Unit 3 Study Notes: Building, Labeling, and Understanding Triads and Seventh Chords

Triad Types (Major, Minor, Augmented, Diminished)

What a triad is

A triad is a three-note chord built by stacking thirds above a starting note called the root. The chord members are named (from the root): root, third, and fifth. Even though a triad can appear in any order (or with doubled notes), you still label and understand it as “some root with a third and a fifth above it.”

Triads matter because they are the basic “harmonic vocabulary” of tonal music. In AP Music Theory, you use triads constantly to:

• identify harmony in four-part writing
• analyze progressions with Roman numerals
• predict and explain voice-leading (which notes tend to move where)

A common misconception is thinking that the lowest-sounding note must be the root. In reality, the lowest note is the bass, and the chord may be inverted. You identify the root by recognizing stacked thirds (or by rearranging the notes conceptually into thirds).

Triad quality: how it’s defined

A triad’s quality (its type) is determined by the sizes of the intervals from root to third and from third to fifth. You can think of it as “two thirds stacked.”

• Major triad: a major third from root to third, then a minor third from third to fifth
• Minor triad: a minor third from root to third, then a major third from third to fifth
• Diminished triad: a minor third + minor third (the fifth ends up diminished)
• Augmented triad: a major third + major third (the fifth ends up augmented)

Another way to hear this: the third (major vs minor) gives the chord much of its “color,” while the fifth (perfect vs altered) affects stability. Diminished and augmented triads tend to sound more tense because they contain an altered fifth.

How to build each triad type (step-by-step)

When you’re asked to build a triad (on paper, at the keyboard, or mentally), use this reliable process:

1. Choose the root (given or implied by a scale degree).
2. Decide the triad quality (major, minor, diminished, augmented).
3. Add the third above the root (major third or minor third).
4. Add the fifth above the root (perfect, diminished, or augmented), consistent with the quality.
5. Spell carefully (letter names matter). In tonal theory, correct spelling is not optional: for example, an augmented fifth above C is G-sharp, not A-flat.

How to recognize triad types quickly

On the exam, you often identify triads in context (for example, from a notated chord or from a Roman numeral task). Two practical methods:

Method A: Identify the intervals above the root

• Find the root by stacking in thirds.
• Measure root-to-third and root-to-fifth.

Method B: Identify the third and fifth qualities

• Major triad: major third + perfect fifth
• Minor triad: minor third + perfect fifth
• Diminished triad: minor third + diminished fifth
• Augmented triad: major third + augmented fifth

Examples (triads in a real key)

Example 1: Triads in C major (diatonic triads)
If you build triads using only notes of the C major scale, you get specific qualities on each scale degree:

• I: C–E–G (major)
• ii: D–F–A (minor)
• iii: E–G–B (minor)
• IV: F–A–C (major)
• V: G–B–D (major)
• vi: A–C–E (minor)
• vii°: B–D–F (diminished)

Notice that diminished occurs naturally on the leading tone (scale degree 7) in major.

Example 2: Why minor keys often use harmonic minor for harmony
In A natural minor, the chord on scale degree 5 would be E–G–B (minor), which is weaker as a dominant. In tonal practice (and in AP-style analysis), the leading tone is often raised, giving A harmonic minor (G-sharp). Then the V chord becomes E–G-sharp–B (major), creating stronger pull to i.

That’s why, in minor, you commonly see:

• V as major (or V7)
• vii° as diminished (or vii°7)

Table: triad qualities at a glance

Exam Focus

• Typical question patterns
  • Identify the quality of a given triad (often embedded in SATB texture) and label it with a Roman numeral.
  • Build a triad of a specified quality on a given pitch (including correct spelling).
  • Recognize diatonic triads in major and minor and explain which scale degrees produce which qualities.
• Common mistakes
  • Assuming the bass note is the root instead of checking for inversion.
  • Enharmonic misspelling (writing A-flat instead of G-sharp in an augmented triad, for example).
  • Forgetting that in minor, dominant-function chords often use the raised leading tone.

