Basic Harmonic Analysis

Basic Harmonic Analysis

1. What Harmonic Analysis Really Means

Think about the last time a song gave you goosebumps. Maybe it was the moment in Adele's Someone Like You when the piano suddenly shifts to a different chord underneath her voice, or the way the Beatles lead you through unexpected chord changes in Something. What you're feeling in those moments is harmony at work-and harmonic analysis is simply the process of understanding how and why those chords create the emotional effects they do.

When you analyze harmony, you're like a detective examining a crime scene. You're looking at each chord, figuring out what it's made of, understanding its relationship to the key, and discovering how it connects to the chords before and after it. You're answering questions like: Why does this chord feel tense? Why does this one feel like coming home? Why does this progression sound sad, and that one sound triumphant?

Let's be clear: harmonic analysis isn't about memorizing rules for their own sake. It's about understanding the architecture of music so you can appreciate what composers and songwriters are doing, and eventually make informed choices in your own music.

The Building Blocks We'll Use

Before we dive into analyzing actual music, let's make sure we're on the same page about what we're working with:

  • Chords: Three or more notes played together
  • Key: The tonal center-the "home base" note and scale that a piece of music is built around
  • Scale degrees: The numbered positions of notes within a scale (1, 2, 3, 4, 5, 6, 7)
  • Roman numerals: A labeling system that tells us which scale degree a chord is built on

These tools help us talk about harmony in a way that works across different keys. When we say "a I-IV-V progression," musicians immediately know what we mean, whether we're in C major or F♯ major.

2. Understanding Roman Numeral Analysis

Here's where harmonic analysis gets its power. Instead of saying "C major, F major, G major," we say "I-IV-V." Why? Because this tells us something much more important than just note names-it tells us the function of each chord within the key.

How the System Works

In any major key, you can build a chord on each note of the scale. Let's use C major as our example because it has no sharps or flats:

How the System Works

Notice the pattern here:

Uppercase Roman numerals (I, IV, V) indicate major chords.
Lowercase Roman numerals (ii, iii, vi) indicate minor chords.
Lowercase with a degree sign (vii°) indicates a diminished chord.

This pattern holds true in every major key. That's the beauty of this system-once you learn it in one key, you understand it in all keys.

Try This Right Now

If you have a piano or keyboard nearby, play these three chords in C major: C-E-G (I), F-A-C (IV), G-B-D (V). Now play the same pattern in G major: G-B-D (I), C-E-G (IV), D-F♯-A (V). Different notes, but the same harmonic relationships-and they feel the same, don't they?

Minor Keys Work Similarly

In natural minor keys, the pattern changes slightly. Let's look at A minor:

Minor Keys Work Similarly

In practice, composers often use harmonic minor or melodic minor for the V chord, creating a major V instead of minor v. This gives a stronger pull back to the tonic. You'll hear this in countless pieces-the raised leading tone creates that classic minor key sound.

3. The Three Primary Functions of Harmony

Here's where harmonic analysis becomes truly powerful. Every chord in tonal music serves one of three basic functions. Think of these as the three jobs that chords can have:

Tonic Function: Home

The tonic (I or i) is home base. It's stable, resolved, and at rest. When a piece ends, it almost always ends on the tonic chord. Picture Dorothy saying "There's no place like home"-that's the tonic chord.

Listen to the final chord of almost any classical piece or pop song. That feeling of "we've arrived" is the tonic function. The Beatles' Let It Be ends on a C major chord (I), and you can feel that sense of completion.

Other chords can have tonic function too, especially vi (the relative minor) and sometimes iii, though they're less stable than I.

Dominant Function: Tension

The dominant (V) creates tension that wants to resolve back to the tonic. It's like a question waiting for an answer. This is the most important relationship in all of tonal music: V → I.

The dominant seventh chord (V7) is even stronger. Try this on a keyboard: Play a G7 chord (G-B-D-F) and then resolve it to C major (C-E-G). Feel that pull? That's the dominant function in action. The F wants to move down to E, and the B wants to move up to C. These are called tendency tones.

The vii° chord also has dominant function because it shares two notes with V7 and creates similar tension.

Subdominant Function: Preparation

The subdominant (IV) moves away from home but doesn't create the intense tension of the dominant. It's a departure, a preparation. Think of it as packing your bags before a journey.

