3.3 Chord Inversions and Figures: Introduction to Figured Bass

TLDR

Chord inversions tell you which chord member sits in the bass: root position has the root on the bottom, first inversion has the third, and second inversion has the fifth. Figured bass uses Arabic numerals to show the intervals above the bass note, so you can attach those figures to Roman numerals (like I6 or V6/4) to label inversions in a key. On the AP Music Theory exam, you read and write these figures to identify chords and realize a figured bass.

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Why This Matters for the AP Music Theory Exam

Figured bass is a core skill that shows up across the harmony work you build later in the course. Once you can connect a bass note plus figures to a specific chord and inversion, you can label progressions with Roman and Arabic numerals, hear the difference between root position and inverted chords, and start filling in upper voices when you realize a figured bass.

This topic supports several kinds of exam thinking:

• Identifying chords and their inversions in notated music using letters and Roman/Arabic numerals.
• Using Roman numerals to show the harmonic progression that a figured bass implies.
• Recognizing inversions by ear as part of the harmonic dictation you keep practicing through the course.

Getting comfortable with figures now sets you up for voice leading, predominant function, and the part-writing tasks in later units.

Key Takeaways

• The bass note (lowest note) decides the inversion, no matter how the upper notes are arranged.
• Root position = root in bass, first inversion = third in bass, second inversion = fifth in bass.
• Triad figures: root position is 5/3 (usually written with no figure), first inversion is 6/3 (usually just 6), second inversion is 6/4.
• Attach Arabic figures to Roman numerals to show both the chord in the key and its inversion, like ii6 or V6/4.
• A figure with a slash or plus sign raises that pitch a half step; an accidental alone raises or lowers the note a third above the bass.
• Lead-sheet symbols use a capital letter for the root plus a quality abbreviation (Cm, E+, F#°), and show up in pop and jazz charts.

Chord Inversions

The notes of a chord can be stacked in different orders, but the note that matters most for labeling is the bass note (the lowest sounding note).

• When the root is in the bass, the chord is in root position.
• When the third is in the bass, the chord is in first inversion.
• When the fifth is in the bass, the chord is in second inversion.

The inversion only depends on which chord member is on the bottom. A G-B-D chord and a D-G-B chord are both the same I chord in G major, but they are in different inversions because their bass notes differ.

Figured Bass

Figured bass is a shorthand that came from an 18th-century practice for indicating harmonies above a bass line. A bass line is written in standard notation, and Arabic numerals (figures) are written near each bass note to show the intervals that should sound above it. You will read and write figured bass on the AP exam, so it is worth getting fluent with it.

How Figured Bass Works

The figures tell you the intervals above the bass when the chord is in close position (notes packed as tightly as possible, cycling through 1-3-5). When you analyze with Roman numerals, you attach the Arabic figures to the Roman numeral so the Roman numeral shows the chord in the key and the figures show the inversion.

Use a G major I chord to see the pattern:

• Root position (G-B-D): G to D is a 5th, G to B is a 3rd, so the full figure is 5/3. In practice you usually just write I.
• First inversion (B-D-G): B to G is a 6th, B to D is a 3rd, so the figure is 6/3. The 3 is almost always dropped, so you write I6.
• Second inversion (D-G-B): D to B is a 6th, D to G is a 4th, so the figure is 6/4. You write I6/4.

These figures work for any chord. A ii6 is a first-inversion ii chord, and a V6/4 is a second-inversion V chord.

Accidentals in Figures

• A figure with a slash (/) or a plus sign (+) means raise that pitch a half step. This often happens to a 6.
• An accidental (sharp, flat, or natural) standing alone, without a number next to it, means inflect the note a third above the bass.
• An accidental placed next to a figure changes the note that figure points to.

For example, in C minor, a chord built on scale degree 7 with a raised 6 above the bass (the figure crossed or slashed) gives you a first-inversion chord with that sixth raised. If a note you are altering is doubled, apply the accidental to both copies of that note.

Basso Continuo

Basso continuo is a Baroque texture built on a figured bass line. A bass instrument plays the written bass line, and a chordal instrument such as harpsichord or organ fills in the harmony using the figures as a guide. When you realize a figured bass, you write in the upper voices above that bass line so the figures are spelled out as actual chords.

Lead-Sheet Symbols

Another way to label chords names the root with a capital letter and adds an abbreviation for the quality.

• Major triad: capital letter alone or with M (G, GM)
• Minor triad: lowercase m (Dm)
• Augmented triad: + (E+)
• Diminished triad: ° (F#°)

These lead-sheet symbols sit above a melody in lead sheets, which give the tune, lyrics, and chords without writing out every voice. If you have played a pop song on guitar or ukulele from a chord chart, you have used this system. Lead sheets are common in jazz and popular music because they leave room for your own voicings and interpretation.

How to Use This on the AP Music Theory Exam

Notation and Analysis

• When you see a bass note with figures, build the chord by stacking the indicated intervals above the bass, then name it with a Roman numeral and the figure (like ii6 or V6/4).
• Remember octave equivalents count, so a pitch can appear in any octave above the bass and still satisfy the figure.
• Watch for slashes, plus signs, and lone accidentals; they change pitches and can turn a chord into a different quality.

Aural Recognition

• Train your ear to hear whether the lowest note is the root, third, or fifth. That bass note is what tells you the inversion.
• Practice hearing root position versus inverted chords inside a progression, not just in isolation, since that is how dictation works on the exam.

Common Trap

• Do not let a wide spacing fool you. The label depends only on which chord member is in the bass, not on how spread out the upper notes are.

Common Misconceptions

• The top note decides the inversion. It does not. Only the bass note (the lowest note) determines whether a chord is root position, first, or second inversion.
• 6 means second inversion. A lone 6 means first inversion (it is short for 6/3). Second inversion is 6/4.
• Figured bass numbers are scale degrees. They are intervals above the bass note, not scale degrees of the key.
• A slash through a figure means a chord change or a slash chord. In figured bass, a slash or plus on a figure raises that pitch a half step. A slash chord like C/E is a lead-sheet symbol, which is a different system.
• Rearranging the upper voices changes the chord. Reordering or revoicing the notes above the bass does not change the Roman numeral or the inversion as long as the bass note stays the same.

Quick check: For a second-inversion subdominant chord in F major, the chord is IV (subdominant), the bass is the fifth, and the figure is 6/4, so you would label it IV6/4. The subdominant in F major is Bb major (Bb-D-F), and in second inversion the bass note is F, giving F-Bb-D.

Related AP Music Theory Guides

• 3.1 Triad and Chord Qualities (M, m, d, A)
• 3.2 Diatonic Chords and Roman Numerals
• 3.5 Seventh Chord Inversions and Figures
• 3.4 Seventh Chords
• Unit 3 Overview: Music Fundamentals III (Triads and Seventh Chords)