All the notes of a chord can be rearranged so that the order from bottom to top may be different. The most important note is the bass note. When the root of the chord appears in the bass, we consider this to be in root position. If a different chord member appears in the bass, we have was is called a chord inversion. Take a look!
Example: Chords in Ab Major
We can see above that when the third of the chord is in the bass, the chord is considered to be in 1st inversion. When the fifth is in the bass, the chord is considered to be in 2nd inversion. During the Common Practice Period (CPP), a.k.a. The Baroque era, chord inversions were labeled using Arabic numerals (the numbers you and I normally know and use: 1, 2, 3, etc.) to denote the intervals seen above the bass note. This system was used extensively by Bach, Handel, and Vivaldi. We call this figured bass.
No, not that type of bass 🙄, but keep reading!
Figured Bass
Figured bass was an important part of the musical language of the Baroque era and was used extensively in the music of the time. It allowed composers to indicate the harmonies of a piece of music in a concise and efficient manner, and it was an important tool for improvisation and interpretation. Figured bass fell out of favor in the classical and romantic periods, but it is still used by some musicians and scholars as a tool for analyzing and understanding the harmonies of music from the Baroque era. Not to mention, we will have to write in figured bass for the AP exam!
How does Figured Bass Work?
The system of figured bass consists of a bass line and a series of numbers written below the bass line. The numbers indicate the intervals above the bass note that should be played or sung, and they are called "figures." When we are looking at a composition through a harmonic lens, these figures (usually written in Arabic numerals) are used to signify the corresponding inversions to each chord.
They indicate the exact interval between the bottom note and the top note when an inversion is in a closed position. Closed position means that the notes are as close as possible, and the chord is some cycling of the 1-3-5 order. For example, root position will be in the order 1-3-5, first inversion will be in the order 3-5-1, and second inversion will be in the order 5-1-3.
Let’s use the example of G Major in order to see how figured bass works. In root position, the order of the I chord will be G-B-D. There is a 5th between G and D, and a 3rd between G and B, so we can write this as a 5/3 chord. When we also analyze the harmonies of a composition through Roman numerals, we can attach the Arabic numerals to the side of Roman numerals to provide information about the inversion (Arabic numerals) of the chord in the key (Roman numerals). So, we could write this as a I 5/3 chord, where 5 is a superscript and 3 is a subscript. Usually for root position, though, we will just write it as a I chord.
In 1st inversion, the notes will be in the order B-D-G. The interval between the bottom note and the top note (B to G) in the closed position is a 6th, and the interval between the bottom note and the middle note (B to D) is a 3rd. Therefore, the first inversion is sometimes indicated that it is a 6/3. But almost all the time the 3 is omitted. We would just write this chord as a I^6 chord
Similarly, in 2nd inversion, the notes will be in the order D-G-B. The number below (such as when we use it in the 2nd inversion) refers to the distance between the bottom note and the next note up, in a closed position. The distance between D and G is a 4th. The outer interval is a 6th, since the distance between the bass note (D) and the outer note (B) is a 6th. Hence, we would write this note as I 6/4.
Take note that this is just an explanation of how figured bass was derived. A G-D-B chord is still a I chord in G major, and a B-D-G is still a I 6/4 chord in G Major. The type of inversion (first, second, third, etc.) only depends on the bottom note of the chord.
Also, note that these numbers work for any chord. A ii6 chord is still a first inversion ii chord, and a V6/4 chord is still a second inversion V chord.
When we analyze the harmonies of a composition through Roman numerals, we can attach the Arabic numerals to the side of Roman numerals to provide information about the inversion (Arabic) of the chord in the key (Roman). It would look a little something like this:
In figured bass, a figure with a slash (/) or a plus sign ➕ indicates the pitch denoted by that figure is to be raised a half step. Usually, this happens to a 6, meaning sharp the note that would be a 6 above the bass in closed position. For example, if you are in c minor and you have a seven chord with the 6 crossed out, that means that we are in first inversion (because of the sixth) and we are raising the 6, so we are raising the Bb. Therefore, the chord will be D-F-B natural.
Notice that this implies that the seven is diminished. In this case, since we are in minor, a vii°6 would be enough to denote this chord.
Rather than the slash or the plus, sometimes there will just be an accidental (flat, sharp, or natural) to the left of the figure (the Arabic number). This means to flat, sharp, or natural whichever note corresponds to that figure.
Remember: if that note happens to be doubled, you should make sure to do that action to both of the instances of that note.
An accidental appearing alone, (without an Arabic numeral) indicates that the third above the bass should be altered according to the accidental.
Basso Continuo
Basso continuo is a type of bass line that employs figured bass, and it is what you will use when you are in the AP exam. In basso continuo, a bass line is played by a bass instrument, such as a cello or double bass, and chordal accompaniment is provided by a keyboard instrument, such as a harpsichord or organ. The bass line (aka the bottom notes of each chord) is notated in standard notation, and the chordal accompaniment is indicated using figured bass notation, which consists of numbers written below the bass line to indicate the intervals above the bass note that should be played.
When you realize a figured bass, you are filling in the upper voices to the basso continuo.
Lead Sheet Symbols
Another system of labeling chords takes the root and uses a capital letter-name (such as G) and attaches the quality of the chord (Major, minor, etc.) with its abbreviation. For example a G-Major chord would look like: GM. A minor chord would have a lowercase m, such as the chord Dm. You might see E+ for an augmented E chord, or F#° for an F-sharp diminished chord.
If you want to write a seventh chord, you might write it as a Mm chord, a mM chord, etc.
You can find this system of labeling chords in lead sheets, and the chord symbols are called lead sheet symbols. A lead sheet is a simplified version of a piece of music that includes the melody, lyrics, and chords of the song. It is a useful tool for musicians who want to play or sing a song but do not have access to the full score or are unfamiliar with the song. If you’ve played a pop song on a guitar or a ukulele, you might have used lead sheets, too.
A typical lead sheet includes the melody of the song written out in standard notation, with the lyrics written below the melody, and the chords written out in terms of the lead sheet symbols. Lead sheets are typically not as detailed as full scores, and they do not include information about the specific instruments or voicings of the chords. Instead, they provide a general outline of the song that musicians can use to create their own arrangements and interpretations. As such, Lead sheets are often used in jazz and popular music, where they provide a flexible and adaptable framework for improvisation and interpretation.
🦜 Polly wants a progress tracker: For a 2nd-inversion subdominant chord in the key of F, what would its figured bass symbols be? How do you spell that chord?
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.