How Harmony Works — Functional Harmony for Guitarists

Streeling University

MUS-003 · Foundations of Music Theory · intermediate · 45 minutes

Generated by the Demerzel Music department — not reviewed by me yet. View source · My journal

Prerequisites: MUS-001

Department of Music | Stage: Albedo (Intermediate) | Duration: 45 minutes

Objectives

After this lesson, you will be able to:

• Classify any diatonic chord by its harmonic function (tonic, predominant, dominant)
• Identify and name the five standard cadence types by ear and on paper
• Explain why the dominant chord creates tension that resolves to the tonic
• Perform functional analysis on common chord progressions in pop, jazz, and blues
• Recognize secondary dominants and explain how tonicization leads to modulation
• Analyze phrase structure in terms of harmonic rhythm, periods, and sentences

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1. The Three Families of Harmony

In tonal music, every chord has a function — a role it plays in the gravitational pull toward the tonic. This idea, first systematized by Hugo Riemann in the 1890s, organizes all seven diatonic chords into three families.

Tonic Function (T) — Home

Tonic chords feel like arrival, rest, resolution. They are where phrases want to end.

Chord	Roman Numeral	Example in G Major
Tonic	I	G
Submediant	vi	Em
Mediant	iii	Bm

The I chord is the strongest tonic. The vi is its most common substitute — it shares two of three notes with I. The iii is the weakest tonic substitute, sharing two notes with I but also two with V, giving it an ambiguous quality.

Predominant Function (PD) — Departure

Predominant chords create momentum away from the tonic. They prepare the ear for dominant tension.

Chord	Roman Numeral	Example in G Major
Supertonic	ii	Am
Subdominant	IV	C

The ii and IV are nearly interchangeable — they share two notes and both point toward the dominant. In classical music, ii (especially ii6) is preferred; in pop and rock, IV dominates.

Dominant Function (D) — Tension

Dominant chords create the strongest pull back to the tonic. They contain the leading tone — the note one semitone below the tonic — which desperately wants to resolve upward.

Chord	Roman Numeral	Example in G Major
Dominant	V	D
Leading-tone diminished	viio	F#dim

The V chord is the engine of tonal music. The viio is its incomplete form — it contains the same tritone but lacks the dominant’s root, making it less stable and used more sparingly.

The Functional Cycle

The fundamental motion of tonal harmony follows one path:

T → PD → D → T

Not every progression uses all three stages, but the direction is always the same. You never hear PD after D in a strong progression — it would feel like going backward.

Guitar Example — Analyzed

Play this progression in G major:

G  →  Em  →  C  →  D
I      vi     IV     V
T-I → T-vi → PD-IV → D-V

Feel how G is home, Em softens the tonic energy, C creates forward motion, and D builds tension that wants to resolve back to G. This is the functional cycle in action. The progression works because it follows the T → PD → D → T arc.

Practice Exercise

Write out the diatonic chords in C major (C, Dm, Em, F, G, Am, Bdim) and label each with its function (T, PD, or D). Then play through I-vi-IV-V in C major and listen for the functional arc.

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2. Cadences — How Phrases End

A cadence is a harmonic punctuation mark — the way a musical phrase comes to a close. Just as sentences end with periods, question marks, or ellipses, musical phrases end with different cadential patterns that convey different degrees of finality.

The Five Standard Cadences

Perfect Authentic Cadence (PAC)

V → I, with both chords in root position and the melody arriving on the tonic note (scale degree 1) in the soprano.

This is the strongest possible ending — the period at the end of a definitive statement. The bass moves from scale degree 5 up to 1 (or down a fifth), and the melody resolves to the tonic.

Guitar example (G major): D → G, with the high G string ringing as the melody note.

Imperfect Authentic Cadence (IAC)

V → I, but one or both conditions of the PAC are not met. Either the melody does not end on scale degree 1, or one of the chords is inverted.

This is a weaker period — the sentence ends, but without full conviction. It often appears at the end of the first phrase in a pair, where the second phrase will conclude with a PAC.

Half Cadence (HC)

Any chord → V. The phrase ends on the dominant, not the tonic.

This is the musical question mark. It creates expectation — you hear the dominant and your ear waits for resolution that does not come. Common approach chords are I, ii, or IV.

Guitar example (G major): C → D (IV → V). Strum the D and let it ring. Notice how your ear refuses to accept this as an ending.

Plagal Cadence

IV → I. The “Amen” cadence, heard at the end of hymns.

