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<h1>Chords</h1>
<p>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 analysis, and tells you what voicings and extensions will work in a given context. The chord symbol is a compact description of its construction; being able to decode and rebuild any symbol is a fundamental skill.</p>

<h2>Intervals — The Building Blocks</h2>

<table>
  <thead><tr><th>Interval name</th><th>Abbreviation</th><th>Semitones</th><th>Example from C</th></tr></thead>
  <tbody>
    <tr><td>Minor 2nd (half step)</td><td>m2</td><td>1</td><td>C → D♭</td></tr>
    <tr><td>Major 2nd (whole step)</td><td>M2</td><td>2</td><td>C → D</td></tr>
    <tr><td>Minor 3rd</td><td>m3</td><td>3</td><td>C → E♭</td></tr>
    <tr><td>Major 3rd</td><td>M3</td><td>4</td><td>C → E</td></tr>
    <tr><td>Perfect 4th</td><td>P4</td><td>5</td><td>C → F</td></tr>
    <tr><td>Tritone (aug 4th / dim 5th)</td><td>TT</td><td>6</td><td>C → F#/G♭</td></tr>
    <tr><td>Perfect 5th</td><td>P5</td><td>7</td><td>C → G</td></tr>
    <tr><td>Minor 6th (aug 5th)</td><td>m6</td><td>8</td><td>C → A♭/G#</td></tr>
    <tr><td>Major 6th</td><td>M6</td><td>9</td><td>C → A</td></tr>
    <tr><td>Minor 7th</td><td>m7</td><td>10</td><td>C → B♭</td></tr>
    <tr><td>Major 7th</td><td>M7</td><td>11</td><td>C → B</td></tr>
    <tr><td>Octave</td><td>P8</td><td>12</td><td>C → C</td></tr>
  </tbody>
</table>

<h2>Triads</h2>
<p>Root, third, and fifth — the basic building block:</p>

<table>
  <thead><tr><th>Triad type</th><th>Construction</th><th>Semitones</th><th>Example (C)</th><th>Sound</th></tr></thead>
  <tbody>
    <tr><td>Major</td><td>Root + M3 + P5</td><td>4 + 3</td><td>C E G</td><td>Bright, resolved, stable</td></tr>
    <tr><td>Minor</td><td>Root + m3 + P5</td><td>3 + 4</td><td>C E♭ G</td><td>Darker, introspective, stable</td></tr>
    <tr><td>Diminished</td><td>Root + m3 + d5</td><td>3 + 3</td><td>C E♭ G♭</td><td>Tense, unstable — wants to resolve</td></tr>
    <tr><td>Augmented</td><td>Root + M3 + A5</td><td>4 + 4</td><td>C E G#</td><td>Ambiguous, floating — symmetrical, no clear root</td></tr>
    <tr><td>Suspended 4th</td><td>Root + P4 + P5</td><td>5 + 2</td><td>C F G</td><td>Unresolved, ambiguous (no 3rd)</td></tr>
    <tr><td>Suspended 2nd</td><td>Root + M2 + P5</td><td>2 + 5</td><td>C D G</td><td>Open, floating (no 3rd)</td></tr>
  </tbody>
</table>

<h2>Seventh Chords</h2>
<p>Add a fourth note (a seventh above the root) for the harmonic richness that jazz and modern harmony rely on:</p>

<table>
  <thead><tr><th>Chord type</th><th>Symbol</th><th>Construction</th><th>Example (C)</th><th>Typical function</th></tr></thead>
  <tbody>
    <tr><td>Major 7th</td><td>maj7, Δ7</td><td>M3 + P5 + M7</td><td>C E G B</td><td>Tonic — stable, lush</td></tr>
    <tr><td>Dominant 7th</td><td>7</td><td>M3 + P5 + m7</td><td>C E G B♭</td><td>Dominant — strong pull to resolution (tritone in 3rd and 7th)</td></tr>
    <tr><td>Minor 7th</td><td>m7, −7</td><td>m3 + P5 + m7</td><td>C E♭ G B♭</td><td>Pre-dominant (ii chord) or tonic (vi chord)</td></tr>
    <tr><td>Minor-major 7th</td><td>m(maj7), mΔ7</td><td>m3 + P5 + M7</td><td>C E♭ G B</td><td>Tonic in minor key (Im with raised 7th) — exotic, unstable</td></tr>
    <tr><td>Half-diminished</td><td>ø7, m7♭5</td><td>m3 + d5 + m7</td><td>C E♭ G♭ B♭</td><td>ii° in minor key — pre-dominant</td></tr>
    <tr><td>Diminished 7th</td><td>°7, dim7</td><td>m3 + d5 + d7</td><td>C E♭ G♭ B♭♭(A)</td><td>Diminished — symmetric, can resolve to any chord a half step above any note</td></tr>
    <tr><td>Major 6th</td><td>6, maj6</td><td>M3 + P5 + M6</td><td>C E G A</td><td>Tonic substitute in jazz (same notes as Am7 in root position)</td></tr>
    <tr><td>Minor 6th</td><td>m6</td><td>m3 + P5 + M6</td><td>C E♭ G A</td><td>Minor tonic substitute</td></tr>
  </tbody>
</table>

