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Roman numeral analysis provides systematic notation for harmonic content (I, ii, iii, IV, V, vi, vii°) with figured bass indicating inversions (root position, first inversion 6, second inversion 6/4). Analysis reveals harmonic structure through functional labels (T = tonic, S = subdominant, D = dominant) and identification of applied chords and modulations. This analytical framework shows how harmony and voice leading work together to create musical form and meaning.
Roman numeral analysis is a reading system for tonal harmony — a way of translating the surface of a piece (specific chords, specific keys) into a description of function and relationship. You already know how to identify individual chord qualities and inversions from your prerequisites. What Roman numeral analysis adds is the functional layer: instead of noting "there is a G major chord here," you note "this is V in C major," which tells you what role the chord plays in the harmonic narrative.
The case of the numeral carries primary information: uppercase means major quality (I, IV, V), lowercase means minor quality (ii, iii, vi), and the diminished symbol ° marks diminished quality (vii°). Case also reflects function: the three major triads in a major key — I, IV, and V — cover the tonic, subdominant, and dominant functions respectively. These three functions define the fundamental harmonic logic of tonal music. Tonic chords (I and vi) feel stable; subdominant chords (IV and ii) feel poised for motion; dominant chords (V and vii°) feel tense and directional. Progressions make harmonic sense when they move through these functions in coherent patterns — typically T → S → D → T, which traces the standard harmonic arc of a phrase.
Figured bass notation in Roman numeral analysis encodes the bass note relative to the chord root. A plain Roman numeral (no figures) means root position — the root is in the bass. A superscript 6 means first inversion — the third is in the bass (abbreviated from the figured bass interval 6/3). A superscript 6/4 means second inversion — the fifth is in the bass. Inversions are not merely cosmetic variations: they change the sound and function of a chord meaningfully. A I6/4 chord (tonic in second inversion) creates a distinctive suspenseful quality and typically appears as a cadential 6/4 immediately before a V chord at a cadence, where it functions as a dissonance resolving into the dominant rather than as a stable tonic. Labeling it correctly — cad. 6/4 or I6/4 — signals that understanding.
The full power of Roman numeral analysis emerges when you extend it to applied chords and modulations. An applied dominant (e.g., V/V) is a secondary dominant: a chord that functions as V in relation to a non-tonic scale degree. Notating it as V/V rather than II (which would obscure its dominant function toward V) reveals the harmonic logic — it's borrowing the V-I momentum and directing it at a temporary target. When a passage modulates to a new key, you annotate where the old key ends and the new Roman numerals begin. This notation turns a harmonic analysis into a map of the piece's tonal journey, showing not just what chords appear but what story they tell.
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