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.
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
Vocabulary
The following words are mentioned explicitly in the College Board Course and Exam Description for this topic.Term | Definition |
|---|---|
accidental | A symbol that modifies the pitch of a note, such as a sharp, flat, or natural. |
Arabic numerals | Numbers (1, 2, 3, etc.) used in figured bass notation to denote specific intervals above a given bass note. |
bass line | The lowest melodic line in a musical composition that often implies harmonic progressions through its note choices. |
chord inversion | A chord voicing in which a chord member other than the root appears in the bass, resulting in first or second inversion. |
chord quality | The classification of a chord based on the specific intervals between its pitches, such as major, minor, diminished, or augmented. |
figured bass | A notational system using Arabic numerals below a bass note to indicate the intervals and pitches of the chord to be played above that bass note. |
first inversion | A chord voicing in which the chordal third appears in the bass. |
harmonic progression | A sequence of chords that move from one harmony to another, creating the harmonic structure of a musical passage. |
intervals | The distance in pitch between two notes, indicated by figured bass numbers to show the relationship between the bass note and upper voices. |
lead sheet | A notated musical score that includes melody with chord labels (letter-name and quality abbreviations) appearing above the staff to indicate chord progressions. |
plus sign | A symbol used in figured bass to indicate that a pitch denoted by a figure should be raised a half step. |
Roman numeral analysis | A system of notation using Roman numerals to identify chords and their harmonic function within a key. |
root position | A chord voicing in which the chordal root appears in the bass (lowest part) of the chord. |
scale degree | The position of a pitch within a scale, identified by name or number relative to the tonic. |
second inversion | A chord voicing in which the chordal fifth appears in the bass. |
slash | A symbol used in figured bass to indicate that a pitch denoted by a figure should be raised a half step. |
triad | A chord whose essence consists of three distinct pitches stacked on adjacent lines or spaces in thirds. |
Frequently Asked Questions
What's the difference between root position and first inversion chords?
Root position vs. first inversion is all about which chord tone is in the bass. In root position the root of the triad is the lowest note (so the chord sounds “rooted”); in figured-bass terms a root-position triad is implied by 5–3 (and often no figures are written). In first inversion the third of the triad is the bass—figured bass shows this as a 6 (or 6–3) because the other chord tones lie a sixth and a third above the bass. On the AP exam you’ll label these with Roman numerals (e.g., I vs. I6) and recognize them from scores or figured bass realizations (see CED PIT-2.A and PIT-2.B). Want extra practice? Review Topic 3.3 (intro to figured bass) on Fiveable (https://library.fiveable.me/music-theory/unit-3/intro-figured-bass/study-guide/4QoPYIsEpxJDxJN6EHl5) and try problems at https://library.fiveable.me/practice/music-theory.
How do I figure out which chord inversion I'm hearing in a song?
Listen for the lowest pitch (the bass) first—that tells you the inversion. Then identify the other chord tones and decide which chord (root and quality) they form. Quick steps: 1. Pick out the bass note (lowest sounding pitch). 2. Find the other notes above it and ask: is the bass the chord’s root, third, or fifth? - If bass = root → root position (figures often omitted or shown as 5–3). - If bass = third → first inversion (labeled 6 or 6/3). - If bass = fifth → second inversion (labeled 6/4). 3. Use interval relationships above the bass (third, sixth, fourth+sixths) to confirm—that’s exactly what figured bass does (CED PIT-2.B.1). 4. Watch for accidentals or slashed figures meaning raised pitches above the bass (CED PIT-2.B.2). On the exam you’ll be asked to ID inversions by ear and in writing, so practice isolating the bass line and naming figures. For a quick study guide, see Fiveable’s Topic 3.3 page (https://library.fiveable.me/music-theory/unit-3/intro-figured-bass/study-guide/4QoPYIsEpxJDxJN6EHl5) and try problems at (https://library.fiveable.me/practice/music-theory).
I don't understand figured bass notation - can someone explain those numbers under the bass notes?
