The augmented chords in major are:

• I⁺   (sometimes written as I⁵)
• IV⁺   (IV⁵)
• V⁺   (V⁵)
• V  (V⁷⁽⁵⁾)
• Also possible, but less common, are I^maj7(5) and IV^maj7(5)

The III⁺  chord occurs in minor keys.

These chords are the result of chromatic passing tones. The raised 5^th acts like a temporary leading tone, lending these chords a dominant or secondary dominant quality.

The I⁺ triad in major

The chromatic passing tone si acts as a temporary leading tone, connecting I to either IV (and its inversions), vi⁽⁶⁾, or V/ii (so – si – la).

The last two examples show the I⁺ with an added 7^th in the bass and an altered version turning the I⁺ chord into a secondary dominant of vi that resolves to a secondary dominant.

The IV⁺ triad in major

The chromatic passing tone di acts as a temporary leading tone, connecting IV to either ii⁽⁶⁾ or V/V (do – di – re).

The V⁺ triad and V chord in major

The chromatic passing tone ri acts as a temporary leading tone to either I (and its inversions), I,  iii⁽⁶⁾, or V/vi. Note that iii can be altered to create a secondary dominant of vi.

The next two examples are especially colorful due to the dissonances ti, ri, and fa that all require strict resolution.

the III⁺ triad in minor

The III⁺ to VI secondary triad connection is available in harmonic minor. Note that the progression is identical to I⁺ to IV in major.

As mentioned in the chapter on Secondary Triads in First Inversion, the III⁺ chord can be used in minor as a substitute for the [ i ] chord leading to V or V⁷.