Seventh Chord Types

What a seventh chord is

A seventh chord is a four-note chord built by stacking thirds to include a seventh above the root. You can think of it as “a triad plus one more third.” The chord members are:

• root
• third
• fifth
• seventh

Seventh chords matter because they increase harmonic tension and direction. In tonal music, adding the seventh often creates tendency tones (notes that strongly want to resolve by step). On the AP exam, seventh chords appear constantly in analysis, voice-leading, and part-writing contexts.

A key misconception: students sometimes label any four-note verticality as a seventh chord. It’s only a seventh chord if the notes can be organized as stacked thirds above a root (even if some notes are doubled or omitted in certain textures).

Seventh chord quality: two layers of information

A seventh chord’s type depends on:

1. the triad quality in the lower three notes (root–third–fifth)
2. the quality of the seventh interval above the root (major, minor, or diminished)

Here are the most common seventh chord types in AP tonal harmony:

• Major seventh (MM7): major triad + major seventh
• Dominant seventh (Mm7): major triad + minor seventh
• Minor seventh (mm7): minor triad + minor seventh
• Half-diminished seventh (ø7): diminished triad + minor seventh
• Fully diminished seventh (°7): diminished triad + diminished seventh

How to build seventh chords

Use the same stacking idea as triads, just one step further:

1. Choose the root.
2. Build the correct triad quality (major, minor, diminished).
3. Add the seventh with the correct size above the root.
4. Check spelling by letter name: the seventh should be some kind of 7th (same letter name as the root, seven letters higher), not an enharmonic shortcut.

Diatonic seventh chords in major (a practical way to learn them)

If you build seventh chords on each scale degree using only notes of a major scale, you get a consistent set of qualities:

• I7: major seventh
• ii7: minor seventh
• iii7: minor seventh
• IV7: major seventh
• V7: dominant seventh
• vi7: minor seventh
• viiø7: half-diminished seventh

In C major, for example:

• V7 is G–B–D–F (major triad plus minor seventh)
• viiø7 is B–D–F–A (diminished triad plus minor seventh)

Seventh chords in minor (why qualities change)

In minor keys, you need to pay attention to whether scale degree 7 is raised (harmonic minor influence). In typical tonal usage (and common AP tasks), you frequently see:

• V7 (with raised leading tone)
• vii°7 (with raised leading tone)

These chords heighten dominant function and create strong resolution into i.

How seventh chords behave (resolution intuition)

In tonal harmony, sevenths usually resolve downward by step when they function traditionally (especially in V7 and vii chords). For example, in a V7 chord, the chordal seventh is a very active dissonance that typically resolves down by step into the third of the following tonic chord.

You don’t need to memorize every possible resolution to start understanding the point: adding a seventh increases instability, which composers use to propel the music forward.

Examples

Example 1: Identify the type of G–B–D–F

• Stack in thirds above G: G (root), B (third), D (fifth), F (seventh).
• G–B–D is a major triad.
• F is a minor seventh above G.
• Result: dominant seventh (Mm7), commonly V7 in C major.

Example 2: Identify the type of B–D–F–A

• B–D–F is diminished.
• A is a minor seventh above B.
• Result: half-diminished seventh, often viiø7 in C major.

Exam Focus

• Typical question patterns
  • Classify a seventh chord by quality (major 7, dominant 7, minor 7, half-diminished 7, diminished 7) and label it in Roman numerals.
  • Identify V7 and vii chords in major or minor and explain their tendency tones.
  • In part-writing contexts, spot the chordal seventh and resolve it correctly.
• Common mistakes
  • Confusing half-diminished (ø7) with fully diminished (°7). The difference is the size of the seventh above the root.
  • Treating any chord with a seventh as “V7.” Many scale degrees can support seventh chords.
  • Misspelling the seventh enharmonically (especially in diminished seventh chords).

Chord Inversions and Figured Bass

What inversion means (and why it matters)

A chord is in root position when the root is in the bass. A chord is in an inversion when some other chord member (third, fifth, or seventh) is in the bass.

