            >>
        \new Staff <<
           \clef F \key c \minor \time 3/4
           \relative c, {
                c32^\markup {\dynamic pp \italic "con pedale" } c' c, c' c, c' c, c' c,8 r c r
                c32 c' c, c' c, c' c, c' c,8 r c r
                c32 c' c, c' c, c' c, c' c,8 r c r
                c32 c' c, c' c, c' c, c' c,8 r c r
                c32 c' c, c' c, c' c, c' c,8 r c r
                c2.\fermata \bar "|."
                }
            >>
    >>  >> }
</score>

The operas of [[Carl Maria von Weber]], particularly ''[[Der Freischütz]]'' and ''[[Euryanthe]]'', featured many passages using this chord. The Wolf's Glen scene in ''[[Der Freischütz]]'' (1821) is an example. [[File:Wolf's Glen music from Freischutz (orchestra only) 01.wav|thumb|Wolf's Glen music from Der Freischütz (orchestra only)]] [[File:Wolf's Glen music from Freischutz (orchestra only) 02.png|thumb|center|800px|Wolf's Glen music from Der Freischütz (orchestra only)]]According to his early biographer, [[Alexander Wheelock Thayer]],<ref>[[Alexander Wheelock Thayer|Thayer, A. W.]] (1921)  ''Life of Beethoven''. Princeton: Princeton University Press (1879)</ref> [[Ludwig van Beethoven]] spoke disparagingly of the 'accumulation of diminished seventh chords' in ''Euryanthe'' (1823). 

Beethoven was himself rather fond of the chord and was well aware of its dramatic potential. Perhaps the clearest instance of the diminished seventh's power to evoke mystery and terror can be found in the passage linking the two final movements of Beethoven's [[Piano Sonata No. 23 (Beethoven)|''Appassionata'' sonata]], Op. 57 (1806). The placid conclusion of the andante movement is interrupted first by a slowly rolled diminished seventh [[arpeggio]] played ''[[Dynamics (music)|pianissimo]]'', followed by the same chord played an [[octave]] above in a sharp, stabbing ''fortissimo''.<ref>Rosen, C. (2002, p. 196) ''Beethoven's Piano Sonatas, a Short Companion'' Yale University Press.</ref>

:<score override_ogg="Beethoven Appassionata Sonata 3 final bars of Andante.wav">
{
      <<
      \new PianoStaff <<
        \new Staff <<
           \key des \major \time 2/4
           \relative c'' {
                <ges bes es>4(_\markup { \dynamic p \italic dim. } <es aes>)
                <des e g des'>2\pp\arpeggio\fermata
                <des' e g des'>2_\markup { \dynamic ff \italic secco }\arpeggio\fermata
                }
            >>
        \new Staff <<
           \clef F \key des \major \time 2/4
           \relative c' {
                <ges bes>4( <aes c>)
                <bes, des e g bes>2\arpeggio\fermata
                \clef treble <bes' des e g bes>2\arpeggio\fermata \bar "||"
                }
            >>
    >>  >> }
</score>

The final movement of [[Hector Berlioz]]'s ''[[Symphonie Fantastique]]'' reflects the influence of Weber <ref>Hovland, E. (2019, p. 20) "Who's afraid of Berlioz?" ''Studia Musicologica Norvegica'', vol 45, no. 1, pp. 9–30.</ref> in its copious use of diminished seventh chords to evoke the spooky atmosphere of a Witch's Sabbath: "a sinister gathering of spectres, monsters and weird, infernal mocking creatures":<ref>[[Hugh Macdonald (musicologist)|Macdonald, H.]] (1969, p. 37) ''Berlioz Orchestral Music''.  London, BBC.</ref>
[[File:Berlioz Symphonie Fantastique finale, bars 1-4 01.wav|thumb|Berlioz's ''Symphonie Fantastique'' finale, bars 1–4]]
[[File:Berlioz Symphonie Fantastique finale, bars 1-4 02.png|thumb|center|500px|Berlioz's ''Symphonie Fantastique'' finale, bars 1-4]]

By the end of the 19th century, composers had used the diminished seventh so much that it became a [[cliché]] of musical expression and consequently lost much its power to shock and thrill. By the turn of the 20th century, many musicians were getting weary of it. In his ''Harmonielehre'' (1911),<ref>[[Arnold Schoenberg|Schoenberg, Arnold]] (1911) ''Harmonielehre'', Wien, Universal Edition.</ref> [[Arnold Schoenberg]] wrote:

