Having seen the two main chords, the major and the minor, let’s see two more that are still considered important. These are chords with a strange name. One is called an augmented chord and the other a diminished chord, and they are somewhat similar to the two main chords: the augmented one comes from the major chord and the diminished one comes from the minor chord.
The augmented C chord is formed by the notes: C; E; G#
The diminished C chord is formed by the notes: C; Eb; Gb
Their representation in the color wheel highlights special features.
The augmented C chord is represented by an equilateral triangle. As in the equilateral triangle the sides and angles are all congruent to each other, the augmented triad also is formed by the same intervals between the notes that form it. Looking at the figure, you can see that the semitones between the notes that form this chord are always 4 (i.e. 2 T). Furthermore, the symmetry of the figure means that this chord can be named starting from each note that forms it, just as an equilateral triangle remains the same whatever side is considered its base. So:
(C-E-G#) = (E-G#-C) = (G#-C-E) = (C-E-G#) etc..
Generalizing, we could say that:
Equilateral triangle = augmented chord
Now, given the regular dodecagon inscribed in a circumference and taking vertices of the dodecagon as vertices of the equilateral triangle, only 4 different equilateral triangles can be built. In the same way, we can only build four different augmented chords which will be: C aug, C# aug; D aug and D# aug. The next chord would be E but, as we have seen, it coincides with C (same equilateral triangle). Here is a representation of the 4 different equilateral triangles (and chords).
The diminished chord is represented instead by an isosceles triangle. Let’s have a look at it:
The interval formula of this triad, as can be deduced from the figure, is:
The equal distance between C-Eb and Eb-Solb makes triangle isosceles. However, it is also a right triangle, since the G-C side coincides with the diameter. Indeed, geometry teaches us that if a triangle inscribed in a circumference has a side coinciding with the diameter, then it is always a right triangle. Generalizing, we can say that:
Right isosceles triangle in the form of 3-3-6 = diminished chord