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Diminished triad

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Two minor thirds above the root

"Diminished chord" redirects here. For the seventh chord, seeDiminished seventh chord.

diminished triad
Component intervals fromroot
diminished fifth (tritone)
minor third
root
Tuning
45:54:64;^[1] 54:45=6:5 &64:45^[2]
Forte no. /Complement
3-10 /9-10

Inmusic theory, adiminished triad is atriad consisting of twominor thirds above theroot.^[3] It is aminor triad with a lowered (flattened)fifth. When usingchord symbols, it may be indicated by the symbols "dim", "^o", "m^♭5", or "MI^(♭5)".^[4] However, in most popular-music chord books, the symbol "dim" or "^o" represents adiminished seventh chord (a four-tone chord), which in some modern jazz books and music theory books is represented by the "dim7" or "^o⁷" symbols.

For example, the diminished triad built on B, written as B^o, has pitches B-D-F:

${ \omit Score.TimeSignature \relative c' { <b d f>1 } }$

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The chord can be represented by theinteger notation {0, 3, 6}.

In thecommon practice period, the diminished triad is considereddissonant because of thediminished fifth (or tritone).

Harmonic function

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${ #(set-global-staff-size 14) \override Score.SpacingSpanner.strict-note-spacing = ##t \set Score.proportionalNotationDuration = #(ly:make-moment 1/2) \new PianoStaff << \new Staff << \relative c'' { \key g \major \time 24/16 g16 b d g d b d b g b g d e g c e c g c g e g e c a c fis a fis c fis c a c a fis g b d g d b d b g b g d } >> \new Staff << \relative c' { \clef F \key g \major \time 24/16 g8.[_\markup { \concat { "I" \hspace #20.5 "IV" \hspace #19.5 "vii" \raise #1 \small "o" \hspace #19.5 "I" } } g,] r g' g[ g,] r g' g[ g,] r g' g[ g,] r g' } >> >> }$

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A diminished triad substituting for dominant chord inJ. S. Bach'sWell-Tempered Clavier I, Prelude in G major.^[5]

Inmajor scales, a diminished triad occurs only on the seventhscale 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 theleading-tone triad. This chord has adominant function. Unlike thedominant triad ordominant seventh, the leading-tone triad functions as aprolongational chord rather than a structural chord since the strong root motion by fifth is absent.^[6]

On the other hand, innatural 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♭). This triad is consequently called thesupertonic diminished triad. Like the supertonic minor triad found in a major key, the supertonic diminished triad has apredominant function, almost always resolving to a dominant functioning chord.^[7]

If the music is in a minor key, diminished triads can also be found on the raised seventh note,♯vii^o. This is because theascending melodic minor scale has a raised sixth and seventh degree. For example, the chord progression♯vii^o–i is common.

The leading-tone diminished triad and supertonic diminished triad are usually found infirst inversion (vii^o⁶ and ii^o⁶, respectively) since the spelling of the chord forms a diminished fifth with the bass.^[6] This differs from thefully diminished seventh chord, which commonly occurs inroot position.^[8] In both cases, the bass resolves up and the upper voices move downwards incontrary motion.^[8]

In popular music

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Walter Everett writes that "Inrock andpop music, the diminished triad nearly always appears on the second scale degree, forming a generally maudlin and dejected ii^o with its members, 2–4–♭6."^[9] Songs that feature ii^o includeSanto & Johnny's "Sleep Walk",Jay and the Americans' "Cara Mia", andthe Hollies' "The Air That I Breathe".^[9] 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 includeOasis' "Don't Look Back in Anger",David Bowie's "Space Oddity", and two inDaryl Hall's "Everytime You Go Away".^[10]

The vii^o in major keys is relatively less common than the ii^o, but still does happen. It is almost always used totonicize the relative minor, in progressions such as vii^o–V⁷/vi–vi, which resembles ii^o–V⁷–i in the relative minor.

Tuning

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In atwelve-tone equal temperament, a diminished triad has threesemitones between the third and fifth, three semitones between the root and third, and six semitones between the root and fifth.

In5-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♭) it is 9:8, 4:3, and 8:5 (135:160:192). According toGeorg Andreas Sorge, thetrumpet, in its overtone series on C, gives the diminished triad E–G–B♭ = 5:6:7 ("perfect diminished chord"^[11]), but the7 is too flat and 45:54:64 is preferred.^[1]Helmholtz describes the diminished triad as₁ − D | F, giving a just minor third and Pythagorean minor third (45:54:64) in the notation system used inOn the Sensations of Tone as a Physiological Basis for the Theory of Music.^[12]

PlayPerfect^ⓘ,Preferred^ⓘ (5-limit major), or5-limit minor^ⓘ on C.

