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Half-diminished seventh chord
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Half-diminished seventh chord : ウィキペディア英語版
Half-diminished seventh chord

In music theory, the half-diminished seventh chord—also known as a half-diminished chord or a minor seventh flat five (m75)—is formed by a root note, a minor third, a diminished fifth, and a minor seventh. Its consecutive intervals are minor 3rd, minor 3rd, major 3rd.
It can be created by playing the tonic, flattened third, flattened fifth, and flattened seventh degrees of any major scale (1, 3, 5 and 7)—for example, C half-diminished is (C E G B). Alternatively, assuming even temperament, it can be derived simply by sharpening (by a semitone) the root note of the major seventh chord whose tonic lies a semitone immediately below its tonic. (cf. Bar 6 of the twelve-bar blues where the half diminished is sometimes used to provide a semitone lift to the harmonic root without apparent change to the remaining harmonizing components).
In diatonic harmony, the half-diminished chord occurs naturally on the 7th scale degree of any major scale including a seventh.〔Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.217. ISBN 978-0-07-294262-0.〕 (for example, B7 in C major). By the same virtue, it also occurs on the second degree of any natural minor scale (e.g., D7 in C minor). It occurs as a leading-tone seventh chord in major〔 and can be represented by the integer notation . It has been described as a "considerable instability".〔Henry, Earl and Rogers, Michael (2004). ''Tonality and Design in Music Theory, Vol. I'', p.295. ISBN 0130811289.〕
==Chord symbols and terminology==
Half-diminished seventh chords are often symbolized as a circle with a diagonal line through it, as in C. It also can be represented as m75, -75, m7(5) etc.
The terms and symbols for this chord break expectations that derive from the usual system of chord nomenclature. Normally a symbol like "Bdim" indicates a diminished triad and "B7" indicates a major triad plus a minor seventh. Thus one would expect the term "Bdim7" to indicate a diminished triad plus a minor seventh. Instead, it means a diminished triad plus a diminished seventh. To make this distinction clear, the term "half-diminished" and the symbol (ø) were invented. Since the term dim7 (as in Bdim7) meant something else, the accurate but unwieldy term "minor seventh flat five" (as in B7))() came to be used.〔Mathieu, W.A. ''Harmonic Experience: Tonal Harmony from Its Natural Origins to Its Modern Expression'' (1997), pp. 371-372, Inner Traditions International, ISBN 0-89281-560-4〕
Jazz musicians typically consider the half-diminished chord as built from one of three scales: the seventh (Locrian mode) of the major scale, the sixth mode of the melodic minor scale (the latter scale is nearly identical to the Locrian mode, except that it has a natural 9 rather than a 9, giving it a somewhat more consonant quality), or the "half-whole" diminished scale (see octatonic scales.) See: chord-scale system.
The "Tristan chord" is sometimes described as a half-diminished seventh chord; however, the term "Tristan chord" is typically reserved for a very specific harmonic function, especially determined by the order of the notes from bottom to top, and sometimes even the way the chord is spelled (e.g. is it G or F?).

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