Chords

A chord is three or more notes played simultaneously to create harmony. Understanding chord construction — how chords are built from intervals — lets you figure out any chord by ear or by analysis, and tells you what voicings and extensions will work.

Triads

The basic building block: a root, a third, and a fifth. Four types:

Major:      Root + M3 + P5        (4 + 3 semitones)   C E G
Minor:      Root + m3 + P5        (3 + 4 semitones)   C E♭ G
Diminished: Root + m3 + d5        (3 + 3 semitones)   C E♭ G♭
Augmented:  Root + M3 + A5        (4 + 4 semitones)   C E G#

Major sounds bright and resolved. Minor sounds darker and introspective. Diminished sounds unstable, tense — it wants to resolve. Augmented sounds ambiguous and floaty; it's symmetrical (three major thirds stacked), which means it has no clear root.

Seventh Chords

Add a fourth note (a seventh above the root) to get the harmonic richness that jazz relies on:

Major 7th (maj7):    Root + M3 + P5 + M7    C E G B       Cmaj7
Dominant 7th (7):    Root + M3 + P5 + m7    C E G B♭      C7
Minor 7th (m7):      Root + m3 + P5 + m7    C E♭ G B♭     Cm7
Minor-major 7th:     Root + m3 + P5 + M7    C E♭ G B      Cm(maj7)
Half-diminished (ø): Root + m3 + d5 + m7    C E♭ G♭ B♭    Cm7♭5
Diminished 7th (°7): Root + m3 + d5 + d7    C E♭ G♭ B♭♭  Cdim7

The dominant seventh chord (C7) is the most harmonically active — the tritone between its major 3rd and minor 7th (E and B♭ in C7) creates tension that resolves strongly to the chord a fifth below (F). This is the engine of tonal music.

Extended Chords

Continue stacking thirds above the seventh to get 9ths, 11ths, and 13ths:

9th above root:  M9 or m9 (same as major/minor 2nd, up an octave)
11th above root: P11 or #11 (same as perfect/augmented 4th, up an octave)
13th above root: M13 or m13 (same as major/minor 6th, up an octave)

Cmaj9:    C E G B D
C9:       C E G B♭ D
Cm9:      C E♭ G B♭ D
C7#11:    C E G B♭ F#   (Lydian dominant sound — the tritone against the root)
C13:      C E G B♭ D A  (typically voiced without the 11th)

In practice, extended chord voicings leave out some notes. A pianist playing Cmaj9 might play C G B D (no 5th) or E B D (rootless voicing for jazz ensemble use). The 3rd and 7th are the identity of the chord — the rest is colour.

Inversions

Put a chord note other than the root in the bass:

C major root position:  C E G  (root in bass)
First inversion:        E G C  (3rd in bass) — written C/E
Second inversion:       G C E  (5th in bass) — written C/G

Inversions change the weight and stability of the chord. A 6/4 chord (second inversion) sounds unstable over a bass note that isn't the root — it works well as a suspension before a resolution. Slash chords in pop (G/B, Am/E) specify which inversion to play.

Suspended Chords

sus2: Root + M2 + P5     C D G    (replace 3rd with 2nd)
sus4: Root + P4 + P5     C F G    (replace 3rd with 4th)

Suspended chords have no 3rd, so they're neither major nor minor — ambiguous and floating. They typically resolve when the suspension moves to the 3rd. A sus4 chord (G7sus4) before a dominant chord (G7) before the tonic (C) is a classic pre-dominant move.