8/9 8. Basic Harmonic Analysis

A Practical Harmonic Analysis Process

Begin by treating harmonic analysis as an explanation of musical relationships rather than a list of simultaneous notes. A useful analysis answers several connected questions: What is the tonal key? What chord is present? Which chord member is in the bass? What is the chord's function? How does it relate to neighboring chords and to the phrase ending?

A reliable sequence

1. Establish the tonal key. Examine the key signature, opening and closing sonorities, accidentals, and the apparent tonic.

2. Locate phrase boundaries. Look for rests, sustained notes, repeated or contrasting motives, changes in texture, and especially cadences.

3. Reduce the texture. Temporarily ignore doublings, register, spacing, and decorative notes. Focus on the essential bass and chord tones.

4. Identify each harmony. Determine the chord's root and quality.

5. Assign a Roman numeral. Relate the chord root to the tonic of the current key.

6. Identify the inversion. Determine which chord member is in the bass and represent it with figured-bass notation.

7. Separate chord tones from nonharmonic tones. Do not create a new harmony for every passing or decorative note.

8. Interpret the progression. Describe tonic, predominant, and dominant functions.

9. Label the cadence. Classify the harmonic arrival at the end of the phrase.

This order prevents isolated vertical sonorities from obscuring melodic motion and phrase-level structure.

Takeaway: Analyze from the largest context to the smallest detail: key and phrase, then harmony, inversion, embellishment, function, and cadence.

Roman-Numeral Labels and Chord Identity

A Roman numeral identifies the scale degree on which a chord is built. In a major key, the common diatonic triads have these identities and functions:

• $\mathrm{I}$: major tonic triad

• $\mathrm{ii}$: minor predominant triad

• $\mathrm{iii}$: minor tonic-related triad

• $\mathrm{IV}$: major predominant triad

• $\mathrm{V}$: major dominant triad

• $\mathrm{vi}$: minor tonic-related triad

• $\mathrm{vii}^{\circ}$: diminished dominant-related triad

Uppercase and lowercase are significant: uppercase indicates a major triad, while lowercase indicates a minor triad. Quality symbols can be added for seventh chords, such as $\mathrm{V}^7$, $\mathrm{ii}^7$, or $\mathrm{vii}^{\circ 7}$.

For example, in C major:

• $\mathrm{C}\text{–}\mathrm{E}\text{–}\mathrm{G}$ is $\mathrm{I}$.

• $\mathrm{D}\text{–}\mathrm{F}\text{–}\mathrm{A}$ is $\mathrm{ii}$.

• $\mathrm{G}\text{–}\mathrm{B}\text{–}\mathrm{D}$ is $\mathrm{V}$.

• $\mathrm{B}\text{–}\mathrm{D}\text{–}\mathrm{F}$ is $\mathrm{vii}^{\circ}$.

In A minor, $\mathrm{E}\text{–}\mathrm{G}\sharp\text{–}\mathrm{B}$ is $\mathrm{V}$, not $\mathrm{v}$, because the raised leading tone $\mathrm{G}\sharp$ creates a major dominant. Roman numerals therefore describe a chord in relation to its key, not by absolute note names.

Takeaway: First identify the chord's root and quality; then express its scale-degree identity with a Roman numeral.

Figured Bass and Inversions

Figured bass describes intervals above the bass note. The bass determines the inversion, even when another voice contains a lower pitch elsewhere in the texture.

Triads

• Root position: the root is in the bass; no figure is normally written.

• First inversion: the third is in the bass; write $6$, as in $\mathrm{I}^6$.

• Second inversion: the fifth is in the bass; write $6/4$, as in $\mathrm{I}^{6/4}$.

For example, $\mathrm{E}\text{–}\mathrm{G}\text{–}\mathrm{C}$ is a C-major triad with E, its third, in the bass. The analysis is $\mathrm{I}^6$. $\mathrm{G}\text{–}\mathrm{C}\text{–}\mathrm{E}$ places the fifth in the bass, so the analysis is $\mathrm{I}^{6/4}$.

Seventh chords

Common inversion figures are:

• Root position: $7$

• First inversion: $6/5$

• Second inversion: $4/3$

• Third inversion: $4/2$ or $2$

Thus, $\mathrm{G}\text{–}\mathrm{B}\text{–}\mathrm{D}\text{–}\mathrm{F}$ in root position is $\mathrm{V}^7$, while $\mathrm{F}\text{–}\mathrm{G}\text{–}\mathrm{B}\text{–}\mathrm{D}$, with the seventh in the bass, is $\mathrm{V}^{4/2}$.

Takeaway: The Roman numeral names the root and scale-degree identity; the figured-bass symbol identifies the bass member and inversion.

Harmonic Function and Progression

Roman numerals identify chords, but harmonic function explains their role in a progression. The three broad functions are:

• Tonic: stability, arrival, and tonal focus. Common examples include $\mathrm{I}$, $\mathrm{vi}$, and sometimes $\mathrm{iii}$.

• Predominant: movement away from tonic toward dominant. Common examples include $\mathrm{ii}$ and $\mathrm{IV}$.

• Dominant: instability and directed motion back toward tonic. Common examples include $\mathrm{V}$ and $\mathrm{vii}^{\circ}$.

A standard progression is:

Its functional reading is:

Function is contextual. The chord $\mathrm{vi}$ may substitute for tonic, but after $\mathrm{V}$ it may create a deceptive motion. A first-inversion chord may also serve as a passing sonority rather than as an independent structural event. Interpret each chord in relation to the surrounding progression.

