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Instrument MI-14-041 · Other

Chord Inversion Calculator

Pick a root note, a chord quality and an inversion, and this instrument shows you the resulting chord tones in order, with the bass note called out.

Instrument MI-14-041
Sheet 1 OF 1
Rev A
Verified
Type 14 — Music Theory SER. 2026-14041

Chord tones, in order

E, G, C

inversion N = triad tones rotated left N places (Nth tone becomes the bass note)

E Bass note
The working Every figure verified twice
  1. C major, inversion 1 -> E, G, C (bass: E)
Worksheet log
  1. No entries yet — change an input to log a scenario.

How this instrument works

A triad — the basic three-note chord built from a root, a third and a fifth — doesn't have to be played with its root note on the bottom. 'Inverting' a chord means rearranging which of its three tones sits lowest, without changing which three notes are in the chord at all: C major is still C, E and G whether it's played root-position (C on the bottom), first inversion (E on the bottom), or second inversion (G on the bottom).

Root position places the root in the bass — this is a triad in its most basic, unrotated form. First inversion moves the third into the bass, with the root and fifth stacked above it. Second inversion moves the fifth into the bass, with the root and third above. Musicians use inversions constantly to create smoother bass lines, avoid awkward leaps between chords in a progression, and vary a chord's color and stability without changing its harmonic function.

This instrument works from a fixed, curated triad table (major, minor, diminished and augmented qualities) using a single sharp-spelled 12-note chromatic scale, the same lookup used across this site's music-theory tools. That keeps every result unambiguous and enharmonically correct in pitch — A# and Bb are the same key on a piano — even where a strict conservatory notation class might spell a particular note with a flat instead of a sharp in certain keys.

tones={(root+i)mod12:iquality intervals}\text{tones} = \{ (\text{root} + i) \bmod 12 : i \in \text{quality intervals} \}inversion(N)=rotate_left(tones,N)\text{inversion}(N) = \text{rotate\_left}(\text{tones}, N)
Each chord quality is a fixed set of semitone offsets from the root (major: root, major third, perfect fifth; minor: root, minor third, perfect fifth; diminished: root, minor third, tritone; augmented: root, major third, augmented fifth). Inverting the chord rotates that ordered list so a different tone becomes the lowest-sounding note, without adding or removing any notes.
  • Choose a Root note from the dropdown — the chord's fundamental note before any inversion is applied.
  • Choose a Chord quality — major, minor, diminished or augmented, which sets the triad's exact interval structure.
  • Choose an Inversion — root position (0), first inversion (1), or second inversion (2).
  • Read Chord tones, in order for the full three-note triad as it's voiced in that inversion.
  • Read Bass note for the single lowest-sounding note of the inverted chord.

Worked example — C major in first inversion

C major in root position is C, E, G — the root, C, sits lowest, built from a major third (4 semitones up from C to E) plus a minor third (3 more semitones up from E to G). Applying first inversion — inversion 1 of the 2 available for any triad — rotates that list left by one place: E, G, C. The third of the chord, E, now sits lowest, making it the bass note, while G and C stack above it in that order.

This is exactly the same three notes as root-position C major — nothing was added, removed, or changed pitch-wise except which one is voiced lowest. In real sheet music, first-inversion C major is often written as 'C/E' (chord symbol over bass note), one of 3 possible bass-note voicings for this triad, a notation directly describing what this instrument's Bass note output tells you.

Questions

Does inverting a chord change which notes are in it?

No — inversion only changes which of the chord's existing notes is played lowest (in the bass); the set of notes stays identical. C major in root, first, or second inversion is always C, E and G in some order — the chord's letter name, quality, and harmonic function don't change, only the voicing does.

Why do musicians use chord inversions instead of always playing root position?

Inversions create smoother, more connected bass lines by letting nearby chords share close bass notes instead of jumping around, they add variety and different tonal color to a progression, and they can make a chord sound less 'grounded' or more transitional, which composers use deliberately for musical effect. A bassline moving root-third-fifth-root through a progression, using inversions strategically, sounds noticeably smoother than one that always jumps to each chord's root.

What does the slash notation like 'C/E' mean?

It's a compact way to write an inverted chord: the letter before the slash is the chord itself (C major), and the letter after the slash is the specific bass note being played (E) — which for a C major triad indicates first inversion, since E is the chord's third. This instrument's Bass note output tells you exactly what would go after the slash for the inversion you selected.

Can every chord be inverted into as many positions as it has notes?

Yes for the triads this instrument covers — a three-note chord has exactly three possible inversions (root position plus two inversions), since there are three notes that could each take a turn in the bass. Four-note chords (like seventh chords) would have a third inversion as well, but that extended case is outside this instrument's current triad-only scope.

Why does A# appear instead of Bb in some results?

This instrument uses a single sharp-spelled chromatic scale for every calculation, since A# and Bb are the exact same pitch on any fixed-pitch instrument like a piano — the choice between sharp and flat spelling is a notation convention tied to key signatures, not a difference in actual sound. If you need traditional flat spelling for a specific key (common in flat-heavy keys like F or Bb major), the pitch is identical; only the letter name written on the page would differ.

References