About

Misidentifying a chord inversion leads to incorrect voice leading, broken harmonic analysis, and poor arrangements. A C major chord in root position (C - E - G) contains the same pitch classes as its first inversion (E - G - C), yet they produce different bass motion and different figured-bass symbols (5/3 vs. 6/3). This tool computes every possible inversion for triads through extended chords, displays the resulting note names and intervals from the bass, and synthesizes audio playback so you can verify the voicing by ear. It assumes equal temperament at A4 = 440 Hz.

Limitations: the calculator produces close-position voicings only. Open voicings, drop-2, and drop-3 arrangements require manual redistribution of chord tones across octaves. Enharmonic spelling follows sharps by default; context-dependent respelling (e.g., D♭ vs. C♯) is not applied automatically.

Formulas

Each chord is defined by a root note and an ordered set of intervals measured in semitones. The MIDI note number for the root in octave o is:

n = 12 × (o + 1) + p

where p is the pitch class index (C = 0, C♯ = 1, …, B = 11). For a chord with k notes stored as interval array I = [i₀, i₁, …, i_k−1], the MIDI pitches in root position are:

M_j = n + i_j

For inversion v (where 0 = root position), the bottom v notes are moved up one octave:

M_j^′ =

{

M_j + 12, if j < vM_j, otherwise

The notes are then sorted ascending and the bass note becomes M_v. Audio frequency for each MIDI number:

f = 440 × 2^{n − 6912} Hz

Reference Data

Chord Quality	Symbol	Intervals (semitones)	Notes from C	Inversions	Figured Bass (Root / 1st / 2nd / 3rd)
Major Triad	C	0 - 4 - 7	C E G	2	5/3 · 6/3 · 6/4
Minor Triad	Cm	0 - 3 - 7	C E♭ G	2	5/3 · 6/3 · 6/4
Diminished Triad	Cdim	0 - 3 - 6	C E♭ G♭	2	5/3 · 6/3 · 6/4
Augmented Triad	Caug	0 - 4 - 8	C E G♯	2	5/3 · 6/3 · 6/4
Suspended 2nd	Csus2	0 - 2 - 7	C D G	2	-
Suspended 4th	Csus4	0 - 5 - 7	C F G	2	-
Dominant 7th	C7	0 - 4 - 7 - 10	C E G B♭	3	7 · 6/5 · 4/3 · 4/2
Major 7th	Cmaj7	0 - 4 - 7 - 11	C E G B	3	7 · 6/5 · 4/3 · 4/2
Minor 7th	Cm7	0 - 3 - 7 - 10	C E♭ G B♭	3	7 · 6/5 · 4/3 · 4/2
Half-Diminished 7th	Cm7♭5	0 - 3 - 6 - 10	C E♭ G♭ B♭	3	ø7 · ø6/5 · ø4/3 · ø4/2
Diminished 7th	Cdim7	0 - 3 - 6 - 9	C E♭ G♭ B♭♭	3	°7 · °6/5 · °4/3 · °4/2
Minor-Major 7th	CmMaj7	0 - 3 - 7 - 11	C E♭ G B	3	-
Augmented 7th	Caug7	0 - 4 - 8 - 10	C E G♯ B♭	3	-
Dominant 9th	C9	0 - 4 - 7 - 10 - 14	C E G B♭ D	4	-
Major 9th	Cmaj9	0 - 4 - 7 - 11 - 14	C E G B D	4	-
Minor 9th	Cm9	0 - 3 - 7 - 10 - 14	C E♭ G B♭ D	4	-
Add9	Cadd9	0 - 4 - 7 - 14	C E G D	3	-
6th	C6	0 - 4 - 7 - 9	C E G A	3	-
Minor 6th	Cm6	0 - 3 - 7 - 9	C E♭ G A	3	-
Power Chord	C5	0 - 7	C G	1	-

Frequently Asked Questions

Root position triads carry the figured bass symbol 5/3 (often omitted). First inversion is 6/3 (abbreviated 6), and second inversion is 6/4. For seventh chords: root = 7, first = 6/5, second = 4/3, third = 4/2 (or 2). These numbers describe the intervals above the bass note, not above the root.

The augmented triad divides the octave into three equal parts of 4 semitones each (0 - 4 - 8). Each inversion produces an identical set of interval distances between adjacent notes. Only the enharmonic spelling of the bass changes. This symmetry property also applies to the diminished seventh chord, which divides the octave into four equal 3-semitone segments.

No. The calculator produces close-position voicings only, where all chord tones are packed within one octave (or as close as possible for extended chords). Drop-2 voicings move the second-from-top note down an octave; drop-3 moves the third-from-top. These rearrangements must be done manually after obtaining the close-position inversion from this tool.

The calculator uses a sharp-based chromatic scale by default: C, C♯, D, D♯, E, F, F♯, G, G♯, A, A♯, B. Context-dependent respelling (e.g., writing D♭ instead of C♯ in an A♭ major chord) is not performed. In formal music theory, correct enharmonic spelling depends on the key signature and harmonic function, which this tool does not infer.

A chord with k notes has k − 1 inversions plus the root position. A ninth chord (5 notes) therefore has 4 inversions. Beyond the 3rd inversion of a seventh chord, inversions become less common in traditional harmony. Extended chord inversions (9th, 11th, 13th) are more relevant in jazz and contemporary arranging.

Dissonance perception depends on the intervals formed above the bass note. Second-inversion triads (6/4) place a perfect fourth above the bass, historically treated as unstable in common-practice harmony. Third-inversion seventh chords place a second (major or minor) above the bass, producing strong tension that demands resolution. The root position typically sounds most stable because the root is reinforced by the bass register.