Construction
| Note | Interval | Degree |
|---|---|---|
| F | Root | 1 |
| A♭ | Minor 3rd | ♭3 |
| C♭ | Diminished 5th | ♭5 |
| E♭ | Minor 7th | ♭7 |
Fingering
| Note | Key color | Right hand | Left hand |
|---|---|---|---|
| F | white | thumb (1) | little finger (5) |
| A♭ | black | index finger (2) | middle finger (3) |
| C♭ | white | middle finger (3) | index finger (2) |
| E♭ | black | little finger (5) | thumb (1) |
Right hand: thumb (1) on F, index finger (2) on A♭, middle finger (3) on C♭, little finger (5) on E♭.
Left hand: little finger (5) on F, middle finger (3) on A♭, index finger (2) on C♭, thumb (1) on E♭.
F Half Diminished Inversions
- Root positionF – A♭ – C♭ – E♭
- 1st inversion (Fm7♭5/A♭)A♭ – C♭ – E♭ – F
- 2nd inversion (Fm7♭5/C♭)C♭ – E♭ – F – A♭
- 3rd inversion (Fm7♭5/E♭)E♭ – F – A♭ – C♭
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 F Major
These are the triads built on each degree of F Major:
How F Half Diminished functions in a key
The same chord takes on a different harmonic role depending on the key it appears in. Here is where F Half Diminished sits diatonically across the common keys:
- In G♭ major, F Half Diminished is the vii° chord — the dominant.
- In E♭ minor, F Half Diminished is the ii° chord — a predominant.
Scales That Include the F Half Diminished
- F# Major (viiø7)
- Eb Minor (iiø7)
- G# Dorian (vi°)
- A# Phrygian (v°)
- B Lydian (#iv°)
- C# Mixolydian (iii°)
- D# Aeolian (ii°)
- E# Locrian (i°)
Same Notes, Other Names
The notes F – A♭ – C♭ – E♭ aren’t exclusive to this chord. Depending on which note is the bass and how the chord functions, the same pitches also spell:
F Half Diminished : Frequently Asked Questions
What notes are in Fm7♭5?
How do you play Fm7♭5 on piano?
What are the inversions of Fm7♭5?
What keys contain Fm7♭5?
What is the difference between Fm7♭5 and Fdim?
What is an easy Fm7♭5 for small hands?
What are the frequencies of Fm7♭5?
What is the set class of Fm7♭5?
How do I transpose Fm7♭5 to another key?
F 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 | Fit |
|---|---|---|---|---|---|---|
| Close, root position | F3 A♭3 C♭3 E♭4 | 10 | 138 mm | none | identical | |
| Close, first inversion | A♭3 C♭3 E♭4 F4 | 9 | 124 mm | none | identical | |
| Close, second inversion | C♭3 E♭4 F4 A♭4 | 9 | 124 mm | none | identical | |
| Close, third inversion | E♭4 F4 A♭4 C♭4 | 8 | 110 mm | none | identical | |
| Drop 2 | C♭2 F3 A♭3 E♭4 | 16 | 220 mm | none | identical | |
| Drop 3 | A♭2 F3 C♭3 E♭4 | 19 | 261 mm | none | identical | |
| Drop 2 and 4 | F2 C♭2 A♭3 E♭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 | Fit |
|---|---|---|---|---|---|---|
| Shell, root ♭7 ♭3 | F2 E♭3 A♭3 | 15 | 206 mm | omits C♭ | subset | |
| Guide tones, ♭3 and ♭7 | A♭3 E♭4 | 7 | 96 mm | omits F and C♭ | subset | |
| Rootless close | A♭3 C♭3 E♭4 | 7 | 96 mm | omits F | 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 | F | F3, A♭3, C♭3, E♭4 | 7 | 10 | 138 mm |
| First inversion: Fm7♭5/A♭ | A♭ | A♭3, C♭3, E♭4, F4 | 6/5 | 9 | 124 mm |
| Second inversion: Fm7♭5/C♭ | C♭ | C♭3, E♭4, F4, A♭4 | 4/3 | 9 | 124 mm |
| Third inversion: Fm7♭5/E♭ | E♭ | E♭4, F4, A♭4, C♭4 | 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 | Fm7♭5 to B♭m7 to E♭m7 | Fm7♭5 opens the phrase |
| vii, I | G♭ major | viim7♭5 | Fm7♭5 to G♭maj7 | Fm7♭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 |
|---|---|---|---|
| Fdim | drops E♭ | 1 ♭3 ♭5 | 3 |
| Fm7 | C♭ becomes C | 1 ♭3 5 ♭7 | 3 |
| Fdim7 | E♭ becomes E♭♭ | 1 ♭3 ♭5 ♭♭7 | 3 |
| Fm9 | C♭ becomes C, G | 1 ♭3 5 ♭7 9 | 3 |
| Fm | C♭, E♭ becomes C | 1 ♭3 5 | 2 |
| F7 | A♭, C♭ becomes A, C | 1 3 5 ♭7 | 2 |
| FmMaj7 | C♭, E♭ becomes C, E | 1 ♭3 5 7 | 2 |
| Faug7 | A♭, C♭ becomes A, C♯ | 1 3 ♯5 ♭7 | 2 |
| F7sus4 | A♭, C♭ becomes B♭, C | 1 4 5 ♭7 | 2 |
| Fm6 | C♭, E♭ becomes C, D | 1 ♭3 5 6 | 2 |
Frequencies
| Note | MIDI | Frequency |
|---|---|---|
| F3 | 53 | 174.61 Hz |
| A♭3 | 56 | 207.65 Hz |
| C♭3 | 59 | 246.94 Hz |
| E♭4 | 63 | 311.13 Hz |
Reference pitch A440, 12-TET, close root position.
Set theory: prime form, Forte number, interval vector
- Absolute pitch class set
- {5, 8, 11, 3}
- Normal order
- [3, 5, 8, 11]
- Prime form
- (0258)
- Forte number
- 4-27
- Interval vector
- <012111>
| Pair | Interval | Semitones | Interval class |
|---|---|---|---|
| F to A♭ | Minor third | 3 | 3 |
| F to C♭ | Tritone | 6 | 6 |
| F to E♭ | Minor seventh | 10 | 2 |
| A♭ to C♭ | Minor third | 3 | 3 |
| A♭ to E♭ | Perfect fifth | 7 | 5 |
| C♭ to E♭ | 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 F, 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.