Takeaway: A complete analysis says not only what a chord is, but also what the chord is doing.

Nonharmonic Tones

A nonharmonic tone does not belong to the harmony sounding at that moment. It may decorate a stable underlying chord without changing the Roman numeral.

Common types include:

• Passing tone: moves by step between two chord tones in the same direction, as in $\mathrm{C}\text{–}\mathrm{D}\text{–}\mathrm{E}$ when C and E belong to the underlying chord.

• Neighbor tone: steps away from a chord tone and returns to the same tone, as in $\mathrm{E}\text{–}\mathrm{F}\text{–}\mathrm{E}$.

• Suspension: is held from the previous harmony, creates dissonance, and usually resolves downward by step.

• Retardation: resembles a suspension but resolves upward.

• Appoggiatura: leaps to a dissonant note and then resolves by step.

• Escape tone: steps away from a chord tone and then leaps to another chord tone.

• Anticipation: arrives before the harmony changes and becomes a chord tone of the coming harmony.

• Pedal point: sustains or repeats one note while harmonies change above it.

Use three questions to test a suspected embellishment:

1. Does the note belong to the chord implied by the other voices?

2. Does it move by step or follow a recognizable melodic pattern?

3. Do the surrounding notes support one underlying harmony?

For example, if the upper voice moves $\mathrm{E}\text{–}\mathrm{F}\text{–}\mathrm{E}$ while the harmony remains C major, F can be a neighbor tone rather than evidence of a new harmony.

Takeaway: Do not assign a new Roman numeral merely because a note is dissonant; first test whether it decorates an existing chord.

Cadences and Phrase Closure

A cadence is a point of harmonic and melodic punctuation, usually at the end of a phrase. Its classification depends on both the final progression and the strength of closure.

Authentic cadences

An authentic cadence moves from dominant to tonic:

A perfect authentic cadence generally has dominant and tonic in root position, with the tonic scale degree in the soprano on the final tonic. An imperfect authentic cadence is still a dominant-to-tonic motion but departs from one or more of those conditions. Analytical conventions may vary, so apply the criteria used in the relevant system.

Other cadence types

• Half cadence: ends on dominant, so it sounds unfinished and invites continuation.

• Plagal cadence: generally moves from subdominant to tonic, as in $\mathrm{IV}\to\mathrm{I}$ or $\mathrm{iv}\to\mathrm{i}$.

• Deceptive cadence: begins with dominant but moves somewhere other than tonic, most commonly $\mathrm{V}\to\mathrm{vi}$ in major or $\mathrm{V}\to\mathrm{VI}$ in minor.

A cadential six-four sonority commonly appears before the dominant:

Although its notes spell a tonic triad in second inversion, its dominant-oriented context makes it part of the dominant area. Some analytical systems label it $\mathrm{I}^{6/4}$, while others interpret it as a dominant embellishment or expansion.

Takeaway: Judge a cadence by its phrase position, harmonic motion, voice leading, and degree of closure—not by a single chord in isolation.

Phrases and Harmonic Syntax

A phrase is a complete musical thought, often comparable to a grammatical sentence. Boundaries may be marked by a cadence, a rest, a sustained note, a texture change, or a repeated or contrasting motive.

A common four-measure pattern can be described sequentially: measure 1 begins with $\mathrm{I}$, establishing tonic; measure 2 uses $\mathrm{ii}^6$, providing predominant motion; measure 3 uses $\mathrm{V}^7$, intensifying the dominant; and measure 4 returns to $\mathrm{I}$, creating cadential arrival.

Not every surface event has the same structural importance. Several chords may prolong tonic, and a dominant may be expanded by passing chords, suspensions, or a cadential six-four. Distinguish among:

• Surface events: every apparent sonority or note pattern.

• Underlying harmonies: the chords that explain the larger progression.

• Phrase-level function: the way the progression creates continuation, intensification, or closure.

For example, the sequence $\mathrm{C}\text{ major}\mid\mathrm{D}\text{ minor with F in the bass}\mid\mathrm{G}\text{ dominant seventh}\mid\mathrm{C}\text{ major}$ becomes:

Its functions are tonic, predominant, dominant, and tonic. If it ends a phrase and the final soprano note is C, the close may qualify as a perfect authentic cadence if the remaining conditions are also satisfied.

Takeaway: Strong analysis connects local chord labels to the larger syntax of continuation and closure.

Integrated Analysis Example

Apply the complete method to a passage in C major:

The bass notes are C, F, G, and C. The upper-voice F between E and E is approached and left by step.

1. Identify the harmonies. The first sonority is C major, the second is D minor with F in the bass, the third is G dominant seventh, and the final sonority is C major.

2. Assign Roman numerals and inversions. The sequence is $\mathrm{I}\text{–}\mathrm{ii}^6\text{–}\mathrm{V}^7\text{–}\mathrm{I}$.

3. Assign functions. The sequence follows tonic, predominant, dominant, and tonic functions.

4. Classify the embellishment. The F between E and E is a neighbor tone over the final tonic harmony; it does not create a new Roman numeral.

5. Evaluate the cadence. Because the passage ends on tonic after dominant, it has an authentic-cadence motion. It is a perfect authentic cadence only if the required root-position and soprano conditions are met.

This example demonstrates why analysis must combine chord identity, inversion, function, nonharmonic-tone classification, and phrase-level interpretation.