This is a softer ending than the PAC — it avoids the leading-tone tension of the dominant entirely. It feels warm, settled, devotional.

Guitar example (G major): C → G (IV → I). Compare this to D → G and notice the difference in urgency.

Deceptive Cadence (DC)

V → vi. The dominant sets up the expectation of resolution to I, but resolves to vi instead.

This is the musical plot twist. The ear expects home but gets diverted to a closely related chord. Because vi shares two notes with I, the deception works — it is close enough to feel like partial resolution but different enough to surprise.

Guitar example (G major): D → Em (V → vi). Play D → G first to set up the expectation, then play D → Em. Hear the surprise.

The Punctuation Analogy

Cadence	Punctuation	Effect
PAC	Period (.)	Full stop, definitive closure
IAC	Comma (,)	Partial closure, more to come
HC	Question mark (?)	Expectation, awaiting answer
Plagal	Ellipsis (…)	Gentle, fading closure
Deceptive	Exclamation/twist (!)	Surprise redirection

Practice Exercise

Listen to any song you know well. Try to identify where phrases end and what type of cadence is being used. Start with hymns or folk songs — their phrase structures are clearest. Then move to pop songs. The final chord of a verse before the chorus is almost always a HC or DC, while the end of the chorus is typically a PAC.

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3. Why the Dominant Wants to Resolve

The pull from V to I is not arbitrary convention — it is rooted in acoustic physics and interval mechanics. Understanding why the dominant resolves is the key to understanding all of tonal harmony.

The Tritone Within V7

When you add a seventh to the dominant chord (V7), you create a chord containing a tritone — the most unstable interval in tonal music.

In G major, the V7 chord is D7: D - F# - A - C.

The tritone lives between F# (the leading tone, scale degree 7) and C (the chordal seventh, scale degree 4):

F# to C = 6 semitones = tritone

This tritone is an interval of maximum tension. It demands resolution.

Resolution by Contrary Motion

The tritone resolves when its two notes move in opposite directions by the smallest possible steps:

• F# (leading tone) rises one semitone to G — the tonic
• C (chordal 7th) falls one semitone to B — the third of the tonic chord

D7           →    G
D  ───────────→   D (or G)
A  ───────────→   G (or B)
F# ─── ↑½ ───→   G     ← leading tone resolves UP
C  ─── ↓½ ───→   B     ← 7th resolves DOWN

This is contrary motion — two voices moving toward each other, collapsing the tritone into the stable major third (G to B) or minor sixth. The acoustic tension literally converges to consonance.

Guitar Example — D7 to G Voice Movements

Play this slowly on guitar, one note at a time, and listen for each resolution:

D7 chord:          G chord:
e|--1-- (C)   →   e|--3-- (G)    C falls to B (on the B string: open)
B|--1-- (F#)  →   B|--0-- (B)    F# would resolve to G, but here
G|--2-- (A)   →   G|--0-- (G)    we hear the full chord redistribution
D|--0-- (D)   →   D|--0-- (D→G bass)

In practice on guitar, the voice leading is distributed across the chord shape rather than following strict four-part writing. But the principle holds: the tension notes find their targets.

Why This Matters

Every instance of dominant-to-tonic resolution in all of Western tonal music — from Bach chorales to blues turnarounds to pop hooks — is driven by this same tritone resolution. When you hear a V7-I and feel satisfaction, you are hearing contrary motion collapsing a tritone into consonance.

Practice Exercise

Play D7 on guitar and sing or hum the F# (second fret, high E string). Now resolve to G and sing the G. Feel the half-step pull upward. Next, sing the C in D7 and resolve it down to B. Train your ear to hear these two resolution tendencies independently before hearing them together.

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4. Functional Analysis in Practice

Now let us apply functional analysis to real chord progressions. The goal is to label every chord with its function and see how the progression maps onto the T → PD → D → T cycle.

The Pop Canon: I - V - vi - IV

This is the most common chord progression in popular music (Axis of Awesome, “Four Chords”).

In G major:

|  G   |  D   |  Em  |  C   |
|  I   |  V   |  vi  |  IV  |
|  T   |  D   |  T   |  PD  |

Analysis: This progression is unusual because it does not follow the standard T → PD → D → T cycle. It moves T → D → T → PD, looping back without a strong cadence. This is precisely why it feels endless — it never fully resolves. The lack of a strong V → I cadence at the end keeps the listener in perpetual motion, which is ideal for pop songwriting.

The deceptive resolution from V to vi (D to Em) gives just enough tonic satisfaction to keep going, while the IV at the end creates predominant momentum that pushes into the next repetition.