{{quote|Whenever one wanted to express pain, excitement, anger, or some other strong feeling – there we find, almost exclusively, the diminished seventh chord. So it is in the music of Bach, [[Haydn]], Mozart, Beethoven, Weber, etc. Even in [[Wagner]]'s early works it plays the same role. But soon the role was played out. This uncommon, restless, undependable guest, here today, gone tomorrow, settled down, became a citizen, was retired a philistine. The chord had lost that appeal of novelty, hence, it had lost its sharpness, but also its luster. It had nothing more in say to a new era. Thus, it fell from the higher sphere of art music to the lower of music for entertainment. There it remains, as a sentimental expression of sentimental concerns. It became banal and effeminate.}}

==Symmetry==

{{Image frame|content=<score>
{
\omit Score.TimeSignature
    \relative c'' {
        <gis b d f>1 <aes b d f> <aes ces d f> <aes ces eses f>  \bar "||"
    }
}
</score>|width=320|caption=The same four pitch classes spelled as four different diminished seventh chords: G{{music|sharp}}dim<sup>7</sup>, Bdim<sup>7</sup>, Ddim<sup>7</sup>, and Fdim<sup>7</sup>.}}Because a diminished seventh chord is composed of three stacked [[Minor third|minor thirds]] which evenly divide the chromatic scale, it is symmetrical and its four [[Chord inversion|inversions]] are composed of the same [[Pitch class|pitch classes]]. Understanding what inversion a given diminished seventh chord is written in (and thus finding its [[Root (chord)|root]]) depends on its [[enharmonic spelling]]. For example, G{{music|sharp}}dim<sup>7</sup> (G{{music|sharp}}–B–D–F) is [[enharmonically equivalent]] to three other inverted diminished chords with roots on the other three pitches in the chord: 

# Bdim<sup>7</sup> (A{{music|b}}–B–D–F)
# Ddim<sup>7</sup> (A{{music|b}}–C{{music|b}}–D–F)
# Fdim<sup>7</sup> (A{{music|b}}–C{{music|b}}–E{{music|bb}}–F)

Nineteenth-century composers in particular often make use of this enharmonic to use these chords for [[modulation (music)|modulations]]. [[Percy Goetschius]] calls it the "enharmonic chord."<ref>[[Percy Goetschius|Goetschius, Percy]] (1913). ''The Material Used in Musical Composition: A System of Harmony''. p. 159, G. Shirmer, Inc.</ref>

{{Image frame|content=<score sound="1">
{
\omit Score.TimeSignature
\relative c' {
<cis e g bes c es fis a>1
} }
</score>

<score sound="1">
 {
\omit Score.TimeSignature
\relative c' {
  \once \override NoteHead.color = #red des8 \once \override NoteHead.color = #blue es \once \override NoteHead.color = #red e! \once \override NoteHead.color = #blue fis \once \override NoteHead.color = #red g \once \override NoteHead.color = #blue a \once \override NoteHead.color = #red bes \once \override NoteHead.color = #blue c
} }
</score>|width=300|caption=Two diminished seventh chords in the octatonic scale (one red, one blue) may be rearranged as the alpha chord}}

Given the symmetry of the chord (and ignoring enharmonic spelling), it follows that there are only three distinct diminished seventh chords (as opposed to twelve), each a conflation of four enharmonic equivalents. Using [[Walter Piston|Piston]]'s incomplete-ninth analysis discussed above, a single diminished seventh chord, without enharmonic change, is capable of the following analyses: V, [[Secondary dominant|V/ii]], V/III (in minor), V/iii (in major), V/iv, V/V, V/VI (in minor), V/vi (in major), V/VII (in minor). Since the chord may be enharmonically written in four different ways without changing the sound, the above can be multiplied by four, yielding a total of forty-eight possible interpretations.<ref>{{Cite book|url=https://archive.org/details/harmony3rdpist/page/201|title=Harmony|last=Piston|first=Walter|author-link=Walter Piston|publisher=W. W. Norton|year=1962|isbn=0393097374|edition=3rd|location=New York|page=[https://archive.org/details/harmony3rdpist/page/201 201]|oclc=2082824|url-access=registration}}</ref> More conservatively, each assumed root may be used as a [[dominant (music)|dominant]], [[tonic (music)|tonic]], or [[supertonic]], giving twelve possibilities.<ref name="Wodehouse">Adela Harriet Sophia Bagot Wodehouse (1890). ''A Dictionary of Music and Musicians: (A.D. 1450–1889)'', p. 448. Macmillan and Co., Ltd.</ref>

