Triad Inversion Practice: Find the Root, Then the Bass
E3–C4–G4–E5 has four sounding notes, but it's still a C major triad. E appears twice, the notes are spread across several octaves, and C isn't at the bottom. Its inversion comes from the lowest pitch: E3, the third of the chord. That's C major in first inversion.
The easy mistake is to rearrange those notes into C–E–G, recognize C major, and call it root position. Rearranging helps you find the root. It also removes the original bass from view.
Keep the original voicing beside a separate root–third–fifth spelling. This triad inversion practice uses both records to separate the effects of spacing, doubling, and bass changes. If building a triad still takes effort, start with triad chord spelling and return for the worksheet.
Root and bass answer different questions
The root names the chord. The bass is its lowest sounding note. A triad's inversion tells you which chord member occupies that lowest position. Music Theory for the 21st-Century Classroom separates root, quality, and bass in its chord-analysis method.
| Lowest chord member | Position | C major example, lowest pitch first |
|---|---|---|
| Root | Root position | C3–E3–G3 |
| Third | First inversion | E3–G3–C4 |
| Fifth | Second inversion | G2–C3–E3 |
All three contain C, E, and G. The root stays C, and the quality stays major.
The register numbers use scientific pitch notation: C4 is middle C, and C5 is the C an octave above it. Every voicing below is written from lowest to highest, with all accidentals supplied and no implied key signature. When working from a score or an unsorted list, find the lowest sounding pitch before using the table.
Interval inversion is a different task: it exchanges the lower-to-upper relationship of two notes. A first inversion triad still has three chord members, and “first” doesn't name the interval above its bass.
Keep a short pitch ledger
For E3–C4–G4–E5, write:
| Record | Result |
|---|---|
| Original bass | E3; keep this while rearranging elsewhere |
| Distinct spelled members | E, C, G; the second E is a doubling |
| Members arranged in thirds | C–E–G |
| Quality check from C | E is 4 semitones above C; G is 7 |
| Bass member and inversion | E is C's third → first inversion |
Use the same sequence for another chord:
- Record the lowest pitch before changing anything.
- On a separate line, remove octave duplicates while preserving letters and accidentals.
- Arrange those three members as two letter thirds: for example, G–B–D or F–A♭–C. Count letter names inclusively: G–A–B makes G to B a third. The first member of the stack is the root.
- Check quality from the root: major uses 0–4–7 semitones; minor 0–3–7; diminished 0–3–6; augmented 0–4–8.
- Return to the original bass and identify it as the root, third, or fifth.
The semitone patterns describe the members placed within one octave above the root, starting at zero. Applying 0–4–7 directly above E3 in the opening voicing would test for E major, which answers the wrong question.
“Third” and “fifth” name the chord members by letter position. A diminished or augmented fifth still counts as the fifth when you identify an inversion.
For this worksheet, each identification contains all three members of a spelled triad. If a different exercise has missing members or extra non-chord tones, don't force it through that assumption.
Change the spacing without changing the inversion
Compare these C major voicings:
| Voicing | Original bass | Position |
|---|---|---|
| C3–E3–G3 | C3 | Root position |
| C3–G3–E4 | C3 | Root position |
| E3–G3–C4 | E3 | First inversion |
| E3–C4–G4–E5 | E3 | First inversion |
| G2–E3–C4–C5 | G2 | Second inversion |
The second row spreads out the upper members. The fourth adds a doubled E as well as wider spacing. Neither operation changes which member is lowest. Open Music Theory discusses identifying triads through doubling and changes of spacing.
Open position triads can look unfamiliar because the notes no longer form a compact stack of thirds. Reconstruct the stack on your scratch line. Keep the actual voicing intact.
Now make a change that does affect inversion: start with E3–G3–C4 and lower C4 to C3. The result, sorted by pitch, is C3–E3–G3, root position. Return to E3–G3–C4 and lower G3 to G2 instead. You get G2–E3–C4, second inversion. Both moves preserve the chord's members but put a different one in the bass.
Read slash symbols in the same order
In a slash symbol, the chord name comes before the slash and the bass note after it. C/E means C major over E; C/G means C major over G. The symbol doesn't specify every upper note's register or doubling. The textbook's inverted-triads lesson explains slash-chord notation.
