8.1 Roman numeral analysis

Roman numeral analysis is a powerful tool for understanding chord relationships in music. It assigns numbers to chords based on their scale degree, helping musicians grasp harmonic structure and function within a key.

This system is crucial for identifying common progressions and cadences. By labeling chords with Roman numerals, we can easily spot patterns like the V-I authentic cadence or the ii-V-I jazz progression, revealing the underlying harmonic framework of a piece.

Chord scale degrees in Roman numerals

Diatonic chord scale degrees and their Roman numerals

• The tonic chord is built on the first scale degree and is labeled with the Roman numeral I (C major)
• The supertonic chord is built on the second scale degree and is labeled with the Roman numeral II (D minor)
• The mediant chord is built on the third scale degree and is labeled with the Roman numeral III (E minor)
• The subdominant chord is built on the fourth scale degree and is labeled with the Roman numeral IV (F major)
• The dominant chord is built on the fifth scale degree and is labeled with the Roman numeral V (G major)
• The submediant chord is built on the sixth scale degree and is labeled with the Roman numeral VI (A minor)
• The leading tone chord is built on the seventh scale degree and is labeled with the Roman numeral VII (B diminished)

Importance of understanding scale degree functions

• Recognizing the scale degree of each chord helps understand its function within a progression
• The tonic (I) and dominant (V) chords are the most important in establishing the key and providing a sense of resolution
• The subdominant (IV) chord provides contrast and often precedes the dominant in cadences
• The supertonic (II), mediant (III), and submediant (VI) chords serve as intermediate chords that connect the primary chords
• The leading tone (VII) chord has a strong pull towards the tonic due to the presence of the leading tone

Chord quality with Roman numerals

Labeling chord quality using case and symbols

• Major chords are labeled with uppercase Roman numerals (I, IV, V)
• Minor chords are labeled with lowercase Roman numerals (ii, iii, vi)
• Diminished chords are labeled with lowercase Roman numerals and a degree symbol (vii°)
• Augmented chords, although less common in diatonic progressions, are labeled with uppercase Roman numerals and a plus sign (III+)

Diatonic chord qualities in major and minor keys

• In major keys, the diatonic chords are I, ii, iii, IV, V, vi, and vii° (C, Dm, Em, F, G, Am, Bdim in C major)
• In minor keys, the diatonic chords are i, ii°, III, iv, v, VI, and VII (Cm, Ddim, E♭, Fm, Gm, A♭, B in C minor)
• The quality of the chord is determined by the intervals between the notes of the chord, specifically the third and fifth above the root
• Understanding the expected chord qualities in a key helps identify non-diatonic chords and modulations

Key determination with Roman numeral analysis

Identifying the tonic and dominant chords

• The tonic chord (I or i) establishes the key center and is the most stable chord in a progression
• The dominant chord (V) is the second most important chord in establishing the key, as it contains the leading tone that resolves to the tonic
• The presence and relationship between the tonic and dominant chords provide strong indications of the key

Using key signatures and accidentals

• The key signature of the excerpt provides information about the sharps or flats in the key, narrowing down the possible keys
• The presence of accidentals in the excerpt can indicate secondary dominants, borrowed chords, or modulations to different keys
• Analyzing the relationship between the chords and their functions within the progression helps determine the overall key of the excerpt

Analyzing chord functions and relationships

• Identifying the function of each chord within the progression (tonic, subdominant, dominant) helps establish the key
• Observing the resolution of chords, particularly the dominant to the tonic, reinforces the key center
• Comparing the Roman numeral analysis to common chord progressions and cadences aids in determining the key

Common chord progressions using Roman numerals

Cadences

• The authentic cadence (V-I) is a common progression that provides a strong sense of resolution and finality (G-C in C major)
• The plagal cadence (IV-I) is often referred to as the "Amen" cadence and provides a sense of conclusion (F-C in C major)
• The deceptive cadence (V-vi) subverts the expected resolution of the dominant to the tonic, creating a sense of surprise or prolongation (G-Am in C major)
• The half cadence (I-V or ii-V) creates a sense of incomplete resolution and is often used in the middle of phrases (C-G or Dm-G in C major)

Common progressions in various genres

• The ii-V-I progression is a common sequence in jazz and popular music, often used for turnarounds and modulations (Dm-G-C in C major)
• The I-vi-IV-V progression is a popular chord sequence used in various genres, including pop, rock, and folk music (C-Am-F-G in C major)
• The circle of fifths progression (I-IV-vii°-iii-vi-ii-V-I) is a sequence of chords that moves through all seven diatonic chords in a key (C-F-Bdim-Em-Am-Dm-G-C in C major)
• The 12-bar blues progression (I-I-I-I-IV-IV-I-I-V-IV-I-I) is a fundamental form in blues and rock music (C-C-C-C-F-F-C-C-G-F-C-C in C major)