How to use this card
Here you'll find ready-made tables for the key of C (axis between E and Eb). For another key, transpose: in G the axis passes between B and Bb, in A between C# and C, in F between A and Ab. General rule: tonic and dominant swap; the other pairs are symmetrical around the axis.
The diatonic triads of C major
| Chord | Notes | Image (notes) | Negative chord | Degrees |
|---|---|---|---|---|
| C | C E G | G Eb C | Cm | I → i |
| Dm | D F A | F D Bb | Bb | ii → bVII |
| Em | E G B | Eb C Ab | Ab | iii → bVI |
| F | F A C | D Bb G | Gm | IV → v |
| G | G B D | C Ab F | Fm | V → iv |
| Am | A C E | Bb G Eb | Eb | vi → bIII |
| B° | B D F | Ab F D | D° | vii° → ii° |
Every major triad becomes minor and vice versa; the diminished stays diminished. The result is the entire harmonic field of C natural minor.
The diatonic seventh chords
Careful: when you add the seventh, the note that mirrors the fifth of the starting chord becomes the root of the negative chord. This is why the names "shift."
| Chord | Notes | Image | Negative chord |
|---|---|---|---|
| Cmaj7 | C E G B | G Eb C Ab | Abmaj7 (= Cm/Ab) |
| Dm7 | D F A C | F D Bb G | Gm7 |
| Em7 | E G B D | Eb C Ab F | Fm7 |
| Fmaj7 | F A C E | D Bb G Eb | Ebmaj7 |
| G7 | G B D F | C Ab F D | Dø7 (= Fm6) |
| Am7 | A C E G | Bb G Eb C | Cm7 |
| Bø7 | B D F A | Ab F D Bb | Bb7 |
Two pairs to remember: G7 ↔ Dø7/Fm6 (dominant ↔ minor subdominant) and Bø7 ↔ Bb7 (the leading-tone seventh chord becomes the backdoor dominant bVII7).
Altered and extended chords (verified examples)
- G9 (G B D F A) → C Ab F D Bb = Bb9 (Bb D F Ab C): the V9 becomes the bVII9 of the backdoor progression.
- C7 (C E G Bb) → G Eb C A = Cm6 (= Aø7).
- F7 (F A C Eb) → D Bb G E = Gm6 (= Eø7).
- E7 (E G# B D, V/vi) → Eb B Ab F, that is Ab B(Cb) Eb F = Abm6 (= Fø7): the V/vi becomes a minor sixth chord on the bVI.
- A7 (A C# E G, V/ii) → Bb F# Eb C, that is C Eb Gb Bb = Cø7 (= Ebm6): secondary dominants also become half-diminished / minor sixth chords, that is, "local" minor subdominants.
Scales and modes
| Scale on C | Notes | Image | Resulting scale |
|---|---|---|---|
| Ionian | C D E F G A B | G F Eb D C Bb Ab | Aeolian (natural minor) |
| Dorian | C D Eb F G A Bb | G F E D C Bb A | Mixolydian |
| Mixolydian | C D E F G A Bb | G F Eb D C Bb A | Dorian |
| Lydian | C D E F# G A B | G F Eb C# C Bb Ab | Phrygian (with Db) |
| Harmonic minor | C D Eb F G Ab B | G F E D C B Ab | Harmonic major |
| Melodic minor | C D Eb F G A B | G F E D C Bb Ab | Mixolydian b6 |
| Major pentatonic | C D E G A | G F Eb C Bb | Minor pentatonic |
| Half-whole diminished | C Db Eb E F# G A Bb | (same set) | itself (symmetrical) |
Locrian on C does not contain G, so its image does not contain C: it leaves the tonal center and is useless in this form. It is a good reminder: Levy's axis is designed for systems in which C and G are both present.
Melodies
Mirroring a melody means inverting its contour around the axis: C E G E C becomes G Eb C Eb G. The arrival notes change (a phrase that ends on C ends on G), so often only the inner cells are mirrored and the final note is kept.
Bass and inversions
A root-position chord mirrored "from above" has as its lowest note the image of the highest note. In practice, choose the bass on functional grounds (for example Fm6 with F in the bass, not D) and then check the voice leading.
Exercise
Print the note table and transcribe one of your own 4-chord loops in negative. Make two versions: fully mirrored and only the chord before the tonic. Compare the emotional character and choose the one to use in the bridge.
Related topics
Negative harmony: principle and axis; applications of negative harmony; backdoor progression; modal interchange; The modes of the major scale.