Daug: D Augmented 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♯	Major third	4
♯5	A♯	Minor sixth	8

Construction

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

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

Fingering

Note	Key color	Right hand	Left hand
D	white	thumb (1)	little finger (5)
F♯	black	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 Augmented Inversions

Root position
D – F♯ – A♯
1st inversion (Daug/F♯)
F♯ – A♯ – D
2nd inversion (Daug/A♯)
A♯ – D – F♯

Key Signature

A Augmented 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♯ aren’t exclusive to this chord. Depending on which note is the bass and how the chord functions, the same pitches also spell the following:

A♯ Augmented→F♯ Augmented→

D Augmented : Frequently Asked Questions

What notes are in Daug?

Daug contains D, F♯ and A♯. The formula is 1, 3, ♯5.

How do you play Daug on piano?

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

What are the inversions of Daug?

3 positions: root position D F♯ A♯, Daug/F♯, Daug/A♯.

What is the difference between Daug and Daug7?

Adds C. 3 of the notes are shared.

What is an easy Daug for small hands?

The root and third only voicing, D3 F♯3, spans 4 semitones or about 55 mm.

What are the frequencies of Daug?

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

What is the set class of Daug?

Prime form (048), Forte 3-12, interval vector <000300>.

How do I transpose Daug to another key?

Keep the 1, 3, ♯5 formula on the new root. Caug is C, E, G♯; D♭aug is D♭, F, A.

D Augmented 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	8	110 mm	none	identical
Close, first inversion	F♯3 A♯3 D4	8	110 mm	none	identical
Close, second inversion	A♯3 D4 F♯4	8	110 mm	none	identical
Open, fifth on top	D2 A♯2 F♯3	16	220 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 F♯3	4	55 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, F♯3, A♯3	5/3	8	110 mm
First inversion: Daug/F♯	F♯	F♯3, A♯3, D4	6/3	8	110 mm
Second inversion: Daug/A♯	A♯	A♯3, D4, F♯4	6/4	8	110 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
Daug7	adds C	1 3 ♯5 ♭7	3
D	A♯ becomes A	1 3 5	2
Dmaj7	A♯ becomes A, C♯	1 3 5 7	2
D7	A♯ becomes A, C	1 3 5 ♭7	2
D6	A♯ becomes A, B	1 3 5 6	2
Dadd9	A♯ becomes A, E	1 3 5 9	2
Dm	F♯, A♯ becomes F, A	1 ♭3 5	1
Ddim	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
F♯3	54	185.00 Hz
A♯3	58	233.08 Hz

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

Set theory: prime form, Forte number, interval vector

Absolute pitch class set: {2, 6, 10}
Normal order: [2, 6, 10]
Prime form: (048)
Forte number: 3-12
Interval vector: <000300>

Pair	Interval	Semitones	Interval class
D to F♯	Major third	4	4
D to A♯	Minor sixth	8	4
F♯ to A♯	Major third	4	4

Where these facts come from

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

Fingerings

D Augmented: notes and degrees