Ddim: D Diminished Piano Chord

Root position: either hand, fingers low note to high
Hand	Notes	Fingers
Right	D, F, A♭	1-3-5
Left	D, F, A♭	5-3-1

Scale degree, note, and interval measured from the root.
Degree	Note	Interval from root	Semitones
1	D	Perfect unison	0
♭3	F	Minor third	3
♭5	A♭	Tritone	6

Construction

D Diminished = Root + Minor 3rd + Diminished 5th = D, F, A♭

Note	Interval	Degree
D	Root	1
F	Minor 3rd	♭3
A♭	Diminished 5th	♭5

Fingering

Note	Key color	Right hand	Left hand
D	white	thumb (1)	little finger (5)
F	white	middle finger (3)	middle finger (3)
A♭	black	little finger (5)	thumb (1)

Right hand: thumb (1) on D, middle finger (3) on F, little finger (5) on A♭.

Left hand: little finger (5) on D, middle finger (3) on F, thumb (1) on A♭.

D Diminished Inversions

Root position
D – F – A♭
1st inversion (Ddim/F)
F – A♭ – D
2nd inversion (Ddim/A♭)
A♭ – D – F

Key Signature

A Diminished chord is built from symmetrical or ambiguous intervals, so it doesn't belong to a single key and has no key signature of its own.

Chords in the Key of D Major

These are the triads built on each degree of D Major:

I — D Major (major)

Degree	Numeral	Chord	Quality
1	I	D Major	Major
2	ii	E Minor	Minor
3	iii	F♯ Minor	Minor
4	IV	G Major	Major
5	V	A Major	Major
6	vi	B Minor	Minor
7	vii°	C♯ Diminished	Diminished

How D Diminished functions in a key

The same chord takes on a different harmonic role depending on the key it appears in. Here is where D Diminished sits diatonically across the common keys:

In E♭ major, D Diminished is the vii° chord — the dominant.
In C minor, D Diminished is the ii° chord — a predominant.

Scales That Include the D Diminished

Eb Major (vii°)
C Minor (ii°)
F Dorian (vi°)
G Phrygian (v°)
Ab Lydian (#iv°)
Bb Mixolydian (iii°)
C Aeolian (ii°)
D Locrian (i°)

D Diminished : Frequently Asked Questions

What notes are in Ddim?

Ddim contains D, F and A♭. The formula is 1, ♭3, ♭5.

How do you play Ddim on piano?

Play D, F and A♭ together. Right hand fingers 1, 3, 5; left hand 5, 3, 1. A♭ is a black key; D and F are white.

What are the inversions of Ddim?

3 positions: root position D F A♭, Ddim/F, Ddim/A♭.

What keys contain Ddim?

2: ii° in C minor, vii° in E♭ major.

What is the difference between Ddim and Dm7♭5?

Adds C. 3 of the notes are shared.

What is an easy Ddim for small hands?

The root and third only voicing, D3 F3, spans 3 semitones or about 41 mm.

What are the frequencies of Ddim?

From D3 at A440 in 12-TET: 146.83, 174.61, 207.65 Hz.

What is the set class of Ddim?

Prime form (036), Forte 3-10, interval vector <002001>.

How do I transpose Ddim to another key?

Keep the 1, ♭3, ♭5 formula on the new root. Cdim is C, E♭, G♭; C♯dim is C♯, E, G.

D Diminished in detail

Exact

Every pitch class is present and nothing outside the chord is added.

Type	Notes	Semitones	Span	Omissions and additions	Set relation
Close, root position	D3 F3 A♭3	6	83 mm	none	identical
Close, first inversion	F3 A♭3 D4	9	124 mm	none	identical
Close, second inversion	A♭3 D4 F4	9	124 mm	none	identical
Open, fifth on top	D2 A♭2 F3	15	206 mm	none	identical

Reduced

A subset of the pitch classes: the identity is incomplete rather than altered.

Type	Notes	Semitones	Span	Omissions and additions	Set relation	Fit
Root and third only	D3 F3	3	41 mm	omits A♭	subset

Spans are measured centre to centre at a 165 mm octave (standard keyboard geometry).

Position	Bass note	Notes in order	Figured bass	Semitones	Span
Root position	D	D3, F3, A♭3	5/3	6	83 mm
First inversion: Ddim/F	F	F3, A♭3, D4	6/3	9	124 mm
Second inversion: Ddim/A♭	A♭	A♭3, D4, F4	6/4	9	124 mm

One position per chord tone in the bass. Spans are for close position: voiced inversions appear under Voicings.

Progression	Key	Role	Sequence	Voice leading
ii°, v, i	C minor	ii°	Ddim to Gm to Cm	Ddim opens the phrase
vii°, I	E♭ major	vii°	Ddim to E♭	Ddim opens the phrase

Root motion, common tones and voice displacement are computed from pitch class sets. Roman numerals follow common practice functional harmony.

Which keys it belongs to

Key	Roman numeral	Function
C minor	ii°	Predominant
E♭ major	vii°	Dominant function

Classification system: common-practice functional harmony.

Change one note

Chords a single note away, and what moving that note does.

Chord	Change	Formula	Common tones
Dm7♭5	adds C	1 ♭3 ♭5 ♭7	3
Ddim7	adds C♭	1 ♭3 ♭5 ♭♭7	3
Dm	A♭ becomes A	1 ♭3 5	2
Dm7	A♭ becomes A, C	1 ♭3 5 ♭7	2
DmMaj7	A♭ becomes A, C♯	1 ♭3 5 7	2
Dm6	A♭ becomes A, B	1 ♭3 5 6	2
D	F, A♭ becomes F♯, A	1 3 5	1
Daug	F, A♭ becomes F♯, A♯	1 3 ♯5	1
Dsus2	F, A♭ becomes E, A	1 2 5	1
Dsus4	F, A♭ becomes G, A	1 4 5	1

Frequencies

Note	MIDI	Frequency
D3	50	146.83 Hz
F3	53	174.61 Hz
A♭3	56	207.65 Hz

Reference pitch A440, 12-TET, close root position.

Set theory: prime form, Forte number, interval vector

Absolute pitch class set: {2, 5, 8}
Normal order: [2, 5, 8]
Prime form: (036)
Forte number: 3-10
Interval vector: <002001>

Pair	Interval	Semitones	Interval class
D to F	Minor third	3	3
D to A♭	Tritone	6	6
F to A♭	Minor third	3	3

Where these facts come from

Every value on this page is derived from the note formula for a diminished applied to the root D, using standard music theory. Nothing here is hand-entered per chord, so the notes, intervals, inversions and frequencies cannot drift out of agreement with each other. Pitches assume 12-TET at A440.

D Diminished

Fingerings

D Diminished: notes and degrees