Construction
| Note | Interval | Degree |
|---|---|---|
| A | Root | 1 |
| C | Minor 3rd | ♭3 |
| E♭ | Diminished 5th | ♭5 |
| G | Minor 7th | ♭7 |
Fingering
| Note | Key color | Right hand | Left hand |
|---|---|---|---|
| A | white | thumb (1) | little finger (5) |
| C | white | index finger (2) | middle finger (3) |
| E♭ | black | middle finger (3) | index finger (2) |
| G | white | little finger (5) | thumb (1) |
Right hand: thumb (1) on A, index finger (2) on C, middle finger (3) on E♭, little finger (5) on G.
Left hand: little finger (5) on A, middle finger (3) on C, index finger (2) on E♭, thumb (1) on G.
A Half Diminished Inversions
- Root positionA – C – E♭ – G
- 1st inversion (Am7♭5/C)C – E♭ – G – A
- 2nd inversion (Am7♭5/E♭)E♭ – G – A – C
- 3rd inversion (Am7♭5/G)G – A – C – E♭
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 A Major
These are the triads built on each degree of A Major:
How A 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 A Half Diminished sits diatonically across the common keys:
- In B♭ major, A Half Diminished is the vii° chord — the dominant.
- In G minor, A Half Diminished is the ii° chord — a predominant.
Scales That Include the A Half Diminished
- Bb Major (viiø7)
- G Minor (iiø7)
- C Dorian (vi°)
- D Phrygian (v°)
- Eb Lydian (#iv°)
- F Mixolydian (iii°)
- G Aeolian (ii°)
- A Locrian (i°)
Same Notes, Other Names
The notes A – C – E♭ – G aren’t exclusive to this chord. Depending on which note is the bass and how the chord functions, the same pitches also spell:
A Half Diminished : Frequently Asked Questions
What notes are in Am7♭5?
How do you play Am7♭5 on piano?
What are the inversions of Am7♭5?
What keys contain Am7♭5?
What is the difference between Am7♭5 and Adim?
What is an easy Am7♭5 for small hands?
What are the frequencies of Am7♭5?
What is the set class of Am7♭5?
How do I transpose Am7♭5 to another key?
A 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 | A3 C4 E♭4 G4 | 10 | 138 mm | none | identical | |
| Close, first inversion | C4 E♭4 G4 A4 | 9 | 124 mm | none | identical | |
| Close, second inversion | E♭4 G4 A4 C5 | 9 | 124 mm | none | identical | |
| Close, third inversion | G4 A4 C5 E♭5 | 8 | 110 mm | none | identical | |
| Drop 2 | E♭3 A3 C4 G4 | 16 | 220 mm | none | identical | |
| Drop 3 | C3 A3 E♭4 G4 | 19 | 261 mm | none | identical | |
| Drop 2 and 4 | A2 E♭3 C4 G4 | 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 | A2 G3 C4 | 15 | 206 mm | omits E♭ | subset | |
| Guide tones, ♭3 and ♭7 | C4 G4 | 7 | 96 mm | omits A and E♭ | subset | |
| Rootless close | C4 E♭4 G4 | 7 | 96 mm | omits A | 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 | A | A3, C4, E♭4, G4 | 7 | 10 | 138 mm |
| First inversion: Am7♭5/C | C | C4, E♭4, G4, A4 | 6/5 | 9 | 124 mm |
| Second inversion: Am7♭5/E♭ | E♭ | E♭4, G4, A4, C5 | 4/3 | 9 | 124 mm |
| Third inversion: Am7♭5/G | G | G4, A4, C5, E♭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 | G minor | iim7♭5 | Am7♭5 to Dm7 to Gm7 | Am7♭5 opens the phrase |
| vii, I | B♭ major | viim7♭5 | Am7♭5 to B♭maj7 | Am7♭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 |
|---|---|---|
| G minor | iim7♭5 | Predominant |
| B♭ 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 |
|---|---|---|---|
| Adim | drops G | 1 ♭3 ♭5 | 3 |
| Am7 | E♭ becomes E | 1 ♭3 5 ♭7 | 3 |
| Adim7 | G becomes G♭ | 1 ♭3 ♭5 ♭♭7 | 3 |
| Am9 | E♭ becomes E, B | 1 ♭3 5 ♭7 9 | 3 |
| Am | E♭, G becomes E | 1 ♭3 5 | 2 |
| A7 | C, E♭ becomes C♯, E | 1 3 5 ♭7 | 2 |
| AmMaj7 | E♭, G becomes E, G♯ | 1 ♭3 5 7 | 2 |
| Aaug7 | C, E♭ becomes C♯, E♯ | 1 3 ♯5 ♭7 | 2 |
| A7sus4 | C, E♭ becomes D, E | 1 4 5 ♭7 | 2 |
| Am6 | E♭, G becomes E, F♯ | 1 ♭3 5 6 | 2 |
Frequencies
| Note | MIDI | Frequency |
|---|---|---|
| A3 | 57 | 220.00 Hz |
| C4 | 60 | 261.63 Hz |
| E♭4 | 63 | 311.13 Hz |
| G4 | 67 | 392.00 Hz |
Reference pitch A440, 12-TET, close root position.
Set theory: prime form, Forte number, interval vector
- Absolute pitch class set
- {9, 0, 3, 7}
- Normal order
- [7, 9, 0, 3]
- Prime form
- (0258)
- Forte number
- 4-27
- Interval vector
- <012111>
| Pair | Interval | Semitones | Interval class |
|---|---|---|---|
| A to C | Minor third | 3 | 3 |
| A to E♭ | Tritone | 6 | 6 |
| A to G | Minor seventh | 10 | 2 |
| C to E♭ | Minor third | 3 | 3 |
| C to G | Perfect fifth | 7 | 5 |
| E♭ to G | 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 A, 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.