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Building Triads Using Intervals

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Intervals: Half Steps, Whole Steps, and Interval NumbersTriads: Major, Minor, Diminished, Augmented+2 more→→Diatonic Triads: Harmonizing Scale DegreesSeventh Chord Types and Their Qualities
triad interval construction harmony

Core Idea

A triad is constructed of two stacked thirds: a root, a third above it, and a fifth above the root. The quality of those thirds (major or minor) determines the chord quality (major, minor, diminished, augmented). Understanding triads as interval stacks clarifies how seventh chords and extensions are built.

Explainer

You know that an interval is a measured distance between two pitches — a major third spans four half steps, a minor third spans three. You also know that a triad has three notes: a root, a third, and a fifth. What you're learning here is how to see those two ideas as one: a triad is nothing more than two stacked thirds. This perspective is more powerful than memorizing chord formulas, because it makes the entire system of chords transparent and extensible.

Start with a C major triad: C–E–G. From C to E is a major third (4 half steps). From E to G is a minor third (3 half steps). So a major triad = M3 on the bottom, m3 on top. Now build a D minor triad: D–F–A. From D to F is a minor third (3 half steps). From F to A is a major third (4 half steps). Minor triad = m3 on the bottom, M3 on top. The two qualities are the same two intervals, just in reverse order. This is why major and minor triads share an interval-content but have opposite "color" — the placement of the larger interval at the bottom versus the top changes the triad's character entirely.

The other two triad qualities follow the same logic. A diminished triad stacks two minor thirds: m3 + m3. C–E♭–G♭ is an example. Because both thirds are small, the fifth from root to top note is only 6 half steps — a diminished fifth (also called a tritone). This interval is unstable and tense, which is why diminished chords have a characteristic restless quality. An augmented triad does the opposite: M3 + M3. C–E–G♯ gives you a major third from C to E, another major third from E to G♯, and a resulting augmented fifth (8 half steps) from root to top. The symmetry makes augmented chords ambiguous — you can't easily tell which note is the "root" by ear.

The real payoff of the interval-stack view is that it makes seventh chords and beyond immediately comprehensible. A seventh chord is just a triad with another third stacked on top. A major seventh chord is M3 + m3 + M3 (three thirds stacked). A dominant seventh chord (the most important in tonal music) is M3 + m3 + m3. A minor seventh chord is m3 + M3 + m3. You don't need to memorize each formula separately — you just need to know what the stacked intervals are and listen for the quality at each step. From there, adding ninths, elevenths, and thirteenths (extended chords in jazz) follows the exact same logic, just adding more thirds above. The triad-as-interval-stack is not just one way to think about chords; it is the generative structure that makes all of tonal harmony coherent.

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Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Literal Equations → Slope-Intercept Form → Point-Slope Form → Writing Linear Equations → Parallel and Perpendicular Line Slopes → Graphing Linear Equations → Piecewise Functions → Step Functions → Composition of Functions → Inverse Functions → Radical Functions and Graphs → Rational Exponents → Exponential Functions and Graphs → Logarithms Introduction → Pitch and Frequency → The Staff and Clefs → Note Names and Octaves → Accidentals: Sharps, Flats, and Naturals → Semitones and Whole Steps: Interval Building Blocks → Intervals: Half Steps, Whole Steps, and Interval Numbers → Interval Counting and Naming → Interval Quality: Major, Minor, Perfect, Augmented, Diminished → Major Scales → Minor Scales: Natural, Harmonic, and Melodic → Relative Major and Minor Keys → Parallel and Relative Major-Minor Relationships → Identifying Relative Major and Minor Keys → Reading and Writing Key Signatures → Triad Construction: Major and Minor → Building Triads Using Intervals

Longest path: 91 steps · 489 total prerequisite topics

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