Roman Numeral Analysis and Figured Bass Explained

Pick up any piece of tonal music — a Bach chorale, a Beethoven sonata, a pop song — and underneath the notes there is a grammar of chords. Two systems let you read and write that grammar. Roman numerals name each chord by its place in the key: uppercase for major, lowercase for minor, a small circle for diminished. Figured bass gives the same information from the other direction: a bass line with numbers that tell a keyboard player exactly which intervals to fill in above each note. Neither system is hard, but each rewards careful counting.

This article covers both, in teaching order. You will learn to label every chord in C major and C minor, attach inversion figures, analyze a progression step by step, and realize a figured bass line from scratch. The free worksheets that go with each step are linked throughout — start with Roman numeral analysis and Figured bass to work alongside the examples here.

Roman numerals: the chord's place in the key

Every major scale has seven notes, and you can build a triad on each one using only the notes of the scale. In C major that means white keys only. The triad on C is C–E–G (major), on D is D–F–A (minor), on E is E–G–B (minor), on F is F–A–C (major), on G is G–B–D (major), on A is A–C–E (minor) and on B is B–D–F (diminished). Each triad gets the Roman numeral of the scale step it stands on.

The case of the numeral carries the quality: uppercase means the triad is major, lowercase means minor, lowercase with a small circle (°) means diminished. So the seven chords of C major are I, ii, iii, IV, V, vi and vii°. You do not need to memorize seven separate qualities — the pattern major–minor–minor–major–major–minor–diminished is the same in every major key, because every major scale puts its two half steps in the same places (between degrees 3 and 4, and between 7 and 8). The chords of a key builds this chord scale in C, G, F and D major with audio so you can hear the qualities change.

The seven chords of C major, one on each scale step. Capital numerals (I, IV, V) mark the major triads; lowercase (ii, iii, vi) mark the minor ones; vii° is diminished.

The three major chords — I, IV and V, called the primary chords — do most of the harmonic work in tonal music. I is home; IV moves away; V creates tension that resolves back to I. The primary chords: I, IV & V names their functions and The Primary Chords in Every Key gives the trio in every key.

Roman numerals in minor keys

Minor keys add one complication: the 7th degree is usually raised to create a leading tone. A natural minor scale built on A gives Am–B°–C–Dm–Em–F–G, or in numerals i, ii°, III, iv, v, VI, VII. That lowercase v (E minor) is too weak to pull home convincingly. Harmonic minor raises the 7th — G becomes G♯ — and three chords change with it: v turns into a major V (E–G♯–B), VII becomes vii° (G♯–B–D), and III becomes an augmented triad (C–E–G♯), though the augmented III is rare. In practice, most music in minor uses V from harmonic minor at cadences and v or VII from natural minor elsewhere.

The standard minor set you will see in textbooks is: i, ii°, III, iv, V (with the raised leading tone), VI, and either VII or vii°. In A minor: Am, B°, C, Dm, E, F, G (or G♯°). The chords of a minor key shows all four minor keys with the natural-to-harmonic comparison and audio for every chord.

A natural minor (top) versus harmonic minor (bottom). Raising G to G♯ turns the minor v into a major V and the major VII into a diminished vii°. Those two changes drive the classical cadence in minor.

Adding inversion figures

A Roman numeral on its own names the chord but not which note is in the bass. Inversions are shown by small superscript figures — the same numbers used in Baroque figured bass — added after the numeral.

For triads:

• Root position (root in the bass): no figure, or the full 5/3 written out
• First inversion (3rd in the bass): 6, short for 6/3
• Second inversion (5th in the bass): 6/4

For seventh chords:

• Root position: 7, short for 7/5/3
• First inversion (3rd in the bass): 6/5
• Second inversion (5th in the bass): 4/3
• Third inversion (7th in the bass): 4/2, sometimes just 2

So in C major, I6 is a C major triad with E in the bass (C/E in lead-sheet notation). V7 is G7 in root position. V6/5 is G7 with B in the bass. These figures come directly from figured bass practice, which is why the two systems fit together so neatly. Roman numeral analysis uses all four inversion figures for seventh chords; its answer key shows I–V6–I–IV–ii6–V7–I as the first progression. The 6/4 chord: three jobs covers the cadential 6/4 (I6/4 going to V at a cadence), the pedal 6/4 and the passing 6/4.

The three positions of I in C major with their Roman numeral labels. I has the root C in the bass; I6 has E; I6/4 has G. The figured bass numbers tell you which bass note to expect.

The four positions of V7 (G7) in C major. Each inversion moves the bass note one step up the chord: G, B, D and F. The 4/2 inversion, with F in the bass, is especially common as a passing chord.

