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The half-diminished seventh chord (also known as a minor seventh flat five) is created by taking the root, minor third, diminished fifth and minor seventh (1, ♭3, ♭5 and ♭7) of any major scale; for example, C half-diminished would be (C E♭ G♭ B♭). In diatonic harmony, the half-diminished chord naturally occurs on the 7th scale tone (for example, Bm7(♭5) in C major). By the same virtue, it also occurs on the second degree of natural minor (eg Dm7 (♭5) in C minor).

Half-diminished seventh chords are often symbolized as a circle with a diagonal line through it.

The terms and symbols for this chord break the usual system of chord nomenclature. Normally a term like "Bdim" indicates a diminished triad and "B7" indicates a major triad plus a minor seventh. Thus the term "Bdim7" should indicate a diminished triad plus a minor seventh. But instead it means a diminished triad plus a diminished seventh. The term "half-diminished" and the ø symbol were invented. Since the term dim7 (as in Bdim7) meant something else, the accurate but unwieldy term "minor seventh flat five" (as in Bm7(♭5)) came to be used.^[1]

Half-diminished seventh chords are often used in jazz, typically functioning as the ii chord in a ii-V-I progression where the I is a minor chord (e.g. Dm7(♭5) - G7alt - Cm(maj7)). They can also be found as incomplete dominant V chords, with the 7th degree of the half diminished ii chord yielding a 9th of an extended V chord.

Jazz musicians typically consider the half-diminished chord to be 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 b9, giving it a somewhat more consonant quality), or the "half-whole" diminished scale (see octatonic scales.)

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 (i.e. is it G♭ or F#?).

1. ^ 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

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