Core Location: Theory and Mapping
Triads are 3 tone chords built by superimposing intervals of 3rds. There are 2 types of 3rds: Major and minor. The Major 3rd is an interval equal to 4 half steps. The minor 3rd is an interval equal to 3 half steps.
With these 2 types of 3rds, we can have 4 combinations: 4-3, 3-4, 3-3, and 4-4. These are the Major, minor, diminished, and augmented, respectively. These are referred to as qualities. Triadic qualities are Major, minor, diminished, and augmented.
As with all parallel naming, the Major is our point of reference [for triads = R-3-5]. Since in the minor, the 3rd is a ½ lower when compared to the Major 3rd, we call this a flat 3rd.
Similarly, the 5th in the diminished is a ½ lower, therefore, it is a flat 5. The diminished triad, when compared to the minor, has a lowered 5 while the 3 is the same [flat 3, ♭3], so we can call this minor flat 5 [this is sub-paralleling - comparing to the minor, or something else that has already been modified]. The diminished triad is indicated with a o sign (a degree sign, typically superscript). Example, in C Major, the viio chord is Bo.
The augmented has a sharp 5, since its 5 has been increased from what is 'normal' [Major]. By increasing the 5, we have 8 half steps between the root and the 5th, rather than 7. The augmented triad first appears as a derivative in the Harmonic minor [chord space III]. The augmented triad is indicated by using a + sign. Example, in