Figured bass numbers tell you which chord tones go above the written bass by naming intervals above that bass note. Basic rules: a 5–3 (often unmarked) means a root-position triad (bass = root). A 6 (or 6–3) shows a first-inversion triad (third in bass). A 6–4 means second inversion (fifth in bass). For seventh chords you’ll see 7 (or 7–5–3), 6–5, 4–3, or 4–2 depending on the inversion. Accidentals or a “/” by a figure raise that specific interval above the bass (a lone sharp means raise the 3rd above the bass). Figures imply the chord pitches (octave equivalents allowed), so you can label harmonies with Roman numerals after spelling the chord. Figured-bass realization and Roman-numeral identification are tested on the AP free-response (part-writing from figured bass), so practice reading and realizing 6, 6–4, and seventh figures. For a focused review, check the Topic 3.3 study guide (https://library.fiveable.me/music-theory/unit-3/intro-figured-bass/study-guide/4QoPYIsEpxJDxJN6EHl5) and try practice problems at (https://library.fiveable.me/practice/music-theory).
What does it mean when there's a slash or plus sign next to the figured bass numbers?
A slash or plus sign next to a figure means: raise that specific interval by a half step. In figured bass the Arabic numerals show intervals above the bass; when a figure has a slash (or a +) it tells you to sharpen the pitch a half step (e.g., a 6 with a slash → raise the note a 6th above the bass by a half step). If an accidental appears by itself (no number), it usually means alter the 3rd above the bass (e.g., “#” under a bass A → the third above is C#). This matters when you realize chords in four parts on the AP exam (Free-Response Q5: part-writing from figured bass) because those raised figures change the chord quality/function. Want more worked examples and practice? Check the Topic 3.3 study guide (https://library.fiveable.me/music-theory/unit-3/intro-figured-bass/study-guide/4QoPYIsEpxJDxJN6EHl5) and try practice problems (https://library.fiveable.me/practice/music-theory).
How do I write Roman numerals for chord inversions in my music theory homework?
Write the Roman numeral for the chord’s root (I, ii, V, etc.)—use uppercase for major, lowercase for minor (CED PIT-2.B). Then show the inversion with figured-bass numbers (Arabic numerals) that tell intervals above the bass: - Triads: - Root position: just the Roman numeral (I, ii). - First inversion (third in bass): add 6 (I6 or I6/3—AP accepts simply “6” as the inversion). - Second inversion (fifth in bass): add 6/4 (I6/4). - Seventh chords: - Root position: add 7 (V7). - First inversion (third in bass): 6/5 (V6/5). - Second inversion (fifth in bass): 4/3 (V4/3). - Third inversion (seventh in bass): 2 (V2). If a figure needs raising or lowering, show accidentals with the figure (e.g., #6). On the AP free-response part-writing/from-figured-bass question you’ll write the Roman numerals under each realized chord (see CED and Topic 3.3 study guide: https://library.fiveable.me/music-theory/unit-3/intro-figured-bass/study-guide/4QoPYIsEpxJDxJN6EHl5). For more review and 1,000+ practice problems, check the unit page (https://library.fiveable.me/music-theory/unit-3) and practice link (https://library.fiveable.me/practice/music-theory).
What's the easiest way to identify if a chord is in second inversion?
Easiest trick: check what note’s in the bass. If the lowest pitch of a triad is the chordal fifth, it’s second inversion. Practically: 1) Identify the three chord tones (root, third, fifth). 2) See which of those is lowest—if it’s the fifth, you have 2nd inversion. In figured-bass notation a triad in second inversion is usually shown by the figures 6–4 (intervals a sixth and a fourth above the bass). Remember context: many 6–4’s are special (cadential, passing, neighbor) and don’t function like a stable chord root—watch voice leading. On the AP exam this matters for part-writing from figured bass (Free-response Q5) and for Roman-numeral analysis (PIT-2.A/PIT-2.B). For a quick review, see the Topic 3.3 study guide (https://library.fiveable.me/music-theory/unit-3/intro-figured-bass/study-guide/4QoPYIsEpxJDxJN6EHl5) and practice lots of figured-bass problems (https://library.fiveable.me/practice/music-theory).
I'm confused about how figured bass relates to actual chord symbols like Cm or F major - are they the same thing?
Short answer: they’re related but not the same. Figured bass is a shorthand that tells you which intervals to play above a given bass note (so it implies the chord and its inversion). Lead-sheet chord symbols (like Cm or F) name the triad’s root and quality but don’t say which note is actually in the bass. Example: a C major triad written as C (or I) could be in root position (C in bass), first inversion (E in bass, shown as 6 or 6/3), or second inversion (G in bass, shown as 6/4). Figured bass shows the intervals above the bass (e.g., “6” = first inversion), while Cm just tells you “C minor triad” regardless of inversion. Figured bass also uses accidentals/slashes to raise figures (CED PIT-2.B.2). On the AP exam you’ll need to realize figured bass in four voices and label Roman numerals (Free-response Q5), so practice both translations. Review Topic 3.3 (figured bass) here (https://library.fiveable.me/music-theory/unit-3/intro-figured-bass/study-guide/4QoPYIsEpxJDxJN6EHl5), the full Unit 3 refresher here (https://library.fiveable.me/music-theory/unit-3), and get more practice problems at (https://library.fiveable.me/practice/music-theory).