<h2>Extended Chords</h2>
<p>Continue stacking thirds above the seventh to get 9ths, 11ths, and 13ths. These numbers refer to the same intervals as the 2nd, 4th, and 6th, raised by one octave:</p>
<pre>
9th  = same pitch class as 2nd (M2 or m2 up an octave from root)
11th = same pitch class as 4th (P4 or #4 up an octave)
13th = same pitch class as 6th (M6 or m6 up an octave)

Common extended chords:
Cmaj9:   C E G B D      (maj7 + major 9th)
C9:      C E G B♭ D     (dom7 + major 9th)
Cm9:     C E♭ G B♭ D    (m7 + major 9th)
C7#11:   C E G B♭ F#    (Lydian dominant — tritone against root)
C13:     C E G B♭ D A   (dom7 + 9th + 13th — leave out 11th usually)
Cmaj13:  C E G B D F# A (all seven notes — rarely voiced complete)
</pre>

<h2>Voicing: Which Notes to Play</h2>
<p>In practice, extended chord voicings leave some notes out. The guiding principle is that the 3rd and 7th define the chord's identity:</p>

<table>
  <thead><tr><th>Note</th><th>Include?</th><th>Why</th></tr></thead>
  <tbody>
    <tr><td>Root</td><td>Sometimes (often bass player's job)</td><td>Bass covers it — rootless voicings are common in jazz piano</td></tr>
    <tr><td>3rd</td><td>Always</td><td>Defines major vs minor quality</td></tr>
    <tr><td>5th</td><td>Often omit</td><td>Least interesting, adds little colour (unless altered)</td></tr>
    <tr><td>7th</td><td>Always (in jazz)</td><td>Defines dominant vs major vs minor character</td></tr>
    <tr><td>9th, 11th, 13th</td><td>Selective</td><td>Colour and context — choose what serves the melody and voice leading</td></tr>
  </tbody>
</table>

<h2>Inversions</h2>
<pre>
C major triad:
  Root position: C E G     (root in bass)
  1st inversion: E G C     (3rd in bass) — written C/E
  2nd inversion: G C E     (5th in bass) — written C/G

Seventh chord inversions:
  Cmaj7 root:   C E G B
  Cmaj7 1st:    E G B C   (3rd in bass) — C/E
  Cmaj7 2nd:    G B C E   (5th in bass) — C/G
  Cmaj7 3rd:    B C E G   (7th in bass) — C/B
</pre>
<p>Inversions change the weight and stability. Second inversion (6/4 chord) sounds unstable over a non-root bass note — useful as a suspension before cadential resolution. Slash chords in pop (G/B, D/F#) specify the bass note of an inverted chord.</p>

<h2>Chord Symbol Decoding</h2>

<table>
  <thead><tr><th>Symbol</th><th>Meaning</th><th>Notes (from C)</th></tr></thead>
  <tbody>
    <tr><td>C</td><td>C major triad</td><td>C E G</td></tr>
    <tr><td>Cm</td><td>C minor triad</td><td>C E♭ G</td></tr>
    <tr><td>C7</td><td>C dominant 7th</td><td>C E G B♭</td></tr>
    <tr><td>Cmaj7 or CΔ</td><td>C major 7th</td><td>C E G B</td></tr>
    <tr><td>Cm7</td><td>C minor 7th</td><td>C E♭ G B♭</td></tr>
    <tr><td>C7sus4</td><td>C dominant, suspended 4th</td><td>C F G B♭</td></tr>
    <tr><td>C7♭9</td><td>C dominant, flat 9</td><td>C E G B♭ D♭</td></tr>
    <tr><td>C7#9</td><td>C dominant, sharp 9 ("Hendrix chord")</td><td>C E G B♭ D#</td></tr>
    <tr><td>Cadd9</td><td>C major triad + 9th (no 7th)</td><td>C D E G</td></tr>
    <tr><td>C/E</td><td>C major in 1st inversion (E in bass)</td><td>E (bass) C E G</td></tr>
  </tbody>
</table>

<h2>References</h2>
<ul>
  <li>Levine — <em>The Jazz Theory Book</em></li>
  <li>Rawlins &amp; Bahha — <em>Jazzology</em></li>
  <li><a href="https://www.musictheory.net/lessons/40" target="_blank" rel="noopener">musictheory.net — Chord Building ↗</a></li>
</ul>