The most common chord progression in Western music is I-IV-V-I: home → departure → tension → resolution. Listen to almost any folk song, hymn, or classic rock tune, and you'll hear this progression. Twist and Shout by The Beatles? I-IV-V. Wild Thing by The Troggs? I-IV-V. It's everywhere.

The ii chord also has subdominant function and is often used to approach V. The progression ii-V-I is fundamental in jazz and common in all styles of music.

Think of harmonic function as a journey:
Tonic = being at home
Subdominant = leaving home
Dominant = the moment before returning home
Tonic = arriving back home

4. Identifying Chords in Real Music

Now let's put this into practice. When you're analyzing a piece of music, you need to identify what each chord is and label it with the appropriate Roman numeral. Here's a step-by-step process:

Step 1: Determine the Key

Look at the key signature, but also check the first and last chords of the piece-they're usually the tonic. Look at where the melody seems to "land" or rest. If you're listening rather than reading music, your ear will tell you which note feels like home.

Step 2: Identify Each Chord's Root

Find the lowest note if the chord is in root position, or identify which note the chord is stacked in thirds from. For example, if you see the notes E-G-C, rearrange them as C-E-G-that's a C major chord.

Step 3: Determine the Chord Quality

Is it major, minor, diminished, or augmented? Count the intervals: a major third plus a minor third makes a major chord; a minor third plus a major third makes a minor chord.

Step 4: Find the Scale Degree of the Root

What position does the chord's root occupy in the key? If you're in C major and you see an F major chord, the root (F) is the 4th scale degree, so this is IV.

Step 5: Add the Roman Numeral Label

Write the appropriate Roman numeral below the chord. Use uppercase for major, lowercase for minor, and add the ° symbol for diminished.

A Real Example: "Let It Be" by The Beatles

The verse of Let It Be is in C major. The progression goes: C - G - Am - F - C - G - F - C

Let's analyze it:
C = I (the tonic)
G = V (the dominant)
Am = vi (relative minor, tonic function)
F = IV (subdominant)
C = I (back home)
G = V (tension again)
F = IV (subdominant)
C = I (final resolution)

So the progression in Roman numerals is: I - V - vi - IV - I - V - IV - I

Notice how it uses only primary chords and the relative minor-simple, but profoundly effective.

5. Common Chord Progressions and Their Effects

Certain chord progressions appear again and again in music because they create specific emotional effects. Let's look at the most important ones:

The Authentic Cadence: V - I

This is the strongest possible ending. Cadence means "musical punctuation"-a moment of arrival or pause. When you hear V → I, especially V7 → I, you hear a definitive period at the end of a sentence.

Listen to the end of almost any Mozart symphony or Beethoven sonata. That final V-I is the authentic cadence. It signals "The End" more clearly than anything else in music.

There are two types:

  • Perfect authentic cadence (PAC): Both chords are in root position, and the melody ends on the tonic note. This is the strongest possible conclusion.
  • Imperfect authentic cadence (IAC): Either one chord is inverted, or the melody doesn't end on the tonic. Still feels conclusive, but slightly less strong.

The Plagal Cadence: IV - I

Often called the "Amen cadence" because you hear it at the end of hymns when the congregation sings "A-men." It's gentler than V-I, more peaceful and settled.

Listen to the end of the Beatles' Hey Jude-after all that repetition, it finally settles on a IV-I cadence. That's not a coincidence; it creates a specific feeling of gentle resolution.

The Half Cadence: Ending on V

This is like ending a sentence with a comma-it creates pause but not conclusion. Many phrases in classical music end on V, creating a question that demands an answer.

Try playing a I-IV-V progression and stopping on V. It feels unfinished, doesn't it? That's the half cadence at work. It propels the music forward because listeners need to hear that V resolve to I.

The Deceptive Cadence: V - vi

This is one of the most emotionally powerful moves in music. You expect V to go to I, but instead it goes to vi (the relative minor). It's a plot twist.

You can hear a deceptive cadence in the opening of Pachelbel's Canon in D. After the initial phrase, instead of resolving to D major, it moves to B minor. That "surprise" creates a beautiful moment of unexpected emotion.