How do I use figured bass to figure out chord progressions for my composition project?
Start by thinking vertically: figured bass tells you the intervals above a written bass note, which imply a chord and its inversion (e.g., no figures or 5–3 = root position; 6 = first inversion; 6–4 = second inversion). Practical steps for your composition project: 1. Pick a key and write a bass line that outlines the harmonic motion you want. 2. Above each bass note, write the figures that give the intervals you want (use slashes/+ to raise a figured pitch or an accidental by itself to alter the 3rd). 3. Convert each figured-chord into a Roman numeral relative to the key to check harmonic function (I, ii, V, V6, etc.). 4. Realize the upper voices following 18th-century voice-leading rules (resolve leading tones and sevenths, avoid parallels). This is exactly what the AP free-response asks in the part-writing from figured bass task (see CED Topic 3.3 and the exam’s Question 5). For step-by-step help and examples, see the Topic 3.3 study guide (https://library.fiveable.me/music-theory/unit-3/intro-figured-bass/study-guide/4QoPYIsEpxJDxJN6EHl5). Practice lots of realizations on Fiveable (https://library.fiveable.me/practice/music-theory) to build speed and accuracy.
What does it mean when there's just a sharp sign with no number in figured bass?
If you see only an accidental (like # or b) with no number in a figured-bass line, it means: alter the pitch a third above the bass. In other words, the chordal third is to be raised or lowered as shown. Example: bass = A, figure = # alone → the note a third above A (C) becomes C#. That shorthand comes from 18th-century thoroughbass practice and is exactly how the CED defines “an accidental appearing alone” (it modifies the third) so the figured bass implies the correct chord quality/inversion. This shows up on AP part-writing and Roman-numeral tasks, so recognize it quickly when you realize a triad’s third is chromatically altered. For a quick refresher, check Topic 3.3 study guide (https://library.fiveable.me/music-theory/unit-3/intro-figured-bass/study-guide/4QoPYIsEpxJDxJN6EHl5) and try practice problems (https://library.fiveable.me/practice/music-theory).
How do I know which inversion to use when I'm writing my own chord progressions?
Pick the inversion that fits the bass motion and harmonic function. Root position (no figures) gives stability and strong harmonic anchor—use it for cadences and tonal “landings.” First inversion (6 or I6) is useful when you want a smoother, stepwise bass or when the chord functions as a passing/pedestal sonority; it’s common to double the soprano or bass third carefully. Second inversion (6-4) is special: often a cadential 6-4, passing 6-4, or neighbor/pedal 6-4 rather than a stable root-level harmony—treat it as a dissonant embellishment that resolves. Always check voice-leading rules from the CED: avoid bad parallels, resolve sevenths down, and follow figured-bass accidentals for raised figures. Practicing part-writing from figured bass (an AP free-response task) will make choices feel natural—use the Topic 3.3 study guide (https://library.fiveable.me/music-theory/unit-3/intro-figured-bass/study-guide/4QoPYIsEpxJDxJN6EHl5), the Unit 3 overview (https://library.fiveable.me/music-theory/unit-3), and 1000+ practice problems (https://library.fiveable.me/practice/music-theory).
What's the difference between using Roman numerals and letter names for chords in lead sheets?
Roman numerals and letter (lead-sheet) chord symbols tell you different things, even though both name the same sonorities. - Roman numerals (I, ii, V6, vii°6/5, etc.) locate a chord in the scale: they show scale degree of the root, the chord quality, and—when combined with figured bass—the inversion (CED PIT-2.B). They emphasize harmonic function and are used on the AP exam (figured bass/part-writing and Roman-numeral analysis tasks). - Letter names (C, Am, G7) name absolute pitch collections and are what you see on lead sheets; they’re great for real-world playing, transposition, and pop/jazz contexts but don’t directly show scale degree or function in a key. So use letters for practical playing and quick changes; use Roman numerals (with figures) when you need functional analysis, inversion info, or to complete AP tasks like realizing a figured bass. For a quick review, see the Topic 3.3 study guide (https://library.fiveable.me/music-theory/unit-3/intro-figured-bass/study-guide/4QoPYIsEpxJDxJN6EHl5) and practice problems (https://library.fiveable.me/practice/music-theory).
