Diminished Triad
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Diminished Triad
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
Diminished triad on B, in C major and C minor About this soundplay  or About this soundPlay just .
Dominant seventh and incomplete dominant seventh in C major: G7 and Bo chords About this soundPlay .

In music, a diminished triad (About this soundPlay ), also known as the minor flatted fifth (m5), is a triad consisting of two minor thirds above the root -- if built on C, a diminished triad would have a C, an E and a G.[3] It resembles a minor triad with a lowered (flattened) fifth. It can be represented by the integer notation {0, 3, 6}.

Diminished triad on C About this soundplay .
iio6 in C minor About this soundplay : first inversion Do chord.
Comparison, in cents, of diminished triad tunings

In the common practice period, the diminished triad is considered dissonant, or unstable, because the dissonant diminished fifth symmetrically divides the octave. The lack of tonal centre or stability, possession of a leading-tone, and the dominant function give the chord drive.

Harmonic considerations

A diminished triad occurs in a major scale only on the seventh scale degree; 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. The leading-tone triad also occurs in the seventh chord built on the fifth degree; in C, this is G dominant seventh (G, B, D, F). For this reason, it has 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 now absent.[4]

On the other hand, the diminished triad in a minor scale 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.[5]

In a twelve-tone equal tempered tuning, a diminished triad has 3 semitones between the third and fifth, 3 between the root and third, and 6 between the root and fifth. It is represented by the integer notation {0, 3, 6}. 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"[6]), 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.[7] Play About this soundPerfect , About this soundPreferred  (5-limit major), or About this sound5-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 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 F7+ 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 G7 7:5 582.51 G- 64:45 609.78 G- 64:45 609.78

Cdim or Co or Cm5 denotes a diminished triad, while Cdim7 or Co7 or Cm65 denotes a diminished seventh chord.

The supertonic diminished triad and leading-tone diminished triad are usually found in first inversion (iio6 and viio6 respectively) since the spelling of the chord forms a diminished fifth with the bass.[4] This differs from the fully diminished seventh chord, which commonly occurs in root position.[8] In both cases resolve the bass up and move the upper voices downwards in contrary motion.[8] The popular music symbol for a diminished triad is a capital letter designating the root (as with a major chord) with MI(5) added.[9] For example, BMI(5) (see also Chord names and symbols (jazz and pop music)).

Diminished triad substituting for dominant chord in Bach's Well-Tempered Clavier I, Prelude in G Major.[10]About this soundPlay  or About this soundPlay 

In popular music

"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."[11] Songs that feature iio include Santo & Johnny's Sleep Walk, Jay and the Americans' "Cara Mia", and The Hollies' "The Air That I Breathe".[11] 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".[12]

If the song is in a minor key, diminished triads are usually on the sharpened seventh note, 7-2-4. This is because the ascending melodic minor scale has a sharpened sixth and seventh degree. For example, the chord progression viio, i is common.

Diminished chord table

Chord Root Minor third Diminished fifth
Cdim C E G
Cdim C E G
Ddim D F (E) Adouble flat (G)
Ddim D F A
Ddim D F A
Edim E G Bdouble flat (A)
Edim E G B
Fdim F A C (B)
Fdim F A C
Gdim G Bdouble flat (A) Ddouble flat (C)
Gdim G B D
Gdim G B D
Adim A C (B) Edouble flat (D)
Adim A C E
Adim A C E
Bdim B D F (E)
Bdim B D F

See also

Sources

  1. ^ a b 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. ^ a b Roig-Francolí, Miguel (2011). Harmony in Context. New York: McGraw-Hill. p. 248. ISBN 9780073137940.
  5. ^ Roig-Francolí, Miguel (2011). Harmony in Context. New York: McGraw-Hill. p. 174. ISBN 9780073137940.
  6. ^ Fétis, François-Joseph; Arlin, Mary I. (1994). Esquisse de l'histoire de l'harmonie. p. 139n9. ISBN 978-0-945193-51-7.
  7. ^ Helmholtz, Hermann (1885). On the Sensations of Tone as a Physiological Basis for the Theory of Music. Longmans, Green. p. 344.
  8. ^ a b Benward; Saker (2009). Music in Theory and Practice: Volume II (8th ed.). p. 76. ISBN 978-0-07-310188-0.
  9. ^ Benward & Saker (2003), p.77.
  10. ^ 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.
  11. ^ a b Everett, Walter (2009). The Foundations of Rock. p. 195. ISBN 978-0-19-531023-8.
  12. ^ Stephenson, Ken (2002). What to Listen for in Rock: A Stylistic Analysis. p. 85. ISBN 978-0-300-09239-4.

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