G♭m7♭5: F♯/G♭ Half Diminished Piano Chord

Root position: either hand, fingers low note to high
Hand	Notes	Fingers
Right	G♭, B♭♭, D♭♭, F♭	2-3-4-5
Left	G♭, B♭♭, D♭♭, F♭	5-4-3-2

Scale degree, note, and interval measured from the root.
Degree	Note	Interval from root	Semitones
1	G♭	Perfect unison	0
♭3	B♭♭	Minor third	3
♭5	D♭♭	Tritone	6
♭7	F♭	Minor seventh	10

Construction

G♭ Half Diminished = Root + Minor 3rd + Diminished 5th + Minor 7th = G♭, B♭♭, D♭♭, F♭

Note	Interval	Degree
G♭	Root	1
B♭♭	Minor 3rd	♭3
D♭♭	Diminished 5th	♭5
F♭	Minor 7th	♭7

Fingering

Note	Key color	Right hand	Left hand
G♭	black	index finger (2)	little finger (5)
B♭♭	white	middle finger (3)	ring finger (4)
D♭♭	white	ring finger (4)	middle finger (3)
F♭	white	little finger (5)	index finger (2)

Right hand: index finger (2) on G♭, middle finger (3) on B♭♭, ring finger (4) on D♭♭, little finger (5) on F♭.

Left hand: little finger (5) on G♭, ring finger (4) on B♭♭, middle finger (3) on D♭♭, index finger (2) on F♭.

G♭ Half Diminished Inversions

Root position
G♭ – B♭♭ – D♭♭ – F♭
1st inversion (G♭m7♭5/B♭♭)
B♭♭ – D♭♭ – F♭ – G♭
2nd inversion (G♭m7♭5/D♭♭)
D♭♭ – F♭ – G♭ – B♭♭
3rd inversion (G♭m7♭5/F♭)
F♭ – G♭ – B♭♭ – D♭♭

Key Signature

A Half Diminished chord is built from symmetrical or ambiguous intervals, so it doesn't belong to a single key and has no key signature of its own.

Chords in the Key of G♭ Major

These are the triads built on each degree of G♭ Major:

I — G♭ Major (major)

Degree	Numeral	Chord	Quality
1	I	G♭ Major	Major
2	ii	A♭ Minor	Minor
3	iii	B♭ Minor	Minor
4	IV	C♭ Major	Major
5	V	D♭ Major	Major
6	vi	E♭ Minor	Minor
7	vii°	F Diminished	Diminished

Scales That Include the G♭ Half Diminished

G Major (viiø7)
E Minor (iiø7)
A Dorian (vi°)
B Phrygian (v°)
C Lydian (#iv°)
D Mixolydian (iii°)
E Aeolian (ii°)
F# Locrian (i°)

Same Notes, Other Names

The notes G♭ – B♭♭ – D♭♭ – F♭ aren’t exclusive to this chord. Depending on which note is the bass and how the chord functions, the same pitches also spell:

A Minor 6th→

G♭ Half Diminished : Frequently Asked Questions

What notes are in G♭m7♭5?

G♭m7♭5 contains G♭, B♭♭, D♭♭ and F♭. The formula is 1, ♭3, ♭5, ♭7.

How do you play G♭m7♭5 on piano?

Play G♭, B♭♭, D♭♭ and F♭ together. Right hand fingers 2, 3, 4, 5; left hand 5, 4, 3, 2. G♭ is a black key; B♭♭, D♭♭ and F♭ are white.

What are the inversions of G♭m7♭5?

4 positions: root position G♭ B♭♭ D♭♭ F♭, G♭m7♭5/B♭♭, G♭m7♭5/D♭♭, G♭m7♭5/F♭.

What keys contain G♭m7♭5?

2: iim7♭5 in E minor, viim7♭5 in G major.

What is the difference between G♭m7♭5 and G♭dim?

Drops F♭. 3 of the notes are shared.

What is an easy G♭m7♭5 for small hands?

The guide tones, ♭3 and ♭7 voicing, B♭♭3 F♭4, spans 7 semitones or about 96 mm.

What are the frequencies of G♭m7♭5?

From G♭3 at A440 in 12-TET: 185.00, 220.00, 261.63, 329.63 Hz.

What is the set class of G♭m7♭5?

Prime form (0258), Forte 4-27, interval vector <012111>.

How do I transpose G♭m7♭5 to another key?

Keep the 1, ♭3, ♭5, ♭7 formula on the new root. Cm7♭5 is C, E♭, G♭, B♭; C♯m7♭5 is C♯, E, G, B.

Is F♯m7♭5 the same as G♭m7♭5?

Enharmonically yes: the same piano keys and the same sound, spelled differently.

G♭ Half Diminished 7th in detail

Exact

Every pitch class is present and nothing outside the chord is added.