Composers use deceptive cadences to extend phrases, avoid predictability, and add emotional depth. When you're expecting resolution and don't get it, the music suddenly feels more complex, more human.

The Circle of Fifths Progression

Moving through chords whose roots are a fifth apart creates strong, logical progressions. The most common is vi - ii - V - I, which moves through the circle of fifths: A - D - G - C (in the key of C major).

This progression underlies countless jazz standards and appears in classical music from Bach to Brahms. In jazz, you'll often see it extended: iii - vi - ii - V - I, or even longer chains.

Play this in C major: Am - Dm - G7 - C. Hear how each chord seems to pull naturally to the next? That's the power of fifth relationships.

The Pop Progression: I - V - vi - IV

This progression has powered thousands of pop hits over the past few decades. In C major, that's C - G - Am - F.

You'll hear it in:

  • Don't Stop Believin' by Journey
  • Let It Be by The Beatles
  • Someone Like You by Adele
  • With or Without You by U2

Why is it so popular? Because it balances stability (I), tension (V), emotion (vi), and departure (IV) in a perfect loop. It can repeat endlessly and never feels boring.

6. Inversions and Figured Bass

So far we've talked about chords in root position-with the root as the lowest note. But chords can be inverted, meaning a different note is in the bass. This changes the chord's stability and function.

Why Inversions Matter

Think about walking up stairs versus taking an elevator. Both get you to the second floor, but the experience is different. Root position chords are stable and grounded. Inverted chords are lighter, more mobile, and create smoother bass lines.

Listen to the bass line in Bach's music-it's constantly moving in steps because he uses inversions to keep the bass line smooth. Compare that to early rock and roll, where the bass often jumps around because chords are mostly in root position.

The Three Positions

For a triad (three-note chord), there are three possible positions:

  • Root position: The root is the lowest note (e.g., C-E-G)
  • First inversion: The third is the lowest note (e.g., E-G-C)
  • Second inversion: The fifth is the lowest note (e.g., G-C-E)

Figured Bass Notation

We indicate inversions using numbers derived from Baroque-era figured bass notation:

Root position = 5/3 (or just the Roman numeral alone)
First inversion = 6/3 (or just 6)
Second inversion = 6/4

These numbers show the intervals above the bass note. In a root position C major chord (C-E-G), the E is a third above C, and the G is a fifth above C, hence 5/3. In first inversion (E-G-C), the G is a third above E, and the C is a sixth above E, hence 6/3.

In practice, we usually abbreviate:

  • Root position: I (no numbers needed)
  • First inversion: I6
  • Second inversion: I6/4

Second Inversion Chords: Handle with Care

Second inversion chords are unstable because they have a fourth in the bass (the interval between the bass note and the root). In classical harmony, 6/4 chords are used in specific ways:

  • Cadential 6/4: A I6/4 that moves to V, typically at cadences. The most common use of second inversion.
  • Passing 6/4: Occurs between two other chords, with the bass note passing through by step
  • Pedal 6/4: Occurs over a sustained bass note (pedal point)
  • Arpeggiated 6/4: The bass arpeggiated the chord rather than jumping

The cadential 6/4 is especially important. In the progression I6/4 - V, the I6/4 acts like a decoration of V, not as an independent tonic chord. You'll see this in countless classical pieces just before a final cadence.

7. Seventh Chords in Harmonic Analysis

Up to now, we've focused on triads-three-note chords. But seventh chords (four-note chords) add richness, color, and additional tension. They're essential in harmonic analysis.

The Dominant Seventh: V7

The most important seventh chord is V7. In C major, that's G-B-D-F. This chord contains two tendency tones that desperately want to resolve:

  • The leading tone (B) wants to rise to the tonic (C)
  • The seventh (F) wants to fall to the third of the tonic chord (E)

Play G7 (G-B-D-F) followed by C major (C-E-G). Listen to how strongly the B pulls up to C and the F pulls down to E. This is the most powerful resolution in tonal music.

Nearly every piece in the Classical period (Mozart, Haydn, early Beethoven) uses V7 → I at major cadences. It's that fundamental.

Other Diatonic Seventh Chords

You can build seventh chords on every scale degree. In C major:

Other Diatonic Seventh Chords

The progression ii7 - V7 - I is the backbone of jazz harmony and appears constantly in classical music too. In C major, that's Dm7 - G7 - Cmaj7.

