Gaug: G Augmented Piano Chord

Root position: either hand, fingers low note to high
Hand	Notes	Fingers
Right	G, B, D♯	1-3-5
Left	G, B, D♯	5-3-1

Scale degree, note, and interval measured from the root.
Degree	Note	Interval from root	Semitones
1	G	Perfect unison	0
3	B	Major third	4
♯5	D♯	Minor sixth	8

Construction

G Augmented = Root + Major 3rd + Minor 6th = G, B, D♯

Note	Interval	Degree
G	Root	1
B	Major 3rd	3
D♯	Minor 6th	♯5

Fingering

Note	Key color	Right hand	Left hand
G	white	thumb (1)	little finger (5)
B	white	middle finger (3)	middle finger (3)
D♯	black	little finger (5)	thumb (1)

Right hand: thumb (1) on G, middle finger (3) on B, little finger (5) on D♯.

Left hand: little finger (5) on G, middle finger (3) on B, thumb (1) on D♯.

G Augmented Inversions

Root position
G – B – D♯
1st inversion (Gaug/B)
B – D♯ – G
2nd inversion (Gaug/D♯)
D♯ – G – B

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 G Major

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

I — G Major (major)

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

Same Notes, Other Names

The notes G – B – D♯ 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:

B Augmented→D♯ Augmented→

G Augmented : Frequently Asked Questions

What notes are in Gaug?

Gaug contains G, B and D♯. The formula is 1, 3, ♯5.

How do you play Gaug on piano?

Play G, B and D♯ together. Right hand fingers 1, 3, 5; left hand 5, 3, 1. D♯ is a black key; G and B are white.

What are the inversions of Gaug?

3 positions: root position G B D♯, Gaug/B, Gaug/D♯.

What is the difference between Gaug and Gaug7?

Adds F. 3 of the notes are shared.

What is an easy Gaug for small hands?

The root and third only voicing, G3 B3, spans 4 semitones or about 55 mm.

What are the frequencies of Gaug?

From G3 at A440 in 12-TET: 196.00, 246.94, 311.13 Hz.

What is the set class of Gaug?

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

How do I transpose Gaug to another key?

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

G 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	G3 B3 D♯4	8	110 mm	none	identical
Close, first inversion	B3 D♯4 G4	8	110 mm	none	identical
Close, second inversion	D♯4 G4 B4	8	110 mm	none	identical
Open, fifth on top	G2 D♯3 B3	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	G3 B3	4	55 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	G	G3, B3, D♯4	5/3	8	110 mm
First inversion: Gaug/B	B	B3, D♯4, G4	6/3	8	110 mm
Second inversion: Gaug/D♯	D♯	D♯4, G4, B4	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
Gaug7	adds F	1 3 ♯5 ♭7	3
G	D♯ becomes D	1 3 5	2
Gmaj7	D♯ becomes D, F♯	1 3 5 7	2
G7	D♯ becomes D, F	1 3 5 ♭7	2
G6	D♯ becomes D, E	1 3 5 6	2
Gadd9	D♯ becomes D, A	1 3 5 9	2
Gm	B, D♯ becomes B♭, D	1 ♭3 5	1
Gdim	B, D♯ becomes B♭, D♭	1 ♭3 ♭5	1
Gsus2	B, D♯ becomes A, D	1 2 5	1
Gsus4	B, D♯ becomes C, D	1 4 5	1

Frequencies

Note	MIDI	Frequency
G3	55	196.00 Hz
B3	59	246.94 Hz
D♯4	63	311.13 Hz

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

Set theory: prime form, Forte number, interval vector

Absolute pitch class set: {7, 11, 3}
Normal order: [3, 7, 11]
Prime form: (048)
Forte number: 3-12
Interval vector: <000300>

Pair	Interval	Semitones	Interval class
G to B	Major third	4	4
G to D♯	Minor sixth	8	4
B to D♯	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 G, 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.

G Augmented

Fingerings

G Augmented: notes and degrees