How to analyze a chord: four steps

Analyzing a passage means labeling every chord with its Roman numeral and inversion figure. Here is the method:

1. Establish the key. Check the key signature and look for a cadence at the end of the phrase. A perfect cadence (V7→I) in the last bar confirms the tonic.
2. Collect the notes of each chord. Gather every pitch that sounds together (or in the same beat or beat group), including repeated notes and octaves. Stack them in thirds — rearrange until every adjacent pair is a 3rd apart. The bottom of that stack is the root.
3. Name the root and quality. Compare the root to the scale: which scale step is it? A major triad → uppercase numeral; minor → lowercase; diminished → lowercase with °; augmented → uppercase with +.
4. Read the bass note and add the figure. Compare the actual bass note to the root. Same note → no figure. The 3rd in the bass → add 6. The 5th → add 6/4. The 7th → add 7 (root position) or 6/5, 4/3, 4/2 for the other three inversions.

The four-step analysis method. The key difference between step 2 and step 4 is that step 2 identifies the root (by stacking in thirds), while step 4 identifies the bass (by reading the lowest note).

A worked analysis: I–IV–V–I in C major

Here is a four-chord progression with one chord per bar.

I–IV–V–I in C major. Bar 1: C–E–G on scale step 1 → I. Bar 2: F–A–C on scale step 4 → IV. Bar 3: G–B–D on scale step 5 → V. Bar 4: return to I. All chords are in root position, so no inversion figure is needed.

Now the same progression with an inversion in bar 2: I6–IV–V7–I.

I6–IV–V7–I. In bar 1 the first inversion I6 (E in the bass) creates a smooth stepwise bass line: E–F–G–C. The V7 in bar 3 is G7 (G–B–D–F), adding F above the triad. At the resolution to I, F falls to E and B rises to C.

Adding a 7th to V is so common that most theory teachers call it V7 as a matter of course. The dominant 7th worksheet shows how V7 resolves: the tritone B–F, the leading tone B rising to C and the chordal 7th F falling to E.

Secondary dominants: V/V

Once you know the diatonic set, you will quickly spot chords that do not belong to the key — a note with an accidental you do not expect. The most common chromatic chord is the secondary dominant: a major triad or dominant seventh built a perfect fifth above one of the diatonic chords, temporarily treating that chord as a tonic.

The most frequent is V/V, "five of five." In C major, V is G. The chord a perfect fifth above G is D. A plain D chord (D–F–A) is already diatonic (ii), but raising F to F♯ turns it into a dominant seventh D7 (D–F♯–A–C) that pulls strongly to G. The F♯ is G's own leading tone, borrowed for a beat. Secondary dominants works through V7/V, V7/ii and V7/vi in C major with audio.

Figured bass: the Baroque shorthand

In the Baroque era (roughly 1600–1750), a keyboard player reading a continuo part saw only the bass line and small numbers beneath it. Those numbers, the figures, named the intervals to build above each bass note. The player filled in the harmony on the spot — this art, called thoroughbass or basso continuo, was the foundation of chamber music performance for over a century.

The logic is straightforward: every figure counts intervals up from the bass note. The bass note itself is always 1. Over the note G, a "6" means the note a 6th above G (the note E in C major), and the full chord is E–B–G read from top down, or G–B–E on the page.

Every figure counts up from the bass. The bass note is 1; the figure is the interval you add above it.

Figured bass is not a chord symbol in the modern sense. It does not name the root — it names the bass note and the intervals above it. The player might add those intervals in any octave and any order, as long as each interval is present.

The eight standard figured bass symbols, organized by chord type. The right column shows how each maps onto a Roman numeral with inversion figure — confirming that the two systems are two faces of the same harmonic grammar.

Reading the figures: common cases

Blank (5/3). Root position is so common that no figures are written. The player adds the 3rd and 5th above the bass.

6 (first inversion). Add the 3rd and 6th above the bass. If the bass is E in C major, the 3rd is G and the 6th is C: a C major triad, first inversion. This is the equivalent of I6.

6/4 (second inversion). Add the 4th and 6th. If the bass is G in C major, those are C and E: again a C major triad, this time with G on the bottom. This is I6/4 — the cadential 6/4 found before many V chords.

7, 6/5, 4/3, 4/2. The four positions of a seventh chord. Over G in C major, 7 means add the 7th (F), 5th (D) and 3rd (B): G7 in root position (V7). Over B, 6/5 means B–D–F–G: G7 first inversion (V6/5).

Accidentals. A sharp, flat or natural standing alone — not next to a number — raises or lowers the 3rd above the bass. Under E in A minor, a lone ♯ means G♯ (the raised leading tone). An accidental placed next to a number alters that specific interval: ♯6 raises the 6th, ♭3 lowers the 3rd. A slash through a number (like 6 with a line through it) means the same as that number with a sharp.

Figured bass shows all of these with audio and a worked A minor example. Realize the figured bass gives you twelve bass notes to realize in Part 1 and two full lines to write out in Part 2.

How to realize a figured bass

Realizing means writing out the full chords implied by the figures, with the left hand on the bass and the right hand filling in the remaining voices. Here is the method:

1. Spell each chord. For each bass note, count up the given intervals (or use the defaults if no figure is written) to find the notes of the chord.
2. Pick an octave for each note. Keep the right-hand notes close together, usually within a 10th of each other. Avoid wide leaps when you can.
3. Move smoothly. When a note is shared between two chords, keep it in the same voice. When voices must move, move by step or small interval rather than a leap. Never move two voices in parallel perfect 5ths or octaves — this rule comes from counterpoint and applies to all four-part writing.
4. Handle the leading tone and 7th. The 7th of a chord almost always steps down. The leading tone (the note a half step below the tonic) almost always rises to the tonic.

