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diminished triad : ウィキペディア英語版
diminished triad

In music, a diminished triad (), 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.〔Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.68. Seventh Edition. ISBN 978-0-07-294262-0.〕 It resembles a minor triad with a lowered (flattened) fifth. It can be represented by the integer notation .
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 center 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.
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.
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 . 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 Sorge, the trumpet, in its overtone series on C, gives the diminished triad e-g-b = 5:6:7 ("perfect diminished chord"〔Fétis, François-Joseph and Arlin, Mary I. (1994). ''Esquisse de l'histoire de l'harmonie'', p.139n9. ISBN 978-0-945193-51-7.〕), but the 7 is too flat and 45:54:64 is preferred.〔 Helmholtz describes the diminished triad as b1−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''.〔Hermann von Helmholtz (1885). ''On the Sensations of Tone as a Physiological Basis for the Theory of Music'', p.344. Longmans, Green.〕 Play , (5-limit major), or on C.
In some sheet music books , Cdim or C° denotes a diminished seventh chord (a four note chord) with root C, and Cm-5 or Cm5 denotes a diminished triad with root C. However, in some modern jazz books and some music theory literature , Cdim or C° denotes a diminished triad, while Cdim7 or C°7 denotes a diminished seventh chord.
The supertonic diminished triad and leading-tone diminished triad are usually found in first inversion (ii6 and vii6 respectively) since the spelling of the chord forms a diminished fifth with the bass.〔 This differs from the fully diminished seventh chord, which commonly occurs in root position.〔Benward & Saker (2009). ''Music in Theory and Practice: Volume II'', p.76. Eighth Edition. ISBN 978-0-07-310188-0.〕 In both cases resolve the bass up and move the upper voices downwards in contrary motion.〔 The popular music symbol for a diminished triad is a capital letter designating the root (as with a major chord) with MI(5) added.〔Benward & Saker (2003), p.77.〕 For example BMI(5) (see also Chord names and symbols (jazz and pop music)).

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