How many semitones is a major thirteenth?

A Major Thirteenth spans 21 semitones: C – A. Count the semitones of any interval with the interval calculator.

What notes are in a 13 chord?

In theory root, third, fifth, seventh, ninth, eleventh and thirteenth. In practice the fifth and eleventh are usually omitted, leaving root, third, seventh and thirteenth.

What is a compound interval?

Any interval wider than an octave. A Major Thirteenth is an octave plus a major sixth, and it keeps the character of that simple interval in a more open, less congested form.

How do I play Major Thirteenth?

On guitar the handiest shape is Two strings up, A 3 · G 14, read as string and fret; the instrument panel draws it from any starting note with the other shapes. On the piano count 21 semitones up from any key, black keys included. Play the notes together for the harmonic form, one after the other for the melodic form.

What is the inversion of Major Thirteenth?

The inversion of Major Thirteenth is the Minor Third: put the lower note an octave higher and the distance that remains is the inversion. The two always add up to an octave, 21 semitones and 3 semitones, and swap their qualities between major and minor, or keep perfect as perfect.

Major Thirteenth Interval: How It Sounds, with Song Examples

Play it on your instrument

Loading the keyboard…

From

On the piano, from every note

From	Notes	Play it on your instrument
C	C – A
C#	C# – A#
D	D – B
Eb	Eb – C
E	E – C#
F	F – D
F#	F# – D#
G	G – E
Ab	Ab – F
A	A – F#
Bb	Bb – G
B	B – G#

Tap a key or a fret to hear it.

Number and quality

An interval has two names. The number counts the letter names from the lower note to the upper one, and the quality counts the semitones inside that number. Major Thirteenth spans 13 letter names, which makes it a thirteenth, and 21 semitones, which makes it major.

DLetter
ELetter
FLetter
GLetter
ALetter
BLetter
CLetter
DLetter
ELetter
FLetter
GLetter
21 semitones

Read on: number and quality · inversion · compound intervals · consonance and dissonance

Every thirteenth

A thirteenth can take these qualities, one semitone apart; choose one to see the upper note move and hear the pair.

Where it lives

Major Thirteenth is in every chord whose formula includes 13M from the root, in every scale that includes it from the tonic, and between these pairs of notes in a major key.

Chords built with it

C13C · E · G · Bb · D · A
Cmaj13C · E · G · B · D · A
Cm13C · Eb · G · Bb · D · A

Scales that contain it

C MajorC · D · E · F · G · A · B
C Melodic MinorC · D · Eb · F · G · A · B
C DorianC · D · Eb · F · G · A · Bb
C LydianC · D · E · F# · G · A · B
C MixolydianC · D · E · F · G · A · Bb
C Major PentatonicC · D · E · G · A
C Major BluesC · D · Eb · E · G · A
C ChromaticC · Db · D · Eb · E · F · Gb · G · Ab · A · Bb · B
C Lydian DominantC · D · E · F# · G · A · Bb
C Half-Whole DiminishedC · Db · Eb · E · F# · G · A · Bb

In C major

C–A
D–B
F–D
G–E

Related intervals

The intervals one step from Major Thirteenth: its inversion, the same sound spelled differently, its simple or compound form, and its nearest neighbours in size.

Minor Third3m · 3 semitones · C – Eb
Inversion: together they make an octave
Major Sixth6M · 9 semitones · C – A
The simple form, an octave narrower
Minor Thirteenth13m · 20 semitones · C – Ab
One size away
Perfect Twelfth12P · 19 semitones · C – G
One size away

Open it in a tool

Understanding Major Thirteenth

Names and symbols

Major Thirteenth is written M13, 13M: the letter is the quality, the number the size. Chord formulas on this site write the number first, as tonal does.

A compound interval is a simple interval plus an octave, and the two names are used interchangeably in chord symbols: a 9th in a chord is the 2nd of the scale an octave up, an 11th the 4th, a 13th the 6th. The compound name says the note sits above the seventh.

How it sounds

A Major Thirteenth spans 21 semitones: C – A. It is an octave plus a major sixth, and compound intervals keep the quality of the simple interval inside them while losing much of its edge — the extra octave gives the two notes room to stop interfering with each other.

Warm and wide — the furthest extension in common use, and the most consonant of them.

How it is used

A 13 chord stacks the whole series up to the thirteenth, though in practice pianists drop the fifth and often the ninth and voice only what matters: root, third, seventh, thirteenth.

Learn this properly

Chapter 5: Intervals

Common questions

How many semitones is a major thirteenth?: A Major Thirteenth spans 21 semitones: C – A. Count the semitones of any interval with the interval calculator.
What notes are in a 13 chord?: In theory root, third, fifth, seventh, ninth, eleventh and thirteenth. In practice the fifth and eleventh are usually omitted, leaving root, third, seventh and thirteenth.
What is a compound interval?: Any interval wider than an octave. A Major Thirteenth is an octave plus a major sixth, and it keeps the character of that simple interval in a more open, less congested form.
How do I play Major Thirteenth?: On guitar the handiest shape is Two strings up, A 3 · G 14, read as string and fret; the instrument panel draws it from any starting note with the other shapes. On the piano count 21 semitones up from any key, black keys included. Play the notes together for the harmonic form, one after the other for the melodic form.
What is the inversion of Major Thirteenth?: The inversion of Major Thirteenth is the Minor Third: put the lower note an octave higher and the distance that remains is the inversion. The two always add up to an octave, 21 semitones and 3 semitones, and swap their qualities between major and minor, or keep perfect as perfect.