The Jazz Workhorse: ii - V - I

This is the fundamental progression of jazz harmony.

In G major:

|  Am7  |  D7   |  Gmaj7 |
|  ii7  |  V7   |  Imaj7 |
|  PD   |  D    |  T     |

Analysis: This is the functional cycle in its purest form — PD → D → T. No filler, no detours. The ii provides smooth voice leading into V7 (Am7 to D7 shares the notes A and C, while the others move by step), and the V7 resolves to I via tritone resolution.

Jazz musicians favor ii-V-I because it gives maximum harmonic motion in minimum space. In a jazz standard, you will find dozens of ii-V-I progressions, sometimes in different keys back to back.

The 12-Bar Blues

| I7  | I7  | I7  | I7  |
| IV7 | IV7 | I7  | I7  |
| V7  | IV7 | I7  | V7  |

In G:

| G7  | G7  | G7  | G7  |
| C7  | C7  | G7  | G7  |
| D7  | C7  | G7  | D7  |

Functional analysis:

| T   | T   | T   | T   |
| PD  | PD  | T   | T   |
| D   | PD  | T   | D   |

Analysis: The blues is fascinating because the I chord is a dominant 7th — it contains its own tritone, giving even the tonic a restless, unresolved quality. The move to IV in measure 5 is a classic predominant departure. The turnaround (measure 12, V7) sets up the next chorus.

Notice the “retrogression” in measures 9-10: V7 → IV7 (D → PD). In classical theory, this is forbidden. In blues, it is essential — it gives the blues its characteristic refusal to follow the rules of European harmony.

Practice Exercise

Take a song you are currently learning on guitar. Write out the chord progression and label each chord with its Roman numeral and function (T, PD, or D). Identify the cadences at the end of each phrase. Does the progression follow the standard functional cycle, or does it break the rules? If it breaks them, consider why — what emotional effect does the rule-breaking create?

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5. Secondary Dominants

So far, every chord has been diatonic — belonging to the key. Secondary dominants are the first step outside the key, and they are the single most common chromatic technique in tonal music.

The Concept

A secondary dominant is a major chord or dominant 7th chord that acts as the V or V7 of a chord other than I. It temporarily points toward a diatonic chord as if that chord were a local tonic.

The notation uses a slash: V7/vi means “the dominant seventh of vi.” To find it, ask: “What chord is a fifth above vi and contains vi’s leading tone?”

Building Secondary Dominants

In G major:

Target Chord	Target Note	V7 of Target	Notes	Non-Diatonic Note
V (D)	D	V7/V = A7	A-C#-E-G	C#
vi (Em)	E	V7/vi = B7	B-D#-F#-A	D#
ii (Am)	A	V7/ii = E7	E-G#-B-D	G#
IV (C)	C	V7/IV = D7	D-F#-A-C	(already diatonic!)
iii (Bm)	B	V7/iii = F#7	F#-A#-C#-E	A#, C#

Note: V7/IV looks identical to V7, so it is usually only labeled as a secondary dominant when the IV chord follows in a context where it sounds like a local resolution rather than a predominant.

Guitar Example — A Chain of Secondary Dominants

G  →  B7  →  Em  →  A7  →  D7  →  G
I     V7/vi   vi    V7/V    V7     I
T     D/vi    T     D/V     D      T

Play this slowly. Each secondary dominant creates a momentary pull toward its target:

• B7 contains D# (the leading tone of E), pulling toward Em
• A7 contains C# (the leading tone of D), pulling toward D
• D7 contains F# (the leading tone of G), pulling toward G

You can hear a “chain of fifths” — each chord is the V7 of the next: B7 → Em, A7 → D, D7 → G. This descending-fifth sequence is one of the most powerful patterns in tonal harmony.

How to Recognize Secondary Dominants

A chord is a secondary dominant if:

1. It is a major triad or dominant 7th that does not belong to the key
2. It resolves to a diatonic chord by root motion of a descending fifth (or ascending fourth)
3. It contains the leading tone of its target chord

If a mystery chord appears in your analysis that has a major quality where you expect minor (like B7 in G major, where diatonic iii is Bm), check whether the next chord is a fifth below. If so, you have found a secondary dominant.

Practice Exercise

Analyze this progression in C major. Identify any secondary dominants and label them:

C  →  E7  →  Am  →  D7  →  G7  →  C

Answer: C = I, E7 = V7/vi, Am = vi, D7 = V7/V, G7 = V7, C = I. It is the same chain-of-fifths pattern transposed to C.

