A 13th chord is built by stacking thirds until the chord reaches the 13th: root, 3rd, 5th, 7th, 9th, 11th, and 13th. The standard dominant 13th chord formula is 1–3–5–♭7–9–11–13. For example, C13 contains C–E–G–B♭–D–F–A.
That seven-note spelling describes the complete chord. In actual guitar and piano playing, several tones are usually omitted so the voicing remains playable and clear. Understanding the underlying extended-chord structure helps you recognize which notes define the harmony and which ones are optional.
What Is the 13th Chord Formula?
The complete dominant 13th chord formula is 1–3–5–♭7–9–11–13. An unqualified chord symbol such as G13 normally means a dominant 13th chord, so it includes a major 3rd and a minor 7th.
The numbers refer to scale degrees measured from the root. Because chord extensions continue beyond the octave, the 9th is the same letter name as the 2nd, the 11th matches the 4th, and the 13th matches the 6th. Their higher numbers show that they belong to an extended harmony built above a seventh chord.
| Chord type | Formula | Notes with C as root | Defining quality |
|---|---|---|---|
| C13 | 1–3–5–♭7–9–11–13 | C–E–G–B♭–D–F–A | Major 3rd, minor 7th |
| Cmaj13 | 1–3–5–7–9–11–13 | C–E–G–B–D–F–A | Major 3rd, major 7th |
| Cm13 | 1–♭3–5–♭7–9–11–13 | C–E♭–G–B♭–D–F–A | Minor 3rd, minor 7th |
The 3rd and 7th do most of the work in distinguishing these chord qualities. If seventh-chord construction is unfamiliar, the dominant seventh formula explains the four-note foundation underneath a dominant 13th.
How Do You Build a 13th Chord?
Build a 13th chord by choosing a root and adding every other note from its scale until you reach the 13th. This process stacks six thirds above the root and produces seven different pitch classes.
Building C13 step by step
Start with the C major scale:
C–D–E–F–G–A–B
Then apply the dominant 13 formula:
- Root: C
- Major 3rd: E
- Perfect 5th: G
- Minor 7th: B♭
- Major 9th: D
- Perfect 11th: F
- Major 13th: A
The result is C–E–G–B♭–D–F–A. The flattened seventh is what makes C13 a dominant chord rather than Cmaj13. This same stacked-third process is covered more broadly in how chords are built.
Building G13 step by step
Apply the same formula to G:
G13 = G–B–D–F–A–C–E
G is the root, B is the major 3rd, D is the perfect 5th, and F is the minor 7th. A, C, and E are the 9th, 11th, and 13th. In functional harmony, G13 often resolves to a chord rooted on C because G is the dominant of C.
The method is cumulative: a theoretical 13th chord contains the seventh and the lower extensions, not merely a triad plus one high note. Compare that construction with the 9th chord formula to see how the same stack grows one extension at a time.
What Is the Difference Between 13, Maj13, and Min13 Chords?
A 13 chord has a major 3rd and minor 7th, a maj13 chord has a major 3rd and major 7th, and a min13 chord has a minor 3rd and minor 7th. The 9th, 11th, and 13th are natural unless the chord symbol explicitly alters them.
Dominant 13 chords
The plain symbol C13 means C dominant 13, not C major 13. Its B♭ creates dominant tension, while E identifies the chord as major-based. C13 commonly points toward an F chord, though context can support other resolutions.
Major and minor 13 chords
Cmaj13 uses B natural instead of B♭, giving it a more stable major-seventh color. Cm13 changes E to E♭ while retaining B♭, producing a minor extended sound. Clear guitar chord symbols matter here: “maj” modifies the seventh, whereas “m” or “min” modifies the third.
Alterations can create formulas such as 13♭9 or 13♯11. Those symbols replace the relevant natural extension; they do not change the basic meaning of the root, 3rd, or 7th unless another symbol says so.
