In 12-tone equal temperament, there are
48 unique triads.  For each possible
root note, there are four flavors of
triad: Major, Minor, Augmented and
Diminished

Numbering the notes from 0 to 11 in
hexadecimal format (0123456789AB), the
possible triads are:

| Augmented | Major | Minor | Diminished |
|-----------+-------+-------+------------|
|      048  |  047  |  037  |  036	 |
|      159  |  158  |  148  |  147	 |
|      26A  |  269  |  259  |  258	 |
|      37B  |  37A  |  36A  |  369	 |
|      480  |  48B  |  47B  |  47A	 |
|      591  |  590  |  580  |  58B	 |
|      6A2  |  6A1  |  691  |  690	 |
|      7B3  |  7B2  |  7A2  |  7A1	 |
|      804  |  803  |  8B3  |  8B2	 |
|      915  |  914  |  904  |  903	 |
|      A26  |  A25  |  A15  |  A14	 |
|      B37  |  B36  |  B26  |  B25	 |

   Here they are again, sorted, with the
   whole set duplicated alongside.  This
 makes it easy to visualize which triads
          "overlap", or share two notes:

| A14 | 147 | 148 | - | 47B | 7B2 | 7B3 |
| A15 | 158 | 159 | - | 048 | 48B | 480 |
| A25 | 258 | 259 | - | 48B | 8B2 | 8B3 |
| A26 | 26A | 269 | - | 58B | 8B2 | 8B3 |
| B25 | 258 | 259 | - | 147 | 47A | 47B |
| B26 | 26A | 269 | - | 148 | 48B | 480 |
| B36 | 36A | 369 | - | 158 | 58B | 580 |
| B37 | 37A | 37B | - | 159 | 590 | 591 |
| 6A1 | A14 | A15 | - | 258 | 58B | 580 |
| 6A2 | A25 | A26 | - | 259 | 590 | 591 |
| 7A1 | A14 | A15 | - | 269 | 690 | 691 |
| 7A2 | A25 | A26 | - | 369 | 690 | 691 |
| 7B2 | B25 | B26 | - | 480 | 803 | 804 |
| 7B3 | B36 | B37 | - | 580 | 803 | 804 |
| 8B2 | B25 | B26 | - | 590 | 903 | 904 |
| 8B3 | B36 | B37 | - | 591 | 914 | 915 |
| 26A | 6A1 | 6A2 | - | 690 | 903 | 904 |
| 036 | 36A | 369 | - | 691 | 914 | 915 |
| 36A | 6A1 | 6A2 | - | 803 | 036 | 037 |
| 037 | 37A | 37B | - | 804 | 047 | 048 |
| 37A | 7A1 | 7A2 | - | 903 | 036 | 037 |
| 37B | 7B2 | 7B3 | - | 904 | 047 | 048 |
| 047 | 47A | 47B | - | 914 | 147 | 148 |
| 47A | 7A1 | 7A2 | - | 915 | 158 | 159 |

 Adjacent triads can be combined to form
  tetrads. For example, the triad 047 (C
   major) is adjacent to 47A and 47B (E
  diminished and E minor). These can be
    combined to produce either 047A (C
     dominant) or 047B (C major 7th).

  Notice that augmented triads always
match with themselves.  This is because,
   in 12-tone equal temperament, an
   augmented triad is formed by two
intervals of 4 scale steps each. 3×4=12,
 so, these chords are symmetrical within
           the temperament.

  In other temperaments, such as other
equal temperaments or in subsets of Just
  Intonation, this property does not
          necessarily hold.