Diminished triad

In music, a diminished triad (also known as the minor flatted fifth) is a triad consisting of two minor thirds above the root.[3] It is a minor triad with a lowered (flattened) fifth. When using popular-music symbols, it is indicated by the symbols "dim", "o", "m♭5", or "MI(♭5)".[4] For example, the diminished triad built on C, written as Co, has pitches C–E♭–G♭:

"Diminished chord" redirects here. For for the seventh chord, see Diminished seventh chord.
diminished triad
Component intervals from root
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

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
A diminished triad substituting for dominant chord in J.S. Bach's Well-Tempered Clavier I, Prelude in G major.[5]

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.[6]

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, A♭). This triad is consequently called the supertonic diminished triad. Like the supertonic triad found in a major key, the supertonic diminished triad has a predominant function, almost always resolving to a dominant functioning chord.[7]

The leading-tone diminished triad and supertonic diminished triad are usually found in first inversion (viio6 and iio6, respectively) since the spelling of the chord forms a diminished fifth with the bass.[8] This differs from the fully diminished seventh chord, which commonly occurs in root position.[9] In both cases, the bass resolves up and the upper voices move downwards in contrary motion.[9]

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 iio with its members, 2–4–♭6."[10] Songs that feature iio include Santo & Johnny's "Sleep Walk", Jay and the Americans' "Cara Mia", and The Hollies' "The Air That I Breathe".[10] 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".[11]

If the song is in a minor key, diminished triads are usually on the raised seventh note, viio. This is because the ascending melodic minor scale has a raised sixth and seventh degree. For example, the chord progression ♯viio–i is common.

Tuning
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–A♭) 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–B♭ = 5:6:7 ("perfect diminished chord"[12]), but the 7 is too flat and 45:54:64 is preferred.[1] 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.[13]

Play Perfect , Preferred  (5-limit major), or 5-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
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
gollark: And protestors insisting that cursing random bacteria to store data was "uNnAtUrAl".
gollark: Yes, and people would happily be using software to backup their data to unbreakable curses and whatnot.
gollark: Really, if the supernatural things some dodecahedra go on about were real, there would be books like this.
gollark: Sadly, the contents do not currently exist.
gollark: I think my favourite is the Netcleaner one.

See also

Sources
  1. Shirlaw, Matthew (2012). The Theory of Harmony, p.304. Forgotten Books. ISBN 978-1-4510-1534-8.
  2. Partch, Harry (1979). Genesis of a Music, p.68-69. ISBN 978-0-306-80106-8.
  3. Benward; Saker (2003). Music: In Theory and Practice, Vol. I (7th ed.). p. 68. ISBN 978-0-07-294262-0.
  4. Benward & Saker (2003), p.77.
  5. Jonas, Oswald (1982) [1934]. Das Wesen des musikalischen Kunstwerks: Eine Einführung in Die Lehre Heinrich Schenkers [Introduction to the Theory of Heinrich Schenker]. Translated by Rothgeb, John. p. 25. ISBN 0-582-28227-6.
  6. Roig-Francolí, Miguel (2011). Harmony in Context. New York: McGraw-Hill. p. 248. ISBN 9780073137940.
  7. Roig-Francolí, Miguel (2011). Harmony in Context. New York: McGraw-Hill. p. 174. ISBN 9780073137940.
  8. Roig-Francolí, Miguel (2011). Harmony in Context. New York: McGraw-Hill. p. 248. ISBN 9780073137940.
  9. Benward; Saker (2009). Music in Theory and Practice: Volume II (8th ed.). p. 76. ISBN 978-0-07-310188-0.
  10. Everett, Walter (2009). The Foundations of Rock. p. 195. ISBN 978-0-19-531023-8.
  11. Stephenson, Ken (2002). What to Listen for in Rock: A Stylistic Analysis. p. 85. ISBN 978-0-300-09239-4.
  12. Fétis, François-Joseph; Arlin, Mary I. (1994). Esquisse de l'histoire de l'harmonie. p. 139n9. ISBN 978-0-945193-51-7.
  13. Helmholtz, Hermann (1885). On the Sensations of Tone as a Physiological Basis for the Theory of Music. Longmans, Green. p. 344.
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