Caug: C Augmented Piano Chord

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

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

Construction

C Augmented = Root + Major 3rd + Minor 6th = C, E, G♯

Note	Interval	Degree
C	Root	1
E	Major 3rd	3
G♯	Minor 6th	♯5

Fingering

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

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

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

C Augmented Inversions

Root position
C – E – G♯
1st inversion (Caug/E)
E – G♯ – C
2nd inversion (Caug/G♯)
G♯ – C – E

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 C Major

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

I — C Major (major)

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

Same Notes, Other Names

The notes C – E – G♯ 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:

E Augmented→G♯ Augmented→

C Augmented : Frequently Asked Questions

What notes are in Caug?

Caug contains C, E and G♯. The formula is 1, 3, ♯5.

How do you play Caug on piano?

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

What are the inversions of Caug?

3 positions: root position C E G♯, Caug/E, Caug/G♯.

What is the difference between Caug and Caug7?

Adds B♭. 3 of the notes are shared.

What is an easy Caug for small hands?

The root and third only voicing, C3 E3, spans 4 semitones or about 55 mm.

What are the frequencies of Caug?

From C3 at A440 in 12-TET: 130.81, 164.81, 207.65 Hz.

What is the set class of Caug?

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

How do I transpose Caug to another key?

Keep the 1, 3, ♯5 formula on the new root. D♭aug is D♭, F, A; Daug is D, F♯, A♯.

C 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	C3 E3 G♯3	8	110 mm	none	identical
Close, first inversion	E3 G♯3 C4	8	110 mm	none	identical
Close, second inversion	G♯3 C4 E4	8	110 mm	none	identical
Open, fifth on top	C2 G♯2 E3	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	C3 E3	4	55 mm	omits G♯	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	C	C3, E3, G♯3	5/3	8	110 mm
First inversion: Caug/E	E	E3, G♯3, C4	6/3	8	110 mm
Second inversion: Caug/G♯	G♯	G♯3, C4, E4	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
Caug7	adds B♭	1 3 ♯5 ♭7	3
C	G♯ becomes G	1 3 5	2
Cmaj7	G♯ becomes G, B	1 3 5 7	2
C7	G♯ becomes G, B♭	1 3 5 ♭7	2
C6	G♯ becomes G, A	1 3 5 6	2
Cadd9	G♯ becomes G, D	1 3 5 9	2
Cm	E, G♯ becomes E♭, G	1 ♭3 5	1
Cdim	E, G♯ becomes E♭, G♭	1 ♭3 ♭5	1
Csus2	E, G♯ becomes D, G	1 2 5	1
Csus4	E, G♯ becomes F, G	1 4 5	1

Frequencies

Note	MIDI	Frequency
C3	48	130.81 Hz
E3	52	164.81 Hz
G♯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: {0, 4, 8}
Normal order: [0, 4, 8]
Prime form: (048)
Forte number: 3-12
Interval vector: <000300>

Pair	Interval	Semitones	Interval class
C to E	Major third	4	4
C to G♯	Minor sixth	8	4
E to G♯	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 C, 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.

C Augmented

Fingerings

C Augmented: notes and degrees