Harmonic Analysis and Roman Numerals (SACE Stage 2 Music)
“Analyse harmony in a score using Roman numerals and figured bass, identifying chords, inversions, non-chord tones and modulations”
Harmonic analysis is labelling every chord in a passage with a Roman numeral that shows its scale degree, quality and inversion, and explaining how those chords function. You first establish the key, then stack each vertical sonority into thirds to find its root, then assign the numeral and any figured-bass inversion symbol. You also identify non-chord tones (notes that decorate the harmony) and mark any modulations.
Jump to a section
What this dot point is asking
You need to take a score, work out its key, label its chords with Roman numerals and figures, distinguish chord tones from decoration, and show where the key changes. This is the practical application of harmony to real music.
Establishing the key
Analysis starts with the key, because Roman numerals are meaningless without one. Read the key signature, then confirm the tonic from the opening and closing chords and the cadences. Remember that a minor key shares its signature with the relative major, so check for the raised leading note (an accidental) to decide between them. Only once the tonic is fixed can you number the chords.
Finding and labelling chords
For each beat or harmonic change, gather the notes sounding together and rearrange them into a stack of thirds to find the root. The root's scale degree gives the Roman numeral (I to vii), upper case for major, lower case for minor, with a circle for diminished and a plus for augmented. The bass note then gives the inversion, shown with figured-bass numbers: 6 for first inversion, 6/4 for second inversion, and 7, 6/5, 4/3, 4/2 for the seventh-chord inversions.
Real music is full of passing notes, suspensions and other decoration that obscure the underlying chord. Before assigning a numeral, mentally strip away the non-chord tones and ask what triad or seventh chord the remaining notes form. Identifying the harmony from the structural chord tones, not from every note on the beat, is the key skill that separates accurate analysis from confusion over apparent extra notes.
Non-chord tones
Notes that do not belong to the prevailing chord are non-chord tones, and naming them is part of analysis:
- Passing note: fills the gap between two chord tones by step.
- Neighbour (auxiliary) note: steps away from a chord tone and back.
- Suspension: a note held over from the previous chord that then resolves down by step.
- Appoggiatura: an accented dissonance approached by leap and resolved by step.
- Anticipation: a note that arrives early, before its chord.
Labelling these shows you understand that the harmony is simpler than the surface suggests.
Marking modulations
When the music changes key, your Roman numerals must change reference. Show the modulation by indicating the new key and renumbering from its tonic, often using a pivot chord that you label in both keys (for example I in the old key equals IV in the new). This makes the functional logic of the modulation explicit rather than forcing foreign chords into the original key.
Four chords appear over a D major signature. Bar 1: D F sharp A, root D, so I. Bar 2: G B D in first inversion with B in the bass, so IV6. Bar 3: A C sharp E G, a dominant seventh, root A, so V7, but a passing note F sharp on the way is marked as a non-chord tone. Bar 4: D F sharp A, root position, I. The progression is I, IV6, V7, I, a textbook approach to a perfect cadence with one passing note decorating the dominant.
A very common error is reading the lowest note as the root and numbering from it. A chord with E in the bass that spells out a C major triad is still I in C major, in first inversion (I6), not iii. Always reorder the pitches into a stack of thirds to find the true root, take the Roman numeral from that root, and use the bass note only to determine the inversion figure.
Why this matters
Harmonic analysis reveals the structural logic of tonal music and is a core analytical skill assessed in the Music suite. It shows how progressions build toward cadences, how non-chord tones decorate a simple framework, and how modulations are engineered. The same skill feeds composition, where you plan progressions, and performance, where understanding the harmony shapes your phrasing. Practise by analysing chorales and short keyboard pieces, always reducing to chord tones first.
Exam-style questions
Questions in the style of SACE Board exam questions on this dot point, each with a worked answer. They are written by ExamExplained unless tagged "Past paper"; the year shows the paper a question is modelled on.
2024 SACE Stage 2-style1 markThe chord marked (ii) in bar 4 is a D7. In the context of this opening section in C minor, tick the box which would best describe the chord's function: The II7 of the relative major, The I7 of the subdominant, The V7 of the dominant key, or The IV7 of the submediant.Show worked answer →
One mark for the correct functional label. The home key is C minor, so work out what D7 does relative to it.
D7 is a dominant-quality seventh chord on D. The relative major of C minor is Eb major, in which D7 is not diatonic. The dominant of C minor is G; the dominant of G (the dominant key) is D, so D7 functions as V7 of the dominant - a secondary dominant (V7/V) that tonicises G before the music returns to the home key.
Tick "The V7 of the dominant key." The giveaway is that a dominant-seventh chord whose root lies a 5th above the local dominant is a classic secondary dominant pushing toward V.
2023 SACE Stage 2-style2 marksRefer to the score for 'Norriture'. Name the common chord progression used in bars 28 to 30, marked (iii).Show worked answer →
Two marks for correctly naming a recognisable, named progression by its Roman numerals or chord symbols.
Work out the chord on each beat from the score, label each with a Roman numeral in the prevailing key, then match the sequence to a standard progression. Common ones examiners look for include the cycle of fifths (for example ii - V - I), the descending tetrachord or lament bass, a I - vi - IV - V "doo-wop" loop, or a circle-of-fifths chain such as vi - ii - V - I.
Give the progression in Roman numerals and, if it has a recognised name, state it. Two marks usually means naming the progression and showing the chords that make it up.
Practise this
Sources & how we know this
- SACE Music subjects: overview and subject outlines — SACE Board