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6. Tonicization to Modulation

Secondary dominants create tonicizations — brief moments where a non-tonic chord is treated as a temporary tonic. When a tonicization is extended and the music establishes a new key center, it becomes a modulation.

Tonicization

A tonicization is typically just one or two chords pointing toward a non-tonic target. The original key is never lost.

In G major:
G  →  B7  →  Em  →  C  →  D  →  G
I     V7/vi   vi    IV    V    I

The B7 → Em is a tonicization of vi.
The key of G major is never in doubt.

Modulation via Pivot Chord

The most common modulation technique is the pivot chord — a chord that belongs to both the old key and the new key, serving as a bridge between them.

Guitar Example: G major to D major

G major:  G  →  C  →  D  →  Em  →  A7  →  D  →  G(D)  →  A  →  D
          I     IV    V     vi
                                  ↑ PIVOT
G key:                    vi     V7/V    V
D key:                    ii     V7      I     IV     V     I

The Em chord is the pivot. In G major, Em is vi. In D major, Em is ii. The ear reinterprets Em’s function the moment A7 arrives — A7 is not diatonic to G major, so the listener’s tonal center shifts.

After the pivot:

• A7 functions as V7 in D major (not V7/V in G major)
• D is now I, not V
• G becomes IV, not I
• The music has arrived in D major

Signs That a Modulation Has Occurred

1. A new tonic is confirmed by a cadence in the new key (especially PAC)
2. The old tonic no longer feels like home
3. Accidentals appear consistently (in our example, C# appears in A7 and stays)
4. The music stays in the new key for several phrases

Closely Related Keys

Modulation is easiest between keys that share many notes. These closely related keys differ by only one accidental:

For G major, the closely related keys are:

• D major (one sharp more)
• C major (one sharp fewer)
• E minor (relative minor)
• B minor (relative minor of D)
• A minor (relative minor of C)

Practice Exercise

Play this progression and listen for the modulation:

Key of G:  G  →  D  →  Em  →  C
Key of D:  Em → A7  →  D   →  G  →  A  →  D

Can you hear the moment where G stops feeling like home and D takes over? The arrival of A7 is the turning point. Play it several times and try to pinpoint the exact chord where your perception shifts.

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7. Phrase Structure and Harmonic Rhythm

Harmony does not exist in isolation — it unfolds within phrases, and the rate at which chords change (the harmonic rhythm) shapes the music’s momentum and drama.

Harmonic Rhythm

Harmonic rhythm is how frequently the harmony changes. It is independent of melodic rhythm or tempo.

Harmonic Rhythm	Effect	Example
One chord per measure	Steady, relaxed	Folk, country ballads
Two chords per measure	Moderate momentum	Pop verses
Chord changes every beat	Driving, intense	Jazz standards, classical sequences
Accelerating	Building tension	Approaching a cadence
Decelerating	Relaxing, arriving	Post-cadence, codas

Key insight: Harmonic rhythm typically accelerates toward cadences. A phrase might sustain one chord per measure for three bars, then change twice in the fourth bar to set up the cadence. This acceleration is one of the primary tools for creating a sense of arrival.

The Period

A period is the most common phrase structure in tonal music. It consists of two phrases:

1. Antecedent — ends with a weak cadence (usually HC or IAC)
2. Consequent — ends with a strong cadence (usually PAC)

The antecedent asks a harmonic question; the consequent answers it.

Antecedent (4 measures):   I  →  IV  →  V  →  V     (ends on HC)
Consequent (4 measures):   I  →  IV  →  V  →  I     (ends on PAC)

The two phrases typically begin the same way, creating a sense of rhyme. The difference comes at the end — where the antecedent leaves you hanging on V, the consequent resolves to I.

Guitar example in G:

Antecedent:  | G    | C    | D    | D    |   ← ends on V (half cadence)
Consequent:  | G    | C    | D    | G    |   ← ends on I (perfect authentic cadence)

Play both phrases. Hear how the first phrase feels incomplete and the second feels finished.

The Sentence

A sentence is another common phrase structure, built from three components:

1. Basic idea (2 measures) — presents the main melodic-harmonic material
2. Repetition (2 measures) — repeats or varies the basic idea (often sequenced up or down)
3. Continuation + Cadence (4 measures) — fragments the idea, accelerates harmonic rhythm, and drives to a cadence

Basic idea (2m):      | I       | V       |
Repetition (2m):      | I       | V       |
Continuation (4m):    | IV  V   | IV  V   | ii    V | I       |
                        ↑ fragmented    ↑ accelerating    ↑ cadence

Notice how the continuation section increases harmonic activity — chords change twice per measure instead of once, building momentum toward the cadence.