Check that the bass belongs to the named triad before assigning one of its inversions. C/D indicates C major over D, but D is neither C's root, third, nor fifth. It isn't a first or second inversion of the C major triad.
Try eight exercises before checking
For 1–6, write the root-order spelling, quality, original bass, and position. For 7–8, explain what changed. Cover the answers while working.
| # | Task |
|---|---|
| 1 | Identify B2–D3–G3. |
| 2 | Identify D3–A3–F♯4. |
| 3 | Identify A♭2–F3–C4. |
| 4 | Identify B2–F3–D4. |
| 5 | Identify F3–B3–D4. |
| 6 | Identify E♯3–C♯4–G♯4. Keep the spellings. |
| 7 | E3–C4–G4–E5 is called root position after someone rewrites it C–E–G. Repair the analysis. Then compare G2–E3–C4–C5: what changed? |
| 8 | Optional spelling challenge: compare B♯2–E3–G♯3 with C3–E3–G♯3. Find each spelled triad's root, quality, and position. |
Answers and reasoning
| # | Root-order spelling and quality | Bass and position | Check |
|---|---|---|---|
| 1 | G–B–D, G major | B2; first inversion | B is G's third. G's position at the top doesn't make it the fifth. |
| 2 | D–F♯–A, D major | D3; root position | The fifth, A3, sits below the third, F♯4. That upper order doesn't change the bass. |
| 3 | F–A♭–C, F minor | A♭2; first inversion | A♭ is 3 semitones above F in root order, so it's the minor third. |
| 4 | B–D–F, B diminished | B2; root position | D and F are 3 and 6 semitones above B. A diminished quality doesn't imply an inversion. |
| 5 | B–D–F, B diminished | F3; second inversion | Same spelled members as 4; the fifth is now lowest. |
| 6 | C♯–E♯–G♯, C♯ major | E♯3; first inversion | C–E–G supplies the letter thirds; E♯ and G♯ are 4 and 7 semitones above C♯. |
| 7 | C–E–G, C major, in both | E3: first inversion; G2: second inversion | The scratch stack identifies the root. The original E bass makes the first answer C/E. The second voicing is C/G because its bass is G. Changing the doubled member from E to C doesn't change the inversion; changing the bass member does. |
| 8 | E–G♯–B♯, E augmented; C–E–G♯, C augmented | B♯2: second inversion; C3: root position | Each spelling gives two letter thirds and distances of 4 and 8 semitones from its root. B♯ is E's augmented fifth; C is the second chord's root. |
In 8, B♯2 sounds at C3, despite the different octave numbers: the sharp raises B2 across the C boundary. The two voicings therefore use the same sounding pitches in equal temperament, with different written analyses. The supplied spelling establishes the root for this exercise. These pitches alone don't give an ear-training listener a unique choice between those augmented-chord names.
Practice the step that went wrong
Check the root, quality, bass, and position separately. If you found the right chord but the wrong inversion, return to your saved bass and ask which member it is. There's no need to respell the whole chord.
If you missed 2, vary the upper spacing while holding the bass fixed. If you missed 4–5, keep the spelled members fixed and change which one is lowest. For 6, preserve E♯ rather than replacing it with F: C♯–E♯–G♯ shows the third and fifth through their letters.
A useful recall card includes the registers and asks for the reasoning:
Front: E3–C4–G4–E5: identify the triad and inversion.
Give the root-order spelling and original bass.
Back: C major, first inversion (C/E).
Root-order spelling: C–E–G. Original bass: E3.
Four notes sound, but there are three distinct members.
After solving on paper, revisit a missed voicing later and answer before revealing it. On another review, change the upper spacing while keeping the bass fixed, so you have to analyze a less familiar shape. The music theory flashcards guide covers writing precise prompts. Keep written analysis separate from listening and playing practice, which need their own work.
Production note: This article was drafted and edited with AI, and its hero illustration is AI-generated. Its original voicings were checked computationally for spelled members, equal-tempered semitone distances, pitch order, and inversion labels. Those checks don't establish listening, performance, or classroom results; no human musician review is claimed.