I keep getting confused between first and second inversion - is there a trick to remember which is which?
Short trick: first inversion = the chordal third is in the bass; second inversion = the chordal fifth is in the bass. So “first = 3” (think 1st inversion → 3 in bass) and “second = 5.” In figured-bass terms first inversion is labeled with a 6 (implied 6–3) and second inversion with 6–4 (I6 and I6/4 in Roman-numeral analysis). Quick ways to remember: - Visual: stack the triad and read the lowest note—if it’s the 3rd above the root → first; if it’s the 5th → second. - Numeric mnemonic: 1 → 3, 2 → 5. AP tip: you’ll need to recognize these in part-writing from figured bass (Free-response Q5) and in Roman-numeral analysis (CED PIT-2.A/PIT-2.B). For extra practice, see the Topic 3.3 study guide (https://library.fiveable.me/music-theory/unit-3/intro-figured-bass/study-guide/4QoPYIsEpxJDxJN6EHl5) and 1,000+ practice problems (https://library.fiveable.me/practice/music-theory).
How do figured bass numbers tell me what pitches to play above the bass note?
Figured bass numbers tell you the intervals (in semitone/diatonic distance) above the written bass that you should supply—so you build the chord relative to that bass note. Common facts to memorize for the AP CED (PIT-2.B): - Triads: no figures or “5–3” = root position (bass = root). “6” (or 6–3) = first inversion (bass = third). “6/4” = second inversion (bass = fifth). Octave equivalents are fine. - Seventh chords: “7” (or “7–5–3”) means add the seventh above the bass (bass is usually root of the seventh-chord inversion depending on other figures). - Accidentals or a slash/plus with a figure raise that specific voice a half step (an accidental alone modifies the 3rd above the bass). - Figures imply specific chords so you can then apply Roman numerals for harmonic function (CED: PIT-2.B). For more targeted practice and AP-style part-writing from figured bass, check the Topic 3.3 study guide (https://library.fiveable.me/music-theory/unit-3/intro-figured-bass/study-guide/4QoPYIsEpxJDxJN6EHl5) and try problems at https://library.fiveable.me/practice/music-theory.
Why do some figured bass examples have no numbers at all under certain bass notes?
Because figured bass shows intervals above the bass, leaving a bass note unfigured usually means “no figures needed”—the default 5–3 (root-position triad) is implied. In other words, when you see no Arabic numerals under a bass note, assume a normal triad with the third and fifth above the bass unless an accidental or other figure tells you otherwise. Two important caveats from the CED: an accidental alone (like a #) under the bass means “raise the third above the bass” (PIT-2.B.2), and sometimes figures are omitted when the harmony continues unchanged or when the context (e.g., a cadential 6-4) is shown elsewhere. On the AP exam you’ll need to realize unfigured bass notes as standard 5-3 chords in part-writing (Free-Response Q5). For a quick refresher, see the Topic 3.3 study guide (https://library.fiveable.me/music-theory/unit-3/intro-figured-bass/study-guide/4QoPYIsEpxJDxJN6EHl5) and try practice problems (https://library.fiveable.me/practice/music-theory).
Can I use figured bass notation in my AP portfolio compositions or should I stick to modern chord symbols?
Short answer: yes—you can use figured bass, but pick the notation that fits the style and the exam task. Why: Figured bass (Arabic figures) is the AP/CED convention for showing inversions and is explicitly tested in the part-writing from figured bass free-response (PIT-2.A, PIT-2.B). It directly implies the chord tones above a bass and maps naturally to Roman-numeral analysis. If you’re writing baroque-style or 18th-century continuo textures, use figured bass. If you’re writing lead-sheet/pop/jazz-style pieces, modern chord symbols (C, Cm, G7, etc.) are fine and clearer for performers. Practical tip: For exam practice and AP tasks, make sure you can read/write figured bass and convert it to Roman numerals (CED PIT-2.B). For composition/portfolio, use whichever communicates your harmonic intent best—but include Roman numerals when you want to show formal harmonic function on AP-style work. Review the topic guide (https://library.fiveable.me/music-theory/unit-3/intro-figured-bass/study-guide/4QoPYIsEpxJDxJN6EHl5) and try practice problems (https://library.fiveable.me/practice/music-theory) to get fluent in both systems.