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half-diminished seventh

Component intervals

root

minor third

diminished fifth (tritone)

minor seventh

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.

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)).

Jazz musicians typically consider the half-diminished chord to be built off one of two scales: the seventh (Locrian) mode of the major scale, or 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.

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#?).

Chords
By Type	Triads	Major · Minor · Augmented · Diminished
	Sevenths	Major · Minor · Dominant · Diminished · Half-diminished · Minor-Major · Augmented major · Augmented minor
	Extended	Ninth · Eleventh · Thirteenth
	Other	Sixth · Augmented sixth · Suspended · Altered · Added tone · Polychord · Quartal and quintal · Tone cluster
By Function	Diatonic	Tonic · Dominant · Subdominant · Submediant
	Altered	Borrowed · Neopolitan sixth · Secondary dominant · Secondary subdominant