	Sorge (perfect)/ 7-limit			Sorge (preferred)/ 5-limit major			5-limit minor (D,F,A♭)
Harmonics
Root	E	5	386.31	F♯+	45	590.22	C♯	135	92.18
Third	G	6	701.96	A+	54	905.87	E	160	386.31
Fifth	B♭	7	968.83	C	64	1200	G	192	701.96
On B
Root	B	15:8	1088.27	B	15:8	1088.27	B	15:8	1088.27
Third	D	9:8	203.91	D	9:8	203.91	D-	10:9	182.40
Fifth	F+	21:16	470.78	F	4:3	498.04	F	4:3	498.04
On C
Root	C	1:1	0	C	1:1	0	C	1:1	0
Third	E♭	6:5	315.64	E♭	6:5	315.64	E♭-	32:27	294.13
Fifth	G♭	7:5	582.51	G♭-	64:45	609.78	G♭-	64:45	609.78

Diminished chord table

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Chord	Root	Minor third	Diminished fifth
Cdim	C	E♭	G♭
C♯dim	C♯	E	G
D♭dim	D♭	F♭ (E)	A (G)
Ddim	D	F	A♭
D♯dim	D♯	F♯	A
E♭dim	E♭	G♭	B (A)
Edim	E	G	B♭
Fdim	F	A♭	C♭ (B)
F♯dim	F♯	A	C
G♭dim	G♭	B (A)	D (C)
Gdim	G	B♭	D♭
G♯dim	G♯	B	D
A♭dim	A♭	C♭ (B)	E (D)
Adim	A	C	E♭
A♯dim	A♯	C♯	E
B♭dim	B♭	D♭	F♭ (E)
Bdim	B	D	F

References

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^^a ^bShirlaw, Matthew (2012).The Theory of Harmony, p. 304. Forgotten Books.ISBN 978-1-4510-1534-8.
^Partch, Harry (1979).Genesis of a Music, pp. 68–69.ISBN 978-0-306-80106-8.
^Benward; Saker (2003).Music: In Theory and Practice, Vol. I (7th ed.). McGraw-Hill. p. 68.ISBN 978-0-07-294262-0.
^Benward & Saker (2003), p.77.
^Jonas, Oswald (1982) [1934].Das Wesen des musikalischen Kunstwerks: Eine Einführung in Die Lehre Heinrich Schenkers [Introduction to the Theory ofHeinrich Schenker]. Translated by Rothgeb, John. Longman. p. 25.ISBN 0-582-28227-6.
^^a ^bRoig-Francolí 2011, p. 248.
^Roig-Francolí 2011, p. 174.
^^a ^bBenward; Saker (2009).Music in Theory and Practice: Volume II (8th ed.). McGraw-Hill. p. 76.ISBN 978-0-07-310188-0.
^^a ^bEverett, Walter (2009).The Foundations of Rock. Oxford University Press, USA. p. 195.ISBN 978-0-19-531023-8.
^Stephenson, Ken (2002).What to Listen for in Rock: A Stylistic Analysis. Yale University Press. p. 85.ISBN 978-0-300-09239-4.
^Fétis, François-Joseph; Arlin, Mary I. (1994).Esquisse de l'histoire de l'harmonie. p. 139n9.ISBN 978-0-945193-51-7.
^Helmholtz, Hermann (1885).On the Sensations of Tone as a Physiological Basis for the Theory of Music. Longmans, Green. p. 344.{{cite book}}: CS1 maint: location missing publisher (link)

Sources

Roig-Francolí, Miguel (2011).Harmony in Context. New York: McGraw-Hill.ISBN 9780073137940.

Degrees andfunctions of thediatonic scale

I / i (Major/Minor)	ii / ii^o	iii / III	IV / iv	V / v	vi / VI	vii^o / VII
Tonic	Supertonic Sp	Mediant Dp,Tkp,tP,[D](Sp)	Subdominant	Dominant	Submediant Tp,sP,tCp	Leading tone D̸⁷	Subtonic dP
C	D	E♮ / E♭ (Major/Minor)	F	G	A♮ / A♭ (Major/Minor)	B♮ / B♭ (Major/Minor)

Chords

By form

Triad	Major Minor Augmented Diminished Suspended
Seventh	Leading-tone Major Minor Dominant Dominant seventh flat five Diminished Half-diminished Diminished major Minor-major Augmented major Augmented minor Altered seventh Nondominant Harmonic seventh
Extended	Ninth Eleventh Thirteenth Upper structure Dominant 7♯9 Polychord Tone cluster
Added / omitted	Sixth Augmented sixth Lydian Seven six
Specific	Alpha Bridge Complexe sonore Dream Elektra Farben Grandmother Magic Mystic Northern lights Petrushka Psalms So What Tristan Viennese trichord
General	Mixed interval Secundal Tertian Quartal Synthetic chord Tetrad

Byfunction

Diatonic	Tonic Supertonic Mediant Subdominant Dominant Submediant Leading tone /Subtonic
Altered	Approach Borrowed Chromatic mediant Neapolitan Passing
Secondary	Secondary dominant Secondary leading-tone Secondary supertonic
Other	Common Contrast Primary triad Subsidiary Substitute