How many semitones is a diminished thirteenth?

A Diminished Thirteenth spans 19 semitones: C – Abb. Count the semitones of any interval with the interval calculator.

Does a diminished thirteenth appear in real music?

Rarely, and almost always as a notational consequence of chromatic voice leading rather than as a deliberate colour.

What is a compound interval?

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

How do I play Diminished Thirteenth?

On guitar the handiest shape is Next string, B 1 · E 15, read as string and fret; the instrument panel draws it from any starting note with the other shapes. On the piano count 19 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 Diminished Thirteenth?

The inversion of Diminished Thirteenth is the Augmented Third: put the lower note an octave higher and the distance that remains is the inversion. The two always add up to an octave, 19 semitones and 5 semitones, and swap their qualities between major and minor, or keep perfect as perfect.

Diminished Thirteenth Interval: How It Sounds, with Song Examples

Play it on your instrument

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From

On the piano, from every note

From	Notes	Play it on your instrument
C	C – Abb
C#	C# – Ab
D	D – Bbb
Eb	Eb – Cbb
E	E – Cb
F	F – Dbb
F#	F# – Db
G	G – Ebb
Ab	Ab – Fbb
A	A – Fb
Bb	Bb – Gbb
B	B – Gb

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. Diminished Thirteenth spans 13 letter names, which makes it a thirteenth, and 19 semitones, which makes it diminished.

DLetter
ELetter
FLetter
GLetter
ALetter
BLetter
CLetter
DLetter
ELetter
FLetter
GLetter
19 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

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

Related intervals

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

Augmented Third3A · 5 semitones · C – E#
Inversion: together they make an octave
Perfect Twelfth12P · 19 semitones · C – G
The same sound, spelled differently
Diminished Sixth6d · 7 semitones · C – Abb
The simple form, an octave narrower
Minor Thirteenth13m · 20 semitones · C – Ab
One size away
Perfect Eleventh11P · 17 semitones · C – F
One size away

Open it in a tool

Understanding Diminished Thirteenth

Names and symbols

Diminished Thirteenth is written d13, 13d: 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 Diminished Thirteenth spans 19 semitones: C – Abb. It is an octave plus a diminished 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.

It measures the same as a perfect twelfth and belongs to chromatic spelling rather than to practical voicing.

How it is used

You will meet it in analysis of dense chromatic textures.

Learn this properly

Chapter 5: Intervals

Common questions

How many semitones is a diminished thirteenth?: A Diminished Thirteenth spans 19 semitones: C – Abb. Count the semitones of any interval with the interval calculator.
Does a diminished thirteenth appear in real music?: Rarely, and almost always as a notational consequence of chromatic voice leading rather than as a deliberate colour.
What is a compound interval?: Any interval wider than an octave. A Diminished Thirteenth is an octave plus a diminished sixth, and it keeps the character of that simple interval in a more open, less congested form.
How do I play Diminished Thirteenth?: On guitar the handiest shape is Next string, B 1 · E 15, read as string and fret; the instrument panel draws it from any starting note with the other shapes. On the piano count 19 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 Diminished Thirteenth?: The inversion of Diminished Thirteenth is the Augmented Third: put the lower note an octave higher and the distance that remains is the inversion. The two always add up to an octave, 19 semitones and 5 semitones, and swap their qualities between major and minor, or keep perfect as perfect.