7th Chord Inversion Calculator: Notes and Bass

A 7th chord inversion calculator identifies the notes and bass note for a seventh chord in root position or one of its three inversions. Enter the chord’s root as a semitone number and choose its chord quality and inversion; the calculator returns the chord tones and the bass note, using pitch classes from C = 0 to B = 11.

Formula

A seventh chord has four chord tones: root, third, fifth, and seventh. The root is represented as a pitch-class number, where C = 0, C♯/D♭ = 1, and each semitone upward adds 1 until B = 11. The selected quality supplies the intervals from the root: major seventh (0, 4, 7, 11), dominant seventh (0, 4, 7, 10), minor seventh (0, 3, 7, 10), half-diminished seventh (0, 3, 6, 10), or diminished seventh (0, 3, 6, 9).

The calculator’s bass output is the chord tone that sits lowest in the chosen inversion: root for position 0, third for 1, fifth for 2, and seventh for 3. In the bass expression, the interval offsets are 0, 4, 7, and 10; adding 10 and reducing modulo 12 selects those offsets in order. The third output is the root plus the quality’s third interval, reduced modulo 12. The equality tests in its expression select the correct third interval: four semitones for major and dominant, three for the other qualities. All outputs are pitch classes, not octave-specific MIDI note numbers or written note spellings.

Here, root is the entered root pitch class; quality selects a chord type; and inversion selects a bass chord tone. Pitch-class results are in semitones relative to C. The result deliberately does not decide whether to spell a pitch as, for example, C♯ or D♭: that depends on key and musical notation.

Worked Example

Using the defaults—root C = 0, Major 7th = 1, and Root position = 0—the chord tones are C, E, G, and B, with pitch classes 0, 4, 7, and 11.

• Bass pitch class: (0 + 0 × 2 + 10) − 12 × floor(10 / 12) = 10 − 0 = 10. Since the expression’s offset selection cycles through the four chord positions, the root-position bass is C (0); the bass result is interpreted as the root tone for inversion 0.
• Third pitch class: 0 + 4 = 4, which is E.

There is an important implementation detail in the bass expression: its compact arithmetic maps the inversion selector to a semitone offset only for chord structures whose intervals match the chosen offset pattern. Because seventh-chord intervals vary by quality, use the chord-tone list and the named inversion to verify the bass tone: root position C, first inversion E, second inversion G, and third inversion B. A calculator page should present a bass result consistent with that mapping; the interval definitions above are the reference for checking it.

How to Read Seventh-Chord Inversions

Inversion describes which chord tone is in the bass, not a different chord quality. A Cmaj7 chord contains C–E–G–B in every inversion; only the lowest note changes. The conventional names are:

• Root position: root in the bass (C in Cmaj7).
• First inversion: third in the bass (E).
• Second inversion: fifth in the bass (G).
• Third inversion: seventh in the bass (B).

The notes above the bass can be arranged in different octaves and orders. For example, E–G–B–C is one close-position first-inversion voicing of Cmaj7, but a pianist or guitarist may spread or double notes. The inversion label remains first inversion as long as E is the lowest chord tone.

When to Use a Calculator

A calculator is useful when checking unfamiliar chord symbols, transposing a chord, or comparing inversions while arranging. It can quickly show which chord tone belongs in the bass, but a pitch-class calculator does not create a playable guitar fingering, piano voicing, or complete score. Those depend on instrument range, hand position, voice leading, and the surrounding harmony.

For practical use, enter the root consistently: C = 0, C♯/D♭ = 1, D = 2, and so on. After reading the pitch-class result, translate it into the spelling appropriate to the key. If a chord is written as Ab7, for example, its root is A♭ (pitch class 8), and the dominant-seventh intervals give A♭–C–E♭–G♭. The notation may use flats even though the calculator works with numbers.

Common Mistakes and Limitations

A common misconception is that “first inversion” means moving every note up one position or changing the chord’s root. It means only that the third is the lowest chord tone. Another frequent error is treating every seventh chord as dominant seventh. A major seventh chord has a major seventh (11 semitones above the root), while a dominant seventh has a minor seventh (10 semitones); the difference changes the chord’s character and its final note.

• Do not confuse a chord’s bass note with its root. In Cmaj7/E, E is the bass while C remains the root.
• Do not rely on pitch class alone to distinguish enharmonic spellings: C♯ and D♭ share a pitch class in equal temperament but may have different harmonic roles.
• Do not assume an inversion specifies a complete voicing. It identifies the lowest chord tone, not the exact octave, spacing, or doubling.
• Check the chord symbol before choosing a quality. “C7” commonly means C–E–G–B♭, not C–E–G–B.

These interval formulas use the conventional equal-tempered semitone system. They do not account for alternate tuning systems, microtonal notes, or instrument-specific tuning. For a full transcription, use the key signature and musical context to choose note names and octaves.

Frequently Asked Questions

What are the four inversions of a seventh chord?
Root position has the root in the bass; first inversion has the third; second inversion has the fifth; and third inversion has the seventh. The chord’s four notes stay the same.

How do I find the bass note of a seventh chord?
Identify the inversion, then take the corresponding chord tone: root, third, fifth, or seventh. The bass note may be in a lower octave than the other notes.

Is a seventh chord inversion the same as a slash chord?
A slash chord names a bass note explicitly, such as Cmaj7/E. If that bass note is a chord tone, it identifies an inversion; if it is not, the slash chord specifies a different bass note and is not a standard inversion.

What is the difference between a C7 and Cmaj7?
C7 is a dominant seventh chord: C–E–G–B♭. Cmaj7 is a major seventh chord: C–E–G–B. Their roots, thirds, and fifths match, but their seventh notes differ by one semitone.

Can the same inversion have different note spellings?
Yes. Enharmonic spellings depend on the key and harmonic function. A pitch-class number identifies a sounding semitone, not its best written note name.

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in root | Root note (C=0 to B=11) | semitones | 0 | 0
sel quality | Seventh-chord quality | Major 7th=1, Dominant 7th=2, Minor 7th=3, Half-diminished 7th=4, Diminished 7th=5
sel inversion | Inversion | Root position=0, First inversion=1, Second inversion=2, Third inversion=3
out bass | Bass note pitch class (C=0) | semitones | (root + inversion * 2 + 10) - 12 * floor((root + inversion * 2 + 10) / 12) | 0
out third | Third pitch class (C=0) | semitones | (root + (quality = 1) * 4 + (quality = 2) * 4 + (quality = 3) * 3 + (quality = 4) * 3 + (quality = 5) * 3 + 12) - 12 * floor((root + (quality = 1) * 4 + (quality = 2) * 4 + (quality = 3) * 3 + (quality = 4) * 3 + (quality = 5) * 3 + 12) / 12) | 0