Which Notes Can You Omit From a 13th Chord?
In a practical 13th-chord voicing, preserve the 3rd, 7th, and 13th whenever possible. The root is useful unless a bass player supplies it, while the 5th, 9th, and 11th can often be omitted without obscuring the chord’s identity.
Essential and optional chord tones
For C13, a compact voicing might use C–E–B♭–A:
- C establishes the root.
- E establishes the major quality.
- B♭ establishes the dominant seventh.
- A supplies the characteristic 13th.
The perfect 5th, G, adds little information because it does not determine whether the chord is major or minor. The 9th, D, adds color but is not required for listeners to hear the 13th quality. On a six-string instrument, note selection is unavoidable because the complete chord has seven pitch classes; guitar chord inversions can help place the retained tones in a comfortable register.
Why the natural 11th is often omitted
In C13, the natural 11th F sits a semitone above the major 3rd E when reduced into the same octave. Across adjacent octaves, E and F can form a harsh minor-ninth interval. Dominant 13 voicings therefore commonly leave out F, place it carefully, or alter it to F♯ for a C13♯11 sound.
This omission does not make the symbol incorrect. Chord symbols describe harmonic identity, while voicings determine which tones are actually distributed among the instruments. The complete formula is a construction map, not a demand that every performer sound all seven notes.
How Are 13th Chords Used in Music?
Thirteenth chords add color and tension to jazz, blues, funk, gospel, R&B, and other harmony-rich styles. Dominant 13 chords most often serve a dominant function, creating motion toward a tonic chord a perfect fifth below.
In a progression such as G13–Cmaj7, the defining tones move efficiently: the F in G13 can descend to E in Cmaj7, while the 13th E may remain as a shared tone. This combination of resolution and common-tone connection makes the change sound rich without requiring a dense seven-note voicing.
On guitar, compact shapes often omit the root when a bassist plays it. On piano, the left hand may play the root and 7th while the right hand supplies the 3rd, 9th, and 13th. Learning the available notes across the guitar fretboard makes it easier to create these reduced voicings instead of memorizing only one fixed shape.
A useful rule is to begin with the guide tones—the 3rd and 7th—then add the 13th. Add the root if the musical setting needs it, and add the 9th only when space allows. Treat the 5th and natural 11th as optional in an ordinary dominant 13 voicing.
Frequently Asked Questions
What notes are essential in a 13th chord?
The 3rd, 7th, and 13th are the most important notes because they communicate the chord quality and its characteristic extension. Include the root when no bass instrument or other performer establishes it.
Is a 13th chord the same as a sixth chord?
No. The 13th and 6th use the same scale degree in different octaves, but the chord symbols imply different harmonic structures. C6 is normally C–E–G–A, while a complete C13 includes a minor 7th and the lower extensions: C–E–G–B♭–D–F–A.
Why is the 11th often omitted from a dominant 13 chord?
The natural 11th can clash with the major 3rd because the two tones are a semitone apart by pitch class. Removing the 11th usually makes the voicing clearer while retaining the dominant quality and 13th color.
What is the difference between C13 and Cmaj13?
C13 contains B♭, the minor 7th, and normally functions as a dominant chord. Cmaj13 contains B natural, the major 7th, and has a major-seventh quality.
Can a guitar play a complete seven-note 13th chord?
A standard six-string guitar cannot sound seven different chord tones at once without doubling, so it cannot play the complete seven-pitch formula simultaneously. Guitarists use reduced voicings that retain the 3rd, 7th, and 13th while omitting less essential tones.
Liam Turner is a guitar theory writer and chord analysis specialist at Chord Calculator. He focuses on chord construction, music theory, scale relationships, harmony tools, and guitar learning resources for musicians, producers, songwriters, and beginners. Liam creates practical, easy-to-follow content around chord progressions, interval formulas, key analysis, and interactive music tools to help users better understand harmony, songwriting, and instrument practice.