How to Use the Chord Inversion Calculator
Select your chord's root note—the tonal centre—from the available pitches. Next, specify the chord quality: major, minor, diminished, augmented, or any seventh/ninth variant. Finally, choose the inversion you want to examine: root position (no rearrangement), first inversion (third in the bass), second inversion (fifth in the bass), or, for seventh chords, third inversion (seventh in the bass). The calculator then displays every note in that inversion and their precise order from lowest to highest. This arrangement determines both the chord's sonority and its harmonic function.
Understanding Chord Inversions
Every chord contains a fixed set of pitches, but their vertical arrangement is fluid. An inversion occurs when you reorder those notes so a different one becomes the lowest pitch. A C major triad contains C, E, and G: in root position, C is lowest; in first inversion, E sits in the bass; in second inversion, G occupies the bass position.
The number of possible inversions equals the number of notes in the chord. A three-note triad has three positions; a four-note seventh chord has four. This reordering creates different harmonic colours and interval relationships while preserving the underlying chord's identity.
Inversion Positions and Interval Structure
Chord inversions are defined by which scale degree of the chord sits in the bass. The intervals measured upward from that bass note reveal the chord's harmonic character in that position.
Root Position: Root in bass (1–3–5 for a triad)
First Inversion: Third in bass (3–5–1 for a triad)
Second Inversion: Fifth in bass (5–1–3 for a triad)
Third Inversion: Seventh in bass (7–1–3–5 for a seventh chord)
Root— The chord's foundational pitchThird— The second scale degree above the rootFifth— The third scale degree above the rootSeventh— The fourth scale degree above the root (seventh chords only)
Notating Chord Inversions: Figured Bass and Slash Chords
Musicians use two main notation systems to denote inversions. Figured bass, rooted in Baroque practice, uses Roman numerals to identify the chord by its scale degree within a key, paired with Arabic numerals indicating intervals above the bass note. For instance, a IV chord in first inversion might be notated as IV⁶, revealing that the sixth (and third above the root) sits in the bass.
Slash chord notation, standard in contemporary music, simply names the chord followed by a slash and the bass note. C major in first inversion becomes C/E—transparent and immediate. Modern composers and songwriters favour this system for its clarity.
Practical Considerations for Chord Inversions
Keep these principles in mind when working with inversions:
- Second inversion creates harmonic ambiguity — Second inversion (fifth in bass) weakens harmonic clarity because the bass note and root lack a strong interval relationship. Reserve it for cadences, passing chords, or deliberate harmonic colouring—not structural pillars.
- Seventh chord inversions expand beyond triads — Only seventh chords and denser harmonies can reach third inversion (seventh in the bass). Standard triads stop at second inversion. Knowing your chord's note count determines how many inversion options exist.
- Voice leading drives inversion choice — Inversions exist primarily to smooth transitions between chords. Rather than leap between distant pitches, inversions allow chord tones to step or repeat, creating singable lines and economical arranging.
- Register affects chord recognition — The same inversion can sound entirely different depending on how far apart the upper notes sit. Close voicing (all notes bunched together) feels intimate; wide voicing spans the staff. Both are the same inversion but carry distinct colours.