Inversions of Seventh Chords

Seventh chords have four possible positions, and we use figured bass to label them:

  • Root position: V7 (intervals: 7/5/3 above the bass)
  • First inversion: V6/5 (the third is in the bass)
  • Second inversion: V4/3 (the fifth is in the bass)
  • Third inversion: V4/2 or V2 (the seventh is in the bass)

The third inversion (with the seventh in the bass) is particularly expressive because it creates a strong downward pull in the bass line. Composers use it to create smooth, stepwise bass motion.

8. Non-Chord Tones and Embellishments

Not every note you see in a piece of music belongs to the chord sounding at that moment. Non-chord tones (also called non-harmonic tones) are melodic decorations that add interest and movement without changing the underlying harmony.

Understanding these is crucial for harmonic analysis because you need to distinguish between notes that are part of the chord structure and notes that are just melodic embellishments.

Passing Tones

A passing tone connects two chord tones by stepwise motion. If the melody goes C - D - E, and the harmony is C major (C-E-G), the D is a passing tone connecting C to E.

Passing tones can be accented (landing on the beat) or unaccented (between beats). Unaccented passing tones are more common and less noticeable.

Sing or play the melody to Twinkle, Twinkle, Little Star. Many of those stepwise connections between chord tones are passing tones.

Neighbor Tones

A neighbor tone (or auxiliary tone) moves by step away from a chord tone and then returns to the same chord tone. If the melody goes E - F - E, and the harmony is C major, the F is an upper neighbor to E.

There are upper neighbors (a step above) and lower neighbors (a step below). Like passing tones, they can be accented or unaccented.

Suspensions

A suspension is a note held over from one chord into the next chord, where it doesn't belong, and then resolves downward by step. It creates a moment of tension and release.

The classic pattern is: preparation (the note is consonant) → suspension (the note becomes dissonant) → resolution (the note resolves down by step).

We label suspensions by the intervals involved. A 4-3 suspension means the suspended note forms a fourth above the bass and resolves to a third. A 7-6 suspension means it forms a seventh and resolves to a sixth.

Listen to the opening of Bach's Jesu, Joy of Man's Desiring. Those sweet, yearning sounds? Many of them are suspensions.

Appoggiaturas

An appoggiatura is similar to a suspension, but instead of being held over, it's approached by leap. It lands on the beat, creating a strong dissonance, and then resolves by step.

The word comes from Italian appoggiare, meaning "to lean." Think of it as a note that leans into the chord tone it resolves to.

Anticipations

An anticipation is the opposite of a suspension-it's a note from the next chord that arrives early. It usually occurs before a cadence, creating a forward momentum toward resolution.

Escape Tones and Appoggiaturas

An escape tone moves by step away from a chord tone and then leaps to another chord tone. A cambiata is a four-note figure combining stepwise motion and leaps in a specific pattern.

These are less common than passing tones, neighbor tones, and suspensions, but you'll encounter them, especially in Renaissance and Baroque music.

Why This Matters for Analysis

When you're analyzing harmony, you need to look past these decorations to see the underlying chord structure. If you tried to label every single note as part of a chord, you'd end up with a chaotic mess that doesn't reflect what's really happening harmonically.

The skill is learning to identify the structural tones-the notes that define the harmony-versus the embellishing tones that decorate it.

9. Analyzing Harmonic Rhythm

Harmonic rhythm refers to the rate at which chords change. This is separate from the meter or the rhythm of the melody-it's about how long each harmony lasts.

Why Harmonic Rhythm Matters

Think about how a car feels when you're accelerating versus coasting. Harmonic rhythm creates similar sensations in music. When chords change frequently, the music feels energetic and intense. When chords change slowly, the music feels stable and spacious.

Compare two pieces:

  • In a typical pop ballad like Let It Be, chords change every one or two measures-slow harmonic rhythm
  • In a bebop jazz tune, chords might change every beat or even faster-rapid harmonic rhythm

Analyzing Harmonic Rhythm

When you analyze a piece, note how frequently chords change:

  • Do chords change on every beat, every measure, every few measures?
  • Does the harmonic rhythm speed up or slow down at certain points?
  • Does the harmonic rhythm accelerate as the piece approaches a cadence?

