Diminished triad

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|caption=A diminished triad substituting for dominant chord in J. S. Bach's Well-Tempered Clavier I, Prelude in G major.{{cite book|title=Das Wesen des musikalischen Kunstwerks: Eine Einführung in Die Lehre Heinrich Schenkers|last=Jonas|first=Oswald|date=1982|isbn=0-582-28227-6|page=[https://archive.org/details/introductiontoth0000jona/page/25 25]|publisher=Longman |translator-last=Rothgeb|translator-first=John|trans-title=Introduction to the Theory of Heinrich Schenker|author-link=Oswald Jonas|orig-year=1934|url=https://archive.org/details/introductiontoth0000jona/page/25}}}}

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.{{sfn|Roig-Francolí|2011|page=248}}

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{{music|b}}). 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.{{sfn|Roig-Francolí|2011|page=174}}

If the music is in a minor key, diminished triads can also be found on the raised seventh note, {{music|#}}vii{{music|dim}}. This is because the ascending melodic minor scale has a raised sixth and seventh degree. For example, the chord progression {{music|#}}vii{{music|dim}}–i is common.

The leading-tone diminished triad and supertonic diminished triad are usually found in first inversion (vii{{music|dim}}⁶ and ii{{music|dim}}⁶, respectively) since the spelling of the chord forms a diminished fifth with the bass.{{sfn|Roig-Francolí|2011|page=248}} This differs from the fully diminished seventh chord, which commonly occurs in root position.{{cite book|title=Music in Theory and Practice: Volume II|last1=Benward|last2=Saker|date=2009|isbn=978-0-07-310188-0|edition=8th|page=76|publisher=McGraw-Hill }} In both cases, the bass resolves up and the upper voices move downwards in contrary motion.

The vii{{music|dim}} in major keys is relatively less common than the ii{{music|dim}}, but still does happen. It is almost always used to tonicize the relative minor, in progressions such as vii{{music|dim}}–V⁷/vi–vi, which resembles ii{{music|dim}}–V⁷–i in the relative minor.

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{{music|b}}) 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{{music|b}} = 5:6:7 ("perfect diminished chord"{{cite book|last1=Fétis|first1=François-Joseph|author1-link=François-Joseph Fétis|last2=Arlin|first2=Mary I.|date=1994|title=Esquisse de l'histoire de l'harmonie|page=[https://archive.org/details/esquissedelhisto0000feti/page/139 139n9]|isbn=978-0-945193-51-7|url=https://archive.org/details/esquissedelhisto0000feti/page/139}}), but the 7 is too flat and 45:54:64 is preferred. 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.{{cite book|first=Hermann|last=Helmholtz|author-link=Hermann von Helmholtz|date=1885|title=On the Sensations of Tone as a Physiological Basis for the Theory of Music|page=344|location=Longmans, Green}}

Play {{audio|Perfect diminished chord on C.mid|Perfect}}, {{audio|Preferred diminished chord on C.mid|Preferred}} (5-limit major), or {{audio|Five-limit minor diminished chord on C.mid|5-limit minor}} on C.

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Sources

• {{cite book|last=Roig-Francolí|first=Miguel|author-link=Miguel Roig-Francolí|title=Harmony in Context|year=2011|publisher=McGraw-Hill|location=New York|isbn=9780073137940}}

{{Degrees}}

{{Chords}}

{{DEFAULTSORT:Diminished Triad Chord}}

Category:Chords