Type	Notes	Semitones	Span	Omissions and additions	Set relation
Close, root position	G♭3 B♭♭3 D♭♭4 F♭4	10	138 mm	none	identical
Close, first inversion	B♭♭3 D♭♭4 F♭4 G♭4	9	124 mm	none	identical
Close, second inversion	D♭♭4 F♭4 G♭4 B♭♭4	9	124 mm	none	identical
Close, third inversion	F♭4 G♭4 B♭♭4 D♭♭5	8	110 mm	none	identical
Drop 2	D♭♭3 G♭3 B♭♭3 F♭4	16	220 mm	none	identical
Drop 3	B♭♭2 G♭3 D♭♭4 F♭4	19	261 mm	none	identical
Drop 2 and 4	G♭2 D♭♭3 B♭♭3 F♭4	22	303 mm	none	identical

Reduced

A subset of the pitch classes: the identity is incomplete rather than altered.

Type	Notes	Semitones	Span	Omissions and additions	Set relation
Shell, root ♭7 ♭3	G♭2 F♭3 B♭♭3	15	206 mm	omits D♭♭	subset
Guide tones, ♭3 and ♭7	B♭♭3 F♭4	7	96 mm	omits G♭ and D♭♭	subset
Rootless close	B♭♭3 D♭♭4 F♭4	7	96 mm	omits G♭	subset

Spans are measured centre to centre at a 165 mm octave (standard keyboard geometry).

Position	Bass note	Notes in order	Figured bass	Semitones	Span
Root position	G♭	G♭3, B♭♭3, D♭♭4, F♭4	7	10	138 mm
First inversion: G♭m7♭5/B♭♭	B♭♭	B♭♭3, D♭♭4, F♭4, G♭4	6/5	9	124 mm
Second inversion: G♭m7♭5/D♭♭	D♭♭	D♭♭4, F♭4, G♭4, B♭♭4	4/3	9	124 mm
Third inversion: G♭m7♭5/F♭	F♭	F♭4, G♭4, B♭♭4, D♭♭5	4/2	8	110 mm

One position per chord tone in the bass. Spans are for close position: voiced inversions appear under Voicings.

Progression	Key	Role	Sequence	Voice leading
ii, v, i	E minor	iim7♭5	F♯m7♭5 to Bm7 to Em7	G♭m7♭5 opens the phrase
vii, I	G major	viim7♭5	F♯m7♭5 to Gmaj7	G♭m7♭5 opens the phrase

Root motion, common tones and voice displacement are computed from pitch class sets. Roman numerals follow common practice functional harmony.

Which keys it belongs to

Key	Roman numeral	Function
E minor	iim7♭5	Predominant
G major	viim7♭5	Dominant function

Classification system: common-practice functional harmony.

Change one note

Chords a single note away, and what moving that note does.

Chord	Change	Formula	Common tones
G♭dim	drops F♭	1 ♭3 ♭5	3
G♭m7	D♭♭ becomes D♭	1 ♭3 5 ♭7	3
G♭dim7	F♭ becomes F♭♭	1 ♭3 ♭5 ♭♭7	3
G♭m9	D♭♭ becomes D♭, A♭	1 ♭3 5 ♭7 9	3
G♭m	D♭♭, F♭ becomes D♭	1 ♭3 5	2
G♭7	B♭♭, D♭♭ becomes B♭, D♭	1 3 5 ♭7	2
G♭mMaj7	D♭♭, F♭ becomes D♭, F	1 ♭3 5 7	2
G♭aug7	B♭♭, D♭♭ becomes B♭, D	1 3 ♯5 ♭7	2
G♭7sus4	B♭♭, D♭♭ becomes C♭, D♭	1 4 5 ♭7	2
G♭m6	D♭♭, F♭ becomes D♭, E♭	1 ♭3 5 6	2

Frequencies

Note	MIDI	Frequency
G♭3	54	185.00 Hz
B♭♭3	57	220.00 Hz
D♭♭4	60	261.63 Hz
F♭4	64	329.63 Hz

Reference pitch A440, 12-TET, close root position.

Set theory: prime form, Forte number, interval vector

Absolute pitch class set: {6, 9, 0, 4}
Normal order: [4, 6, 9, 0]
Prime form: (0258)
Forte number: 4-27
Interval vector: <012111>

Pair	Interval	Semitones	Interval class
G♭ to B♭♭	Minor third	3	3
G♭ to D♭♭	Tritone	6	6
G♭ to F♭	Minor seventh	10	2
B♭♭ to D♭♭	Minor third	3	3
B♭♭ to F♭	Perfect fifth	7	5
D♭♭ to F♭	Major third	4	4

Where these facts come from

Every value on this page is derived from the note formula for a half diminished 7th applied to the root G♭, using standard music theory. Nothing here is hand-entered per chord, so the notes, intervals, inversions and frequencies cannot drift out of agreement with each other. Pitches assume 12-TET at A440.

G♭ Half Diminished

Fingerings

G♭ Half Diminished 7th: notes and degrees