Diminished triad

Template:Short description Template:Redirect Template:Infobox chordIn music theory, a diminished triad is a triad consisting of two minor thirds above the root.<ref>Template:Cite book</ref> It is a minor triad with a lowered (flattened) fifth. When using chord symbols, it may be indicated by the symbols "dim", "Template:Music", "m^{Template:Music5}", or "MI^{(Template:Music5)}".<ref>Benward & Saker (2003), p.77.</ref> However, in most popular-music chord books, the symbol "dim" or "Template:Music" 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 "Template:Music⁷" symbols.

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

<score sound="1">

{ \omit Score.TimeSignature \relative c' { 1 } } </score>

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

In the common practice period, the diminished triad is considered dissonant because of the diminished fifth (or tritone).

Harmonic function

In major scales, a diminished triad occurs only on the seventh 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 triad. This chord has a dominant function. Unlike the dominant triad or dominant seventh, the leading-tone triad functions as a prolongational chord rather than a structural chord since the strong root motion by fifth is absent.Template:Sfn

On the other hand, in 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, ATemplate:Music). 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 function, almost always resolving to a dominant functioning chord.Template:Sfn

If the music is in a minor key, diminished triads can also be found on the raised seventh note, Template:MusicviiTemplate:Music. This is because the ascending melodic minor scale has a raised sixth and seventh degree. For example, the chord progression Template:MusicviiTemplate:Music–i is common.

The leading-tone diminished triad and supertonic diminished triad are usually found in first inversion (viiTemplate:Music⁶ and iiTemplate:Music⁶, respectively) since the spelling of the chord forms a diminished fifth with the bass.Template:Sfn This differs from the fully diminished seventh chord, which commonly occurs in root position.<ref name="B&S2">Template:Cite book</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 and pop music, the diminished triad nearly always appears on the second scale degree, forming a generally maudlin and dejected iiTemplate:Music with its members, 2–4–Template:Music6."<ref name="Everett">Template:Cite book</ref> Songs that feature iiTemplate:Music 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' "Don't Look Back in Anger", David Bowie's "Space Oddity", and two in Daryl Hall's "Everytime You Go Away".<ref name="Stephenson">Template:Cite book</ref>

The viiTemplate:Music in major keys is relatively less common than the iiTemplate:Music, but still does happen. It is almost always used to tonicize the relative minor, in progressions such as viiTemplate:Music–V⁷/vi–vi, which resembles iiTemplate:Music–V⁷–i in the relative minor.

Tuning

File:Comparison of diminished triads (0,3,6).png

Comparison, in cents, of diminished triad tunings

In a twelve-tone equal temperament, a diminished triad has three semitones 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–ATemplate:Music) it is 9:8, 4:3, and 8:5 (135:160:192). According to Georg Andreas Sorge, the trumpet, in its overtone series on C, gives the diminished triad E–G–BTemplate:Music = 5:6:7 ("perfect diminished chord"<ref>Template:Cite book</ref>), but the 7 is too flat and 45:54:64 is preferred.<ref name="Shirlaw" /> Helmholtz describes the diminished triad as ₁ − D | 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>Template:Cite book</ref>

Play {{#if:Perfect diminished chord on C.mid|{{#ifexist:Media:Perfect diminished chord on C.mid|<phonos file="Perfect diminished chord on C.mid">Perfect</phonos>|{{errorTemplate:Main other|Audio file "Perfect diminished chord on C.mid" not found}}Template:Category handler}}}}, {{#if:Preferred diminished chord on C.mid|{{#ifexist:Media:Preferred diminished chord on C.mid|<phonos file="Preferred diminished chord on C.mid">Preferred</phonos>|{{errorTemplate:Main other|Audio file "Preferred diminished chord on C.mid" not found}}Template:Category handler}}}} (5-limit major), or {{#if:Five-limit minor diminished chord on C.mid|{{#ifexist:Media:Five-limit minor diminished chord on C.mid|<phonos file="Five-limit minor diminished chord on C.mid">5-limit minor</phonos>|{{errorTemplate:Main other|Audio file "Five-limit minor diminished chord on C.mid" not found}}Template:Category handler}}}} on C.

	Sorge (perfect)/ 7-limit			Sorge (preferred)/ 5-limit major			5-limit minor (D,F,ATemplate:Music)
Harmonics
Root	E	5	386.31	FTemplate:MusicTemplate:Music	45	590.22	CTemplate:Music	135	92.18
Third	G	6	701.96	ATemplate:Music	54	905.87	E	160	386.31
Fifth	Template:Nowrap	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	FTemplate:MusicTemplate:Music	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	ETemplate:Music	6:5	315.64	ETemplate:Music	6:5	315.64	ETemplate:MusicTemplate:Music	32:27	294.13
Fifth	GTemplate:MusicTemplate:Music	7:5	582.51	GTemplate:MusicTemplate:Music	64:45	609.78	GTemplate:MusicTemplate:Music	64:45	609.78

Diminished chord table

Chord	Root	Minor third	Diminished fifth
Cdim	C	ETemplate:Music	GTemplate:Music
CTemplate:Musicdim	CTemplate:Music	E	G
DTemplate:Musicdim	DTemplate:Music	FTemplate:Music (E)	ATemplate:Music (G)
Ddim	D	F	ATemplate:Music
DTemplate:Musicdim	DTemplate:Music	FTemplate:Music	A
ETemplate:Musicdim	ETemplate:Music	GTemplate:Music	BTemplate:Music (A)
Edim	E	G	BTemplate:Music
Fdim	F	ATemplate:Music	CTemplate:Music (B)
FTemplate:Musicdim	FTemplate:Music	A	C
GTemplate:Musicdim	GTemplate:Music	BTemplate:Music (A)	DTemplate:Music (C)
Gdim	G	BTemplate:Music	DTemplate:Music
GTemplate:Musicdim	GTemplate:Music	B	D
ATemplate:Musicdim	ATemplate:Music	CTemplate:Music (B)	ETemplate:Music (D)
Adim	A	C	ETemplate:Music
ATemplate:Musicdim	ATemplate:Music	CTemplate:Music	E
BTemplate:Musicdim	BTemplate:Music	DTemplate:Music	FTemplate:Music (E)
Bdim	B	D	F

See also

• Half-diminished seventh chord
• Secondary leading-tone chord
• Augmented triad
• Diminished seventh chord

References

Template:Reflist Sources

• Template:Cite book