A realized figured bass in A minor, from our Figured bass handout. The bass climbs A–B–C–D–E and returns to A. The ♯ under B raises the sixth above the bass to G♯ (the raised leading tone), giving the ♯6/4/3 figure — E7 in second inversion, V4/3; the lone ♯ under E asks for G♯ again, making V. Notice the right-hand voices moving by step rather than leap.

A complete worked example in C major

Here is a short progression: I–I6–IV–V7–I in C major, analyzed both ways.

Roman numeral reading: Bar 1 is a C major triad in root position (I). Bar 2 is the same C major triad with E in the bass — first inversion (I6). The smooth ascending bass E–F–G–C connects it to IV (bar 3), V7 (bar 4) and home. Bar 4 is G–B–D–F, the dominant seventh (V7). Bar 5 resolves to I.

Figured bass reading: Under C in bar 1, no figure (root position). Under E in bar 2, a "6" (the C is a 6th above E). Under F in bar 3, no figure. Under G in bar 4, a "7" (the F is a 7th above G). No figure under the final C.

Both readings describe exactly the same chords — only the perspective differs. Roman numerals look at the chord from the root; figured bass looks from the bass note up.

I–I6–IV–V7–I in C major annotated both ways. The Roman numerals appear below the bass staff; the figured bass numbers appear directly under each bass note. Bar 2's "6" and bar 4's "7" are the only figures needed — the rest are root-position chords, which are left blank.

Cadences: how progressions end

A cadence is a two-chord closing formula. The four main cadences all use Roman numerals:

• Perfect cadence (authentic cadence): V or V7 → I. The strongest ending; nearly every tonal phrase ends this way.
• Plagal cadence: IV → I. The soft "Amen" landing found at the end of hymns.
• Half cadence: any chord → V. A comma, not a period: the phrase pauses on tension.
• Deceptive cadence: V → vi. The expected I is replaced by vi, which shares two notes with I. It sounds like a surprise.

Cadences shows all four with audio in every key. The primary chords in minor shows the same cadences in minor keys, where the perfect cadence uses a major V, not the natural v.

Putting both systems together

Roman numerals and figured bass were designed for the same music — Baroque and Classical chorales, sonatas and chamber works — and they complement each other perfectly. Roman numerals give you the bird's-eye view: where is this chord in the key, what is its function, how does the progression move from tonic to dominant and back? Figured bass gives you the craftsman's view: which exact notes to play above this bass note, how to voice them, how to move from one chord to the next without parallel fifths.

When you work through Name the chords of the key, you are practicing Roman numeral analysis. When you sit down with Realize the figured bass, you are practicing the continuo player's ear and hand coordination. Both exercises reward the same skill: knowing your intervals cold, so you can count up from any bass note and hear the chord before you name it.

A Tissimo teacher can sit with you at the keys and hear your realizations in real time — catching a parallel fifth or a voice that leaps when it should step — in ways a worksheet answer key cannot. One or two lessons on a Bach chorale will make the figures feel as natural as reading rhythm.

Free worksheets for this lesson

• Roman numeral analysis — analyze three progressions in C major, G major and A minor, triads and seventh chords with inversion figures
• Figured bass — the complete reference handout with audio for every symbol and a worked A minor realization
• Realize the figured bass — twelve individual chords to realize plus two full lines to write in G major and D minor
• The chords of a key — build the seven-chord diatonic set in four major keys with audio
• The chords of a minor key — the natural-minor and harmonic-minor chord sets side by side
• The primary chords: I, IV & V — the three primary chords and their functions
• The primary chords in minor: i, iv & V — primary chords and cadences in minor
• Secondary dominants — V/V, V/ii and V/vi in C major with audio
• The 6/4 chord: three jobs — cadential, pedal and passing 6/4 chords
• Name the chords of the key — twenty chords to identify in four major keys
• Triads & their inversions — root position, first and second inversion with audio
• Cadences in Every Key — all four cadences with audio in your chosen key
• The dominant 7th — V7 structure, resolution and tritone with audio

Sources

• Aldwell, E., Schachter, C., & Cadwallader, A. — Harmony and Voice Leading, 4th ed. (Cengage, 2010)
• Caplin, W. E. — Tonal Function in Harmonic Progressions in Music Theory Spectrum 24/1 (2002)
• Gjerdingen, R. O. — Music in the Galant Style (Oxford University Press, 2007)
• Holtmeier, L. — "Heinichen, Rameau, and the Italian Thoroughbass Tradition" in Journal of Music Theory 51/1 (2007)
• Oxford Music Online — "Figured bass" (Grove Music Online)
• Piston, W. — Harmony, 5th ed., revised by Mark DeVoto (Norton, 1987)
• Rameau, J.-Ph. — Traité de l'harmonie (Paris, 1722); English translation by P. Gossett (Dover, 1971)