Inversions matter because they change:

• the sound and stability of the harmony
• the bass line shape (which is crucial in tonal style)
• how you label chords (figured bass and Roman numeral inversion symbols)

A frequent mistake is to think inversion changes the chord’s identity. It does not. C–E–G is still a C major triad whether C, E, or G is in the bass; inversion only changes the voicing and bass note.

Triad inversions

For triads, there are three positions:

• Root position: root in bass
• First inversion: third in bass
• Second inversion: fifth in bass

Figured bass: what the numbers actually mean

Figured bass is a shorthand system indicating the intervals above the bass note.

Think of it like this: if the bass note is the “reference,” the figures tell you which other chord tones appear above it, measured as generic intervals (3rd, 5th, 6th, etc.). In many contexts, some figures are omitted because they’re assumed.

For triads:

• Root position is written 5/3, usually shortened to just the Roman numeral with no figures.
• First inversion is 6/3, usually shortened to 6.
• Second inversion is 6/4.

For seventh chords, there are four positions:

• Root position: 7 (full form 7/5/3)
• First inversion: 6/5
• Second inversion: 4/3
• Third inversion: 4/2 (often written 2)

Important: the figures describe intervals above the bass, not above the root.

How to determine inversion (a reliable method)

When you see a chord on the staff:

1. Identify the chord’s pitch classes (ignore doublings at first).
2. Determine the root by arranging the notes in stacked thirds.
3. Identify the bass note (lowest sounding note).
4. Compare bass note to the chord members:
   • if bass is root, it’s root position
   • if bass is third, first inversion
   • if bass is fifth, second inversion
   • if bass is seventh (only for seventh chords), third inversion

Examples: triad inversions

Use a C major triad (C–E–G):

• Root position: C in bass (C–E–G). Figured bass 5/3 (often unmarked).
• First inversion: E in bass (E–G–C). Figured bass 6/3 (often shown as 6).
• Second inversion: G in bass (G–C–E). Figured bass 6/4.

Notice: the letters don’t change; only which one is in the bass.

Examples: seventh chord inversions

Use G7 (G–B–D–F):

• Root position: G in bass. Figured bass 7.
• First inversion: B in bass. Figured bass 6/5.
• Second inversion: D in bass. Figured bass 4/3.
• Third inversion: F in bass. Figured bass 4/2 (or 2).

Why figured bass and inversion show up in AP tasks

On the AP exam, inversion labeling is not just terminology; it affects voice-leading expectations. For example, a 6/4 sonority often behaves differently than a root-position chord in tonal style. Even when you’re not asked to write a full progression, correctly identifying inversion helps you understand what the bass is doing and what chord function is likely.

Exam Focus

• Typical question patterns
  • Given a chord, identify its inversion and supply the correct figured bass (or choose the correct inversion label).
  • Realize a Roman numeral with figures into notes (spell and voice a chord from the symbol).
  • In listening or score analysis, identify whether a harmony is in root position or inversion based on the bass.
• Common mistakes
  • Using figured bass numbers as scale degrees instead of intervals above the bass.
  • Labeling inversion by the top note rather than the bass note.
  • Mixing up 4/2 and 4/3 for seventh-chord inversions; always tie the label to which chord member is in the bass.

Roman Numeral Analysis

What Roman numeral analysis is

Roman numeral analysis labels chords by their scale-degree root in a key and indicates the chord’s quality and inversion. It answers the question: “What chord is this, and what is its role in the key?”

This matters because tonal music is organized around key-centered functions (tonic, predominant, dominant). Roman numerals give you a compact way to describe harmonic structure across many styles of common-practice music.

A common misconception is that Roman numerals name chords by absolute letter (like “C major”). Instead, they name chords relative to the key (like “I” in C major, D major, or A-flat major). That’s why Roman numerals are powerful: they show patterns that transpose.