Combining Phrases

Larger musical forms are built from combining periods and sentences:

• Parallel period: antecedent and consequent begin identically
• Contrasting period: consequent begins differently
• Double period: four phrases, with the strongest cadence only at the very end
• Sentence + Period: a sentence as the first half, a period as the second

Harmonic Rhythm on Guitar

Guitar players often control harmonic rhythm through strumming patterns. A whole-note strum (one strum per measure) creates slow harmonic rhythm. Subdivided strumming with chord changes on upbeats creates rapid harmonic rhythm. The same four chords can feel entirely different depending on how the harmonic rhythm is managed.

Practice Exercise

Take a simple 8-bar progression you know and determine whether it forms a period or a sentence:

• Does it have two parallel 4-bar phrases with different endings? → Period
• Does it have a 2-bar idea, a 2-bar repeat, and a 4-bar drive to cadence? → Sentence

Then experiment with harmonic rhythm: play the same progression with one chord per measure, then two chords per measure. Notice how the energy changes even though the harmony is identical.

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Key Terms

Term	Definition
Tonic function (T)	Chords that feel like home or rest: I, vi, iii
Predominant function (PD)	Chords that create departure momentum: ii, IV
Dominant function (D)	Chords that create tension pulling toward tonic: V, viio
Cadence	A harmonic punctuation mark ending a phrase
PAC	Perfect Authentic Cadence: V → I, root position, melody on scale degree 1
IAC	Imperfect Authentic Cadence: V → I with weaker conditions
HC	Half Cadence: phrase ends on V (the musical question mark)
Deceptive cadence	V → vi, surprising redirection of expected resolution
Tritone	An interval of 6 semitones; the engine of dominant tension
Contrary motion	Two voices moving in opposite directions to resolve tension
Secondary dominant	A V or V7 chord that targets a diatonic chord other than I
Tonicization	Brief treatment of a non-tonic chord as a temporary tonic
Modulation	Change of key center, confirmed by cadence in the new key
Pivot chord	A chord belonging to both old and new keys, bridging a modulation
Harmonic rhythm	The rate at which chords change within a passage
Period	Two phrases: antecedent (weak cadence) + consequent (strong cadence)
Sentence	Phrase structure: basic idea + repetition + continuation to cadence

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Self-Check Assessment

1. Classify these chords in C major by function: Am, G, F, Em.

Am (vi) = Tonic. G (V) = Dominant. F (IV) = Predominant. Em (iii) = Tonic.

2. What type of cadence is this: Dm → G → Am in C major?

The G → Am is a deceptive cadence (V → vi). The dominant sets up expectation for C (I) but resolves to Am instead.

3. In the progression C → E7 → Am → D7 → G → C, identify the secondary dominants and their targets.

E7 = V7/vi (targets Am). D7 = V7/V (targets G). Both are secondary dominants creating a descending-fifths chain: E7 → Am → D7 → G → C.

4. Why is the ii-V-I progression stronger than IV-V-I, even though both follow PD → D → T?

The ii chord provides smoother voice leading into V. In the move from ii to V, most voices move by step (common tones and half steps), while IV to V creates more disjunct motion. Additionally, ii-V-I forms a cycle-of-fifths root motion (down a 5th, down a 5th), which is the strongest root progression pattern in tonal music.

Pass criteria: Given any diatonic chord progression in a major key, assign Roman numerals, label functions (T/PD/D), identify cadences, and spot secondary dominants with their targets.

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Research Basis

• Hugo Riemann’s Vereinfachte Harmonielehre (1893) established the three-function model (T/S/D) that all modern functional harmony descends from
• Kostka & Payne, Tonal Harmony (7th ed., 2013) — standard undergraduate text for diatonic and chromatic harmony
• Aldwell & Schachter, Harmony and Voice Leading (4th ed., 2011) — authoritative treatment of voice-leading principles and phrase structure
• The tritone resolution mechanism is acoustically grounded in combination tones and frequency-ratio convergence
• Secondary dominant and modulation pedagogy follows the graduated approach: diatonic → tonicization → modulation
• Sources: Streeling Department of Music curriculum, Western harmony pedagogy consensus
• Belief state: T(0.85) F(0.03) U(0.08) C(0.04)