In classical music, it's common for the harmonic rhythm to increase (chords change more frequently) as a phrase approaches a cadence. This creates momentum and intensifies the sense of arrival.

Try this: Listen to the final measures of any movement of a Mozart or Beethoven symphony. Count how often the chords change in the last eight measures compared to the middle of the movement. You'll almost certainly find the harmonic rhythm accelerates toward the cadence.

10. Putting It All Together: A Complete Analysis

Let's walk through a complete harmonic analysis of a simple, well-known piece: the first phrase of Amazing Grace. This will show you how all these concepts work together in real music.

The Music

Amazing Grace is in the key of G major, in 3/4 time. Here's the first phrase (simplified):

Melody: G - B - B - A - G - E - G - G - D - D - G
Bass line: G - G - G - D - G

The harmony unfolds like this:

Measure 1: G major chord (I)
Measure 2-3: G major chord continuing (I)
Measure 4: D major chord (V)
Measure 5: G major chord (I)

Step-by-Step Analysis

Key identification: The piece begins and ends on G major, confirming G major as the key.

Harmonic progression: I - I - I - V - I. This is an extremely simple progression, which is one reason the tune is so accessible and memorable.

Functional analysis:
→ Tonic (I): Establishes home
→ Tonic (I): Remains stable
→ Tonic (I): Continues stability
→ Dominant (V): Creates tension and expectation
→ Tonic (I): Resolves back to home

Cadence: The phrase ends with V - I, which is an authentic cadence. Since both chords are in root position and the melody ends on the tonic note (G), this is specifically a perfect authentic cadence.

Non-chord tones: Most of the melody notes are chord tones, but there are a few passing tones and neighbor tones connecting them. For example, when the melody moves G - A - B over a G major chord, the A is a passing tone.

Harmonic rhythm: Very slow-the tonic chord lasts for three full measures before moving to the dominant. This creates a sense of spaciousness and calm, appropriate for the hymn's meditative character.

What This Analysis Tells Us

The analysis reveals why Amazing Grace feels so stable and singable. It stays on tonic for a long time, uses only the two most fundamental chords (I and V), and ends with the strongest possible cadence. There's nothing ambiguous or complex about the harmony-it's pure and direct.

This simplicity is a compositional choice. The composer wanted the focus on the melody and lyrics, so the harmony supports rather than competes.

11. Common Analysis Mistakes to Avoid

As you begin analyzing harmony, here are some pitfalls to watch out for:

Labeling Every Note as a Chord

The most common beginner mistake is trying to give every single note a Roman numeral. Remember: not every note is a chord tone. Look for non-chord tones and identify the underlying harmonic structure.

Ignoring the Context of the Key

Always establish the key first. A C major chord might be I in C major, IV in G major, or V in F major. The Roman numeral depends entirely on the key context.

Confusing Inversions

Make sure you're identifying the actual root of the chord, not just the bass note. If you see C-E-G with E in the bass, it's still a C major chord (I6 in C major), not an E minor chord.

Overlooking the Function

Roman numerals are just labels. The real understanding comes from recognizing function: Is this chord acting as tonic, dominant, or subdominant? That tells you how it relates to the chords around it.

Forgetting About Tendency Tones

Certain notes have strong tendencies to resolve in specific directions, especially the leading tone (scale degree 7) and the seventh of dominant seventh chords. When you spot these, note how they resolve-or don't resolve, which might be a deliberate expressive choice by the composer.

12. Taking Your Analysis Further

Once you're comfortable with the basics, harmonic analysis opens up much deeper levels of understanding.

Tonicization and Secondary Dominants

Sometimes a chord temporarily acts like the dominant of a chord other than the tonic. For example, in C major, you might see a D major chord (which isn't in the key) moving to G major. That D major is functioning as V/V-the dominant of the dominant.

This creates a brief tonicization of the V chord without changing the overall key. It adds color and forward momentum. You'll hear this constantly in jazz and classical music.

Modulation

When music changes key, we call it modulation. Analyzing modulations means identifying when the tonal center shifts, how the composer makes the transition, and what the relationship is between the old key and the new key.

Common modulations include moving to the dominant key (G major to D major), the relative minor (C major to A minor), or the parallel minor (C major to C minor).

