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Inversions and figured bass

Move the C of a C major chord to the top and the chord is still C major, but with E in the bass it sounds lighter and less settled.

Root and bass are different things

The bass is the lowest note sounding, whatever instrument plays it. The root is the note the chord is built on. In root position the two are the same: C E G has C as both root and bass. But the notes can be arranged in other orders. Put the third in the bass, E G C, and the chord is in first inversion. Put the fifth in the bass, G C E, and it is in second inversion. The root is still C in every case; only the bass changes.

C major in root position, first inversion and second inversion. The bass note changes; the root stays C.

To find the root of an inverted chord, rearrange its notes into the tightest stack of thirds. E G C is not stacked in thirds (G to C is a fourth), but moving C down gives C E G, so the root is C and E in the bass means first inversion. A quick visual hint: in an inversion the chord on the staff has a gap, a fourth, between two neighbouring notes, and the root is the upper note of that fourth.

Writing inversions: slash chords and figures

Popular music shows the bass with a slash: C/E means a C chord with E in the bass, and C/G a C chord with G in the bass. Classical analysis uses figured bass, numbers that count intervals above the bass. A root-position triad has a fifth and a third above the bass (5 over 3), usually left unwritten. First inversion has a sixth and a third (6 over 3), shortened to 6. Second inversion has a sixth and a fourth, written 6 over 4 in full so it cannot be confused with first inversion. With Roman numerals: I, I⁶, I⁶₄.

Position	Bass	Figures	On C
Root position	Root	(5/3)	C
First inversion	Third	6	C/E
Second inversion	Fifth	6/4	C/G

Why bother? Inversions let a bass line move by small steps instead of jumping from root to root. Playing C, then G/B, then Am gives a bass that walks down C, B, A while the chords change underneath the melody. First-inversion chords sound lighter than root position and are common in the middle of phrases; second-inversion chords are less stable still, and classical composers used them in a few specific places, especially just before the dominant at a cadence.

BackgroundThe idea that C E G, E G C and G C E are one chord seems obvious today, but it had to be argued. In 1722 the French composer Jean-Philippe Rameau published his Treatise on Harmony in Paris. Among other things it set out the principle that a chord keeps its identity when its notes are rearranged (inversion) and that music can be explained by a "fundamental bass" of chord roots, even when the actual lowest note is different. The book made Rameau known as the most learned musician of his time.

A C major chord with E in the bass is in…
- First inversion
- Root position
- Second inversion
- Third inversion
What is the root of G-C-E?
- C
- G
- E
- A
What is the bass of C/G?
- G
- C
- E
- B
Which figure stands for a first-inversion triad?
- 6
- 6/4
- 5/3
- 7
Which figure stands for a second-inversion triad?
- 6/4
- 6
- 4/2
- 5/3
Identify the chord: A-C-F.
- F major, first inversion
- A minor, root position
- F major, second inversion
- D minor, first inversion
Write a G major chord with B in the bass as a slash chord.
In root position, which intervals lie above the bass?
- A fifth and a third
- A sixth and a third
- A sixth and a fourth
- A seventh and a fifth
Who published the Treatise on Harmony in 1722?
- Rameau
- Bach
- Heinichen
- Diletskii
C, G/B, Am: what does the bass do?
- Steps down C, B, A
- Jumps C, G, A
- Stays on C
- Steps up C, D, E
How many inversions (not counting root position) does a triad have?

Key points

Bass = lowest note; root = note the chord is built on.
First inversion: third in bass (6). Second inversion: fifth in bass (6/4).
Slash chords: C/E, C/G.
Restack in thirds to find the root.

Sources for this course (9)

Open Music Theory 2e (Viva Pressbooks; ideas only, no sentences copied): "Triads" (a chord is three or more pitch classes sounding together, triads stack in thirds on all lines or all spaces, root/third/fifth, four qualities named for the third (major, minor) or the fifth (diminished, augmented), common expressive associations, chord symbols C, Cmi, C°, C+, spelling with the root's major key signature, doubling and spacing do not change identity, triad qualities on each degree of major and minor; viva.pressbooks.pub/openmusictheory/chapter/triads/)
"Seventh Chords" (five qualities, other names, qualities on each degree in major; viva.pressbooks.pub/openmusictheory/chapter/seventh-chords/)
"Inversion" (bass vs root, first/second/third inversion, slash symbols; viva.pressbooks.pub/openmusictheory/chapter/inversion/)
"Figured Bass and Roman Numerals with Figures" (5/3, 6/3, 6/4, 7, 6/5, 4/3, 4/2, abbreviations; viva.pressbooks.pub/openmusictheory/chapter/figured-bass/)
"Roman Numerals" (uppercase major, lowercase minor, ° diminished, + augmented, ø7 and °7; viva.pressbooks.pub/openmusictheorycopy/chapter/roman-numerals)
"Introduction to Harmony, Cadences, and Phrase Endings" (tonic, predominant, dominant functions with chord lists, phrase model, PAC/IAC/HC definitions; viva.pressbooks.pub/openmusictheory/chapter/intro-to-harmony/)
Robert Hutchinson, Music Theory for the 21st-Century Classroom, "Cadences" (plagal IV-I, deceptive V-vi, the prelude to Act I of Wagner's Tristan und Isolde as a famous deceptive cadence; no bar number given in the text; musictheory.pugetsound.edu/mt21c/cadences.html) and "Figured Bass Inversion Symbols" (musictheory.pugetsound.edu/mt21c/FiguredBassInversionSymbols.html)
Wikipedia "Treatise on Harmony" (Rameau, Paris 1722, fundamental bass and inversion of chords; en.wikipedia.org/wiki/Treatise_on_Harmony)
musictheory.net lessons 40-47 used as a cross-check only. frequencies with f = 440 x 2^((m - 69) / 12) (C4 261.63, E4 329.63, G4 392.00 Hz).

Checked: 2026-10-17