Daug7: D Augmented 7th Piano Chord

Root position: either hand, fingers low note to high
Hand	Notes	Fingers
Right	D, F♯, A♯, C	1-2-3-5
Left	D, F♯, A♯, C	5-3-2-1

Scale degree, note, and interval measured from the root.
Degree	Note	Interval from root	Semitones
1	D	Perfect unison	0
3	F♯	Major third	4
♯5	A♯	Minor sixth	8
♭7	C	Minor seventh	10

Construction

D Augmented 7th = Root + Major 3rd + Minor 6th + Minor 7th = D, F♯, A♯, C

Note	Interval	Degree
D	Root	1
F♯	Major 3rd	3
A♯	Minor 6th	♯5
C	Minor 7th	♭7

Fingering

Note	Key color	Right hand	Left hand
D	white	thumb (1)	little finger (5)
F♯	black	index finger (2)	middle finger (3)
A♯	black	middle finger (3)	index finger (2)
C	white	little finger (5)	thumb (1)

Right hand: thumb (1) on D, index finger (2) on F♯, middle finger (3) on A♯, little finger (5) on C.

Left hand: little finger (5) on D, middle finger (3) on F♯, index finger (2) on A♯, thumb (1) on C.

D Augmented 7th Inversions

Root position
D – F♯ – A♯ – C
1st inversion (Daug7/F♯)
F♯ – A♯ – C – D
2nd inversion (Daug7/A♯)
A♯ – C – D – F♯
3rd inversion (Daug7/C)
C – D – F♯ – A♯

Key Signature

A Augmented 7th 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

Same Notes, Other Names

The notes D – F♯ – A♯ – C aren’t exclusive to this chord. Depending on which note is the bass and how the chord functions, the same pitches also spell:

D 7♯5→

D Augmented 7th : Frequently Asked Questions

What notes are in Daug7?

Daug7 contains D, F♯, A♯ and C. The formula is 1, 3, ♯5, ♭7.

How do you play Daug7 on piano?

Play D, F♯, A♯ and C together. Right hand fingers 1, 2, 3, 5; left hand 5, 3, 2, 1. F♯ and A♯ are black keys; D and C are white.

What are the inversions of Daug7?

4 positions: root position D F♯ A♯ C, Daug7/F♯, Daug7/A♯, Daug7/C.

What is the difference between Daug7 and Daug?

Drops C. 3 of the notes are shared.

What is an easy Daug7 for small hands?

The guide tones, 3 and ♭7 voicing, F♯3 C4, spans 6 semitones or about 83 mm.

What are the frequencies of Daug7?

From D3 at A440 in 12-TET: 146.83, 185.00, 233.08, 261.63 Hz.

What is the set class of Daug7?

Prime form (0248), Forte 4-24, interval vector <020301>.

How do I transpose Daug7 to another key?

Keep the 1, 3, ♯5, ♭7 formula on the new root. Caug7 is C, E, G♯, B♭; D♭aug7 is D♭, F, A, C♭.

D Augmented 7th 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 F♯3 A♯3 C4	10	138 mm	none	identical
Close, first inversion	F♯3 A♯3 C4 D4	8	110 mm	none	identical
Close, second inversion	A♯3 C4 D4 F♯4	8	110 mm	none	identical
Close, third inversion	C4 D4 F♯4 A♯4	10	138 mm	none	identical
Drop 2	A♯2 D3 F♯3 C4	14	193 mm	none	identical
Drop 3	F♯2 D3 A♯3 C4	18	248 mm	none	identical
Drop 2 and 4	D2 A♯2 F♯3 C4	22	303 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
Shell, root ♭7 3	D2 C3 F♯3	16	220 mm	omits A♯	subset
Guide tones, 3 and ♭7	F♯3 C4	6	83 mm	omits D and A♯	subset
Rootless close	F♯3 A♯3 C4	6	83 mm	omits D	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, F♯3, A♯3, C4	7	10	138 mm
First inversion: Daug7/F♯	F♯	F♯3, A♯3, C4, D4	6/5	8	110 mm
Second inversion: Daug7/A♯	A♯	A♯3, C4, D4, F♯4	4/3	8	110 mm
Third inversion: Daug7/C	C	C4, D4, F♯4, A♯4	4/2	10	138 mm

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

Change one note

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

Chord	Change	Formula	Common tones
Daug	drops C	1 3 ♯5	3
D7	A♯ becomes A	1 3 5 ♭7	3
D9	A♯ becomes A, E	1 3 5 ♭7 9	3
D	A♯, C becomes A	1 3 5	2
Dmaj7	A♯, C becomes A, C♯	1 3 5 7	2
Dm7	F♯, A♯ becomes F, A	1 ♭3 5 ♭7	2
Dm7♭5	F♯, A♯ becomes F, A♭	1 ♭3 ♭5 ♭7	2
D7sus4	F♯, A♯ becomes G, A	1 4 5 ♭7	2
D6	A♯, C becomes A, B	1 3 5 6	2
Dadd9	A♯, C becomes A, E	1 3 5 9	2

Frequencies

Note	MIDI	Frequency
D3	50	146.83 Hz
F♯3	54	185.00 Hz
A♯3	58	233.08 Hz
C4	60	261.63 Hz

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

Set theory: prime form, Forte number, interval vector

Absolute pitch class set: {2, 6, 10, 0}
Normal order: [10, 0, 2, 6]
Prime form: (0248)
Forte number: 4-24
Interval vector: <020301>

Pair	Interval	Semitones	Interval class
D to F♯	Major third	4	4
D to A♯	Minor sixth	8	4
D to C	Minor seventh	10	2
F♯ to A♯	Major third	4	4
F♯ to C	Tritone	6	6
A♯ to C	Major second	2	2

Where these facts come from

Every value on this page is derived from the note formula for a augmented 7th 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 Augmented 7th

Fingerings

D Augmented 7th: notes and degrees