Half-Diminished

Diminished triad + minor seventh; functions as leading-tone to minor tonic (viiø7).

Half-Diminished Seventh Chord (Minor 7♭5)

The Half-Diminished Seventh, written as m7♭5 or ø7, occupies a unique place between the stability of the minor seventh and the tension of the fully diminished seventh.

It combines a diminished triad (minor third + diminished fifth) with a minor seventh, producing a color that’s somber, expectant, and harmonically rich.

In jazz and classical music, it’s a crucial pre-dominant chord, often functioning as the iiø7 in minor keys.

Structure

Formula:

Root – Minor 3rd – Diminished 5th – Minor 7th

Semitone steps from root: 0 – 3 – 6 – 10

Example (B Half-Diminished):

B – D – F – A

Interval	Distance	Note	Function
Root	0	B	Tonal center
Minor 3rd	+3	D	Establishes minor color
Diminished 5th	+6	F	Creates instability
Minor 7th	+10	A	Adds tension without total collapse

Interval Structure (Stacked Thirds)

From	To	Interval	Size	Effect
Root → 3rd	Minor 3rd	3 semitones	Dark coloration
3rd → 5th	Minor 3rd	3 semitones	Diminished bite
5th → 7th	Major 4th	4 semitones	Expands the tension slightly
Root → 7th	Minor 7th	10 semitones	Gentle outer dissonance

The minor seventh prevents the chord from collapsing inward, giving it a fragile balance — tense but not terminal.

Roman Numeral Function

Scale Degree	In Major Key	In Minor Key	Function
viiø7	Locrian	iiø7	Pre-dominant in minor
iiø7	–	Natural minor ii	Leads to V7

In minor key harmony, iiø7 → V7 → i is one of the most characteristic cadences (e.g., Bm7♭5 → E7 → Am).

Inversions

Inversion	Notes (Bø7)	Symbol	Bass Note	Function
Root Position	B–D–F–A	Bm7♭5	B	Core minor iiø7
1st Inversion	D–F–A–B	Bm7♭5/D	D	Softened tension
2nd Inversion	F–A–B–D	Bm7♭5/F	F	Chromatic or passing bass
3rd Inversion	A–B–D–F	Bm7♭5/A	A	Used in smooth voice-leading

Sound and Character

The chord’s natural tension makes it ideal for harmonies that linger in uncertainty before resolving.

Common Progressions

Progression	Function	Example (in A minor)
iiø7 – V7 – i	Standard minor cadence	Bm7♭5 – E7 – Am
viiø7 – i	Soft leading tone	G#ø7 – Am
i – iiø7 – V7	Modal interchange	Am – Bm7♭5 – E7
iiø7 – V7 – i6	Classical minor	Bm7♭5 – E7 – Am/C

Real-World Examples

Song	Artist / Composer	Use
“Round Midnight”	Thelonious Monk	iiø7 – V7 – i motif
“Stella by Starlight”	Victor Young	Frequent iiø7 setups
“Nardis”	Miles Davis	Modal use in minor contexts
“My Funny Valentine”	Rodgers & Hart	iiø7 in chromatic motion
“Ain’t Misbehavin’”	Fats Waller	Half-diminished passing chords

Application Tips

Summary

Attribute	Value
Formula	1 – ♭3 – ♭5 – ♭7
Semitones	0 – 3 – 6 – 10
Tonality	Minor / diminished hybrid
Emotional Color	Dark, suspenseful, introspective
Function	Pre-dominant in minor, transitional
Inversions	Four
Common Progressions	iiø7–V7–i
Used In	Jazz, film, classical, fusion, minor key pop