The basic components of a Roman numeral label

A complete Roman numeral label typically includes:

1. The Roman numeral (I, ii, V, etc.), showing the scale degree of the chord’s root
2. Case (uppercase or lowercase), showing triad quality
   • uppercase: major
   • lowercase: minor
3. Quality symbols for altered triads
   • diminished: small circle symbol (often written as °)
   • augmented: plus symbol (written as +)
4. Inversion figures (figured bass numbers)
5. Added sevenths (7, 6/5, 4/3, 4/2), or symbols like ø for half-diminished

Case and symbols: how to show chord quality

Here’s how quality is encoded in typical AP-style notation:

• Major triad: uppercase numeral (V)
• Minor triad: lowercase numeral (v)
• Diminished triad: lowercase with diminished symbol (vii°)
• Augmented triad: uppercase with plus (III+)

For seventh chords:

• dominant seventh: V7 (quality is implied by the scale degree in major/minor contexts)
• half-diminished seventh: viiø7 (or iiø7 in minor)
• fully diminished seventh: vii°7
• major seventh: I7 or IV7 (in major, diatonic)

How to analyze a chord with Roman numerals (a step-by-step workflow)

When you’re given a chord in notation and asked to label it:

1. Identify the key (look at the key signature, accidentals, and melodic/harmonic context).
2. List the chord tones (spell what notes are present; ignore doublings).
3. Find the root by stacking in thirds.
4. Determine chord quality (major, minor, diminished, augmented; and for seventh chords, the seventh quality).
5. Determine inversion by the bass note and choose the figured bass.
6. Convert the root to a scale degree in the key and write the correct Roman numeral (case and symbols included).

If you do these steps in order, you avoid the two classic traps: guessing the numeral from the bass line and forgetting that inversion does not change the root.

Accidentals in Roman numeral analysis

When a chord root is chromatically altered relative to the key, you show this with accidentals before the Roman numeral (for example, flat-six would be written as a flat sign before VI). This is common in mixture and chromatic harmony, but even within the triads-and-sevenths topic, you may see altered leading tones in minor (raised scale degree 7) reflected in the chord spelling and function.

The key idea: Roman numerals are scale-degree labels. If the scale degree is raised or lowered, the numeral reflects that alteration.

Examples (worked analyses)

Example 1: In C major, analyze the chord D–F–A

1. Key: C major.
2. Notes: D, F, A.
3. Stack in thirds: D–F–A is already stacked.
4. Quality: D to F is a minor third; F to A is a major third, so it’s a minor triad.
5. Inversion: if D is in the bass, it’s root position.
6. Scale degree: D is scale degree 2 in C major.

Label: ii (root position, no figures needed).

Example 2: In C major, analyze the chord B–D–F–A with B in the bass

1. Key: C major.
2. Notes: B, D, F, A.
3. Stack in thirds: B–D–F–A.
4. Quality: diminished triad (B–D–F) plus a minor seventh (A above B), so half-diminished seventh.
5. Inversion: B is in the bass, so root position.
6. Scale degree: B is scale degree 7.

Label: viiø7.

Example 3: In C major, analyze G–C–E with G in the bass

1. Key: C major.
2. Notes: G, C, E.
3. Stack in thirds: reorder to C–E–G, so the root is C.
4. Quality: C–E–G is major.
5. Inversion: G (the fifth of C) is in the bass, so second inversion.
6. Scale degree: C is scale degree 1.

Label: I6/4.

Why Roman numerals connect everything in this unit

Roman numeral analysis is where triad quality, seventh-chord quality, and inversion all come together:

• triad and seventh chord types tell you what quality symbols and case to use
• inversion tells you which figured bass numbers to attach
• scale degree tells you which numeral to write

If any one piece is wrong (for example, you misidentify the root), the entire label becomes inconsistent.

Exam Focus

• Typical question patterns
  • Given a notated excerpt, label chords with Roman numerals including inversion figures (triads and seventh chords).
  • Given a Roman numeral progression, realize it by writing the correct chord tones (sometimes in four voices).
  • Identify the correct Roman numeral for a chord that includes accidentals (especially in minor, where raised scale degree 7 affects V and vii chords).
• Common mistakes
  • Choosing the Roman numeral based on the bass note instead of the chord root.
  • Using incorrect case (writing V when the chord is minor, or v when the chord is major).
  • Forgetting inversion figures for inverted chords, especially seventh-chord inversions (6/5, 4/3, 4/2).