A 13th chord is an eleventh chord with the thirteenth added on top. The formula is: root + major third + perfect fifth + seventh + ninth + eleventh + thirteenth. That’s seven distinct note names, making it the richest and most complete extended chord commonly used in music.
The thirteenth is the same note as the sixth, but one octave higher. If you have a C11 chord and add the thirteenth, you’re adding an A — but the A sits three octaves above the root, creating the interval of 21 semitones. A Cmaj13 contains all those notes: C, E, G, B, D, F, A (which is, remarkably, every note of the C major scale).
13th chords are the epitome of jazz sophistication. Because they contain so many notes, they require careful, selective voicing on guitar. Most players omit multiple notes to keep the chord playable, focusing on the most colorful extensions (the 7th, 9th, 13th) and omitting some of the basic notes (the 3rd or 5th) that other instruments in an ensemble are likely covering.
How the 13th Chord Formula Works
A 13th chord builds on an eleventh chord by adding one final note. Let’s build a Cmaj13 to see the full structure.
Start with Cmaj11: C (root), E (major third, 4 semitones), G (perfect fifth, 7 semitones), B (major seventh, 11 semitones), D (major ninth, 14 semitones), F (perfect eleventh, 17 semitones). Now add the thirteenth: A is 9 semitones above C, but we want it in the upper octave. Count 21 semitones: C to C# (1), C# to D (2), D to D# (3), D# to E (4), E to F (5), F to F# (6), F# to G (7), G to G# (8), G# to A (9), A to A# (10), A# to B (11), B to C (12), C to C# (13), C# to D (14), D to D# (15), D# to E (16), E to F (17), F to F# (18), F# to G (19), G to G# (20), G# to A (21). That A is your thirteenth.
So Cmaj13 = C, E, G, B, D, F, A. That’s all seven notes of the C major scale. A complete diatonic harmony. Remarkably, playing every note of the major scale stacked as intervals creates a thirteenth chord.
Understanding how extended chords are structured shows that 13th chords represent the completion of basic diatonic harmony. Beyond the 13th, you’re adding more extensions (which repeat the pattern) or getting into more exotic territory.
The Three Types of 13th Chords
Major 13th (Cmaj13): Major chord + major seventh + ninth + eleventh + thirteenth. Formula: root + major third + perfect fifth + major seventh + major ninth + perfect eleventh + major thirteenth. Cmaj13 = C, E, G, B, D, F, A. Creates an open, sophisticated, complete harmonic sound.
Dominant 13th (C13): Major chord + minor seventh + ninth + eleventh + thirteenth. Formula: root + major third + perfect fifth + minor seventh + major ninth + perfect eleventh + major thirteenth. C13 = C, E, G, Bb, D, F, A. Creates a bluesy, jazzy, sophisticated sound.
Minor 13th (Cm13): Minor chord + minor seventh + ninth + eleventh + thirteenth. Formula: root + minor third + perfect fifth + minor seventh + major ninth + perfect eleventh + major thirteenth. Cm13 = C, Eb, G, Bb, D, F, A. Creates a dark, complex, jazzy sound.
The thirteenth remains the same (major thirteenth, 21 semitones) in all three. The chord quality and seventh quality determine the overall character. Each variation has its own sophisticated, jazz-influenced sound.
In practice, 13th chord voicings on guitar almost always omit multiple notes. A Cmaj13 might be voiced with just the root, seventh, ninth, and thirteenth (C, B, D, A), skipping the third, fifth, and eleventh. This focuses the voicing on the most colorful, extended sounds while keeping it playable.
Building 13th Chords on Guitar
Playing 13th chords on guitar is all about strategic voicing choices. Because the chord has seven notes and the guitar has six strings (or seven with extended instruments), you must choose which notes matter most for your context.
A jazz guitarist might voice a C13 as: C on the low E string, Bb (the seventh) on the D string, D (the ninth) on the G string, and A (the thirteenth) on the high E string. That’s four notes emphasizing the color tones (7th, 9th, 13th) and the root. The listener hears a sophisticated C13 without needing all seven notes.
Another voicing might emphasize different notes: E (third), G (fifth), B (seventh), D (ninth) — omitting the root and eleventh. As long as the thirteenth is present, the chord is technically a 13th. But for clarity, you usually want at least the root to anchor the voicing.
When building extended chords, experienced jazz musicians develop an intuition for which notes to keep and which to omit. The principle is: keep the root (usually), keep the seventh (color tone), keep the ninth (color tone), and definitely keep the thirteenth (defines the chord). The third and fifth are optional because other ensemble members likely have those covered.
Common 13th Chord Examples
Here are 13th chords in different keys with their full note content:
Cmaj13: C, E, G, B, D, F, A
C13: C, E, G, Bb, D, F, A
Cm13: C, Eb, G, Bb, D, F, A
Gmaj13: G, B, D, F#, A, C, E
G13: G, B, D, F, A, C, E
Gm13: G, Bb, D, F, A, C, E
Dmaj13: D, F#, A, C#, E, G, B
D13: D, F#, A, C, E, G, B
Each 13th chord contains the most complete diatonic harmony possible within a single chord. They sound rich, sophisticated, and complete. Jazz musicians use them to create complex harmonic textures that can sustain entire sections of music without harmonic movement.
When to Use 13th Chords
13th chords are almost exclusively a jazz tool. A jazz standard might use Cmaj13, Dm13, and G13 chords in a sophisticated progression. Film composers also use 13th chords when they want lush, complex harmonic backgrounds for emotional scenes.
Because 13th chords contain so many notes, they work best when there’s space for harmonic complexity. A slow, spacious jazz ballad is perfect for 13th chords. A fast, driving rock song isn’t.
Understanding jazz chord theory requires understanding that extended chords like 13ths aren’t about playing all the notes — they’re about choosing voicings that emphasize the extensions while maintaining harmonic clarity. A well-voiced 13th chord with four notes can sound richer than a poorly voiced one with all seven.
Interestingly, simpler music often sounds better than complex music. A basic I-IV progression is more memorable than a I13-IV13 progression. 13th chords are tools for specific contexts where harmonic sophistication adds value, not always the default choice.
Frequently Asked Questions
Do I need to play all seven notes of a 13th chord?
Absolutely not. Most 13th chord voicings use four to five notes strategically selected. As long as the thirteenth is present, it’s a 13th chord. Omitting some notes keeps the voicing clear and playable.
Why are 13th chords primarily used in jazz?
13th chords represent the maximum diatonic richness — they include all seven notes of the scale. Jazz values this harmonic complexity, while rock and pop generally prefer simpler harmonic structures that leave space for melody and rhythm.
What’s the thirteenth interval in semitones?
The thirteenth is 21 semitones from the root. On the same string, that’s 21 frets. It’s the sixth scale degree, one octave higher.
Can a 13th chord function as a resting chord?
Yes. A 13th chord is complete and stable — it doesn’t need to resolve anywhere. It can sit for multiple bars or end a phrase, providing sophisticated harmonic grounding.
How is a 13th chord different from playing an entire scale?
A thirteenth chord built from a major scale uses all seven scale degrees stacked as intervals. But the voicing (which octave each note sits in) and the arrangement (which notes are omitted) make it a chord rather than a scale.
Is there a 15th or 17th chord?
Theoretically, yes. You could keep adding extensions. But 15th and 17th chords repeat notes from lower extensions (15th is another third, 17th is another fifth), so they’re rarely used. The 13th represents the practical limit of chord extension.