We will now see the process of "augmenting" a chord
- this usually produces an "augmented triad" sound but it may also keep its tetrad shape.

Definition
Here is how augmentation works
- the substitution of Orbit 3 by Orbit 1, Incompleteness 1(3)
     can be chromaticized toward its resolution to Orbit 2.

-We have first the basic DOMINANT-TONIC progression,
          with the TONIC as Real Triad.
     The Orbit progression 1-1 is, by itself, in Line 1.
     The 3 other Orbit progressions (3-2, 2-1, 0-0) are together, in Line 2.
     The Fundamental Bass is in Line 3.
- We then have incompleteness 1(3) in the top voice of line 2 (D replacing F).
- Finally this substitution has been chromaticized to D#.
     The clash with the D of line 1 has generally been considered too violent
     and Line 1 is usually left out.

Augmented Triads

Dominantize

-We have here the last half of the circle,
     starting with the ANTE-3, Voice-leading A.
The 1-1 Orbit line has been left out
     and each chord has been dominantized.

Incompleteness and Augmentation

-Then, incompleteness 01(3) has been applied to each chord
     and each triad has been augmented
          by chromaticizing the substitution of Orbit 3.
This gives us a series of 4 augmented triads.

12 Augmented triads
On the "turn-around" progression (C⁶-Am⁷-Dm⁷-G⁷), presented 3 times,

-If each chord is presented as a Real Triad (C-Am-Dm-G),
     C-Am being an open Metamorphosis 4 and not a progression,
          (notice that they are in the same bar) and
- if each triad is dominantized and augmented (C⁺⁵-A⁺⁵-D⁺⁵-G⁺⁵),
     we have a series of 12 augmented triads covering a complete octave.

Augmented Tetrads

We saw in the first example that it is not impossible to maintain Orbit line 1-1 (D-C)
     while chromaticizing the substitution 1(3) in an augmentation (D#-E).

-We have here -
in the Soprano voice, the Orbit 1-1 line,
in the Alto voice, the Orbit 3-2 line with chromaticized substitution 1(3),
in the Tenor voice, the Orbit 0-0 line, and
in the Bass voice, the Orbit 2-1 line.
     (The Fundamental Bass has been left out.)
This disposition is particularly pleasant
     and the discordance of the DOMINANT Chord is rendered acceptable
     by the perfect Voice-leading to the TONIC Chord.

You might like to see
further "development" of this example.