Augmented Triads
An augmented triad contains a Root (1), Major 3ʳᵈ (3), and Augmented 5ᵗʰ (♯5).
Formula: 1–3–♯5
Unlike major and minor triads, an augmented triad is built from two major 3ʳᵈs, making it a symmetrical chord.
Example: C+ (Caug) = C–E–G♯
Inversions
Because every pair of notes is separated by a Major 3ʳᵈ, the interval pattern remains the same in every inversion.
Root Position: C–E–G♯

1ˢᵗ Inversion: E–G♯–C

2ⁿᵈ Inversion: G♯–C–E

Notice that every inversion still consists of two Major 3ʳᵈs.
Equivalent Chords
Since the notes simply rotate, each inversion can also be viewed as another augmented chord in root position.
C+ Root = E+ 1ˢᵗ = G♯+ 2ⁿᵈ
E+ Root = G♯+ 1ˢᵗ = C+ 2ⁿᵈ
G♯+ Root = C+ 1ˢᵗ = E+ 2ⁿᵈ
Because of this symmetry:
C+ = E+ = G♯+
Each chord has three names depending on which note is treated as the root.
Only Four Unique Augmented Triads
Since the pattern repeats every Major 3ʳᵈ (4 half-steps), there are only four unique augmented triads in the twelve-note system.
C+ • C♯+ • D+ • D♯+
All remaining augmented chords are inversions of one of these four.
On the Fretboard
The symmetry of the augmented triad causes the shape to repeat every 4 frets.

The same fingering produces:
• Root Position
• 1ˢᵗ Inversion
• 2ⁿᵈ Inversion
simply by shifting the shape four frets.
Using the NANDI Method
The interval pattern of fourths provides a simple way to locate the chord tones.


Starting from the Root (1):
• Fourth above 1 = 4 → one fret lower = 3
• Fourth above 3 = 6 → one fret lower = ♯5
Pattern: 1 → 4 ↓1 = 3 → 6 ↑1 = ♯5

The same fourth-based logic can be applied from any chord tone, allowing augmented triads to be located anywhere on the fretboard without memorizing shapes.