Chords: Triads & Seventh Chords

Music Theory Fundamentals

Chapter 5 · Chords: Triads & Seventh Chords

A chord is simply several intervals stacked on top of each other and sounded together. This chapter builds every basic chord type directly out of Chapter 4's own third intervals — and shows that the most common chord in all of Western music isn't an arbitrary invention, but a direct mathematical consequence of Chapter 1's own overtone series.

Triads: Stacking Two Thirds

A triad is built from a root note plus two stacked thirds. Which specific quality of third goes where determines the triad's own real quality:

Triad quality	Lower third	Upper third	Example
Major	Major 3rd	Minor 3rd	C–E–G
Minor	Minor 3rd	Major 3rd	A–C–E
Diminished	Minor 3rd	Minor 3rd	B–D–F
Augmented	Major 3rd	Major 3rd	D–F♯–A♯

The Major Triad Is Hiding in the Overtone Series

Take the 4th, 5th, and 6th harmonics of any real fundamental frequency — 4f, 5f, and 6f. Their real ratio, 4:5:6, is exactly a major triad: the interval from the 4th to the 5th harmonic is a real 5:4 ratio (a major third, per Chapter 1's own table), the interval from the 5th to the 6th harmonic is a real 6:5 ratio (a minor third), and the interval from the 4th to the 6th harmonic is a real 6:4 = 3:2 ratio (a perfect fifth, also from Chapter 1). Stack a major third and a minor third on top of each other, per this chapter's own table above, and you get exactly a major triad.

A direct echo of Chapter 1

The major triad isn't a cultural convention layered on top of physics — it's already sitting inside the overtone series of a single vibrating string or air column, three real harmonics apart. This is a strong real reason the major triad sounds so stable across virtually every musical tradition that uses harmony at all: any single fundamental tone already implies it.

Seventh Chords: One More Third on Top

Stack one further third on top of any triad, and you get a seventh chord — named for the real interval this new top note forms with the root. Five real, standard types cover the vast majority of seventh chords in practice:

Seventh chord	Triad	Added 7th	Example
Major 7th	Major	Major 7th	C–E–G–B
Dominant 7th	Major	Minor 7th	C–E–G–B♭
Minor 7th	Minor	Minor 7th	D–F–A–C
Half-diminished 7th	Diminished	Minor 7th	B–D–F–A
Diminished 7th	Diminished	Diminished 7th	B–D–F–A♭

Historically, sevenths began as real embellishing tones that destabilized an otherwise-stable triad, demanding resolution — a real tension this course revisits directly when it covers cadences.

Hands-On Exercises

Exercise 1

Using this chapter's own triad-construction table, build a diminished triad starting on C, and identify the two real interval qualities stacked to produce it.

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Exercise 2

A dominant 7th chord is a major triad plus a minor 7th. Build the dominant 7th chord on G (i.e. G7), and name all four notes.

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Exercise 3

Using this chapter's own real 4:5:6 harmonic-ratio explanation, show the arithmetic confirming that the interval between the 4th and 6th harmonics really is a perfect fifth (3:2 ratio), not some other interval.

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Chapter 5 Quick Reference

Triads stack two thirds: major (M3+m3), minor (m3+M3), diminished (m3+m3), augmented (M3+M3)
The real 4:5:6 harmonic ratio (4th, 5th, 6th overtones) is exactly a major triad — a direct mathematical consequence of Chapter 1's own overtone series
Seventh chords add one more third on top of a triad: major 7th, dominant 7th, minor 7th, half-diminished 7th, diminished 7th
Sevenths historically functioned as tension requiring resolution — revisited when this course covers cadences
Next chapter: Rhythm, Meter & Time Signatures