The [[octatonic scale]] (or diminished scale), a [[symmetric scale]], may be conceived of as two interlocking diminished seventh chords, which may be rearranged into the [[alpha chord]].
{{Clear}}

==Diminished seventh chord table==
:{| class="wikitable"
!Chord
!Root
!Minor third
!Dim. fifth
!Dim. seventh
|-
!C{{music|b}}{{music|dim}}<sup>7</sup>
|C{{music|b}}
|E{{music|bb}} (D)
|G{{music|bb}} (F)
|B{{music|bbb}} (A{{music|b}})
|-
!C{{music|dim}}<sup>7</sup>
|C
|E{{music|b}}
|G{{music|b}}
|B{{music|bb}} (A) 
|-
!C{{music|#}}{{music|dim}}<sup>7</sup>
|C{{music|#}}
|E
|G
|B{{music|b}}
|-
!D{{music|b}}{{music|dim}}<sup>7</sup>
|D{{music|b}}
|F{{music|b}} (E) 
|A{{music|bb}} (G) 
|C{{music|bb}} (B{{music|b}}) 
|-
!D{{music|dim}}<sup>7</sup>
|D
|F
|A{{music|b}}
|C{{music|b}} (B) 
|-
!D{{music|#}}{{music|dim}}<sup>7</sup>
|D{{music|#}}
|F{{music|#}}
|A
|C
|-
!E{{music|b}}{{music|dim}}<sup>7</sup>
|E{{music|b}}
|G{{music|b}}
|B{{music|bb}} (A) 
|D{{music|bb}} (C) 
|-
!E{{music|dim}}<sup>7</sup>
|E
|G
|B{{music|b}}
|D{{music|b}}
|-
!E{{music|#}}{{music|dim}}<sup>7</sup>
|E{{music|#}}
|G{{music|#}}
|B
|D
|-
!F{{music|b}}{{music|dim}}<sup>7</sup>
|F{{music|b}}
|A{{music|bb}} (G)
|C{{music|bb}} (B{{music|b}})
|E{{music|bbb}} (D{{music|b}})
|-
!F{{music|dim}}<sup>7</sup>
|F
|A{{music|b}}
|C{{music|b}}(B) 
|E{{music|bb}}(D) 
|-
!F{{music|#}}{{music|dim}}<sup>7</sup>
|F{{music|#}}
|A
|C
|E{{music|b}}
|-
!G{{music|b}}{{music|dim}}<sup>7</sup>
|G{{music|b}}
|B{{music|bb}} (A) 
|D{{music|bb}} (C) 
|F{{music|bb}} (E{{music|b}}) 
|-
!G{{music|dim}}<sup>7</sup>
|G
|B{{music|b}}
|D{{music|b}}
|F{{music|b}} (E) 
|-
!G{{music|#}}{{music|dim}}<sup>7</sup>
|G{{music|#}}
|B
|D
|F
|-
!A{{music|b}}{{music|dim}}<sup>7</sup>
|A{{music|b}}
|C{{music|b}} (B) 
|E{{music|bb}} (D) 
|G{{music|bb}} (F) 
|-
!A{{music|dim}}<sup>7</sup>
|A
|C
|E{{music|b}}
|G{{music|b}}
|-
!A{{music|#}}{{music|dim}}<sup>7</sup>
|A{{music|#}}
|C{{music|#}}
|E
|G
|-
!B{{music|b}}{{music|dim}}<sup>7</sup>
|B{{music|b}}
|D{{music|b}}
|F{{music|b}} (E) 
|A{{music|bb}} (G) 
|-
!B{{music|dim}}<sup>7</sup>
|B
|D
|F
|A{{music|b}}
|-
!B{{music|#}}{{music|dim}}<sup>7</sup>
|B{{music|#}}
|D{{music|#}}
|F{{music|#}}
|A
|}

==See also==
*[[Enharmonic scale]]
*[[Diminished seventh|Diminished seventh interval]] 
*[[Leading-tone#Leading-tone_seventh_chord|Leading tone seventh chord]] 
*[[Irregular resolution]]
*[[Half diminished chord]]
*[[Subtonic]]
*[[Triad (music)]]
*[[Tritone]]
*[[Seventh chord]]
*[[Close and open harmony]]
*[[Harmony]]
*[[Octatonic scale]]

==References==
{{reflist}}

{{Chords}}

{{DEFAULTSORT:Diminished Seventh Chord}}
[[Category:Seventh chords]]
[[Category:Musical symmetry]]