Chromatic Harmony

When composers use notes outside the diatonic scale, they're employing chromatic harmony. This includes augmented sixth chords, Neapolitan chords, borrowed chords from parallel modes, and other colorful options.

Chromatic harmony adds emotional intensity, surprise, and sophisticated color. Think of the dramatic moments in Romantic-era music-Chopin, Liszt, Wagner-and you're hearing chromatic harmony at work.

Learning from the Masters

The best way to develop your analytical skills is to analyze real music, lots of it. Start with simple pieces-folk songs, hymns, simple Classical-era pieces. Then gradually work up to more complex works.

Some excellent pieces for early analysis practice:

  • Bach chorales (clear four-part harmony, beautiful voice leading)
  • Mozart piano sonatas (elegant and clear harmonic structures)
  • Beatles songs (sophisticated but accessible pop harmony)
  • Jazz standards from the Great American Songbook (rich harmonic vocabulary)

Each time you analyze a piece, you're learning the vocabulary of harmony. Eventually, these patterns become part of your musical intuition.

Key Terms

Authentic Cadence
A harmonic progression from V (or V7) to I, creating a strong sense of conclusion. The perfect authentic cadence has both chords in root position with the melody ending on the tonic note.
Cadence
A harmonic or melodic formula that creates a sense of pause or conclusion at the end of a musical phrase, similar to punctuation in language.
Chromatic
Using notes outside the diatonic scale, often creating richer harmonic colors and increased tension.
Deceptive Cadence
A cadence where V resolves to vi instead of the expected I, creating surprise and emotional depth.
Diatonic
Using only the seven notes that belong to a particular major or minor scale, without chromatic alterations.
Dominant
The fifth scale degree and the chord built on it (V). The dominant creates tension that strongly desires to resolve to the tonic.
Figured Bass
A Baroque-era notation system using numbers to indicate intervals above the bass note, now used to show chord inversions in harmonic analysis.
Half Cadence
A cadence ending on the dominant (V) chord, creating a sense of pause but not conclusion, like a comma in a sentence.
Harmonic Function
The role a chord plays within a key: tonic (stability), dominant (tension), or subdominant (departure).
Harmonic Rhythm
The rate at which chords change in a piece of music, independent of the rhythmic activity in the melody.
Inversion
A chord position where a note other than the root is in the bass. First inversion has the third in the bass; second inversion has the fifth in the bass.
Leading Tone
The seventh scale degree, which has a strong tendency to resolve upward by half step to the tonic.
Modulation
The process of changing from one key to another within a piece of music.
Non-Chord Tone
A note that doesn't belong to the current chord, serving as a melodic embellishment. Examples include passing tones, neighbor tones, suspensions, and appoggiaturas.
Passing Tone
A non-chord tone that connects two chord tones by stepwise motion, creating smooth melodic flow.
Plagal Cadence
A cadence with the progression IV to I, often called the "Amen cadence." It creates a gentler sense of resolution than V to I.
Roman Numeral Analysis
A system of labeling chords by their scale degree using Roman numerals (I, ii, iii, IV, V, vi, vii°), with uppercase indicating major chords and lowercase indicating minor chords.
Root Position
A chord arrangement where the root is the lowest sounding note.
Scale Degree
The position of a note within a scale, numbered 1 through 7 (or 8 for the octave).
Secondary Dominant
A chord that temporarily functions as the dominant of a scale degree other than the tonic, creating brief tonicization. Labeled as V/x (for example, V/V is the dominant of the dominant).
Subdominant
The fourth scale degree and the chord built on it (IV). The subdominant creates a sense of departure from tonic without the strong tension of the dominant.
Suspension
A non-chord tone held over from one chord into the next where it creates dissonance, then resolves downward by step.
Tendency Tone
A note with a strong inclination to resolve to a specific neighboring pitch, such as the leading tone resolving to the tonic.
Tonic
The first scale degree and the chord built on it (I or i). The tonic is the home base of a key, providing stability and resolution.
Tonicization
The temporary emphasis of a scale degree other than the tonic, often through the use of its own dominant chord, without fully modulating to a new key.
Voice Leading
The smooth, logical movement of individual musical lines (voices) from one chord to the next, following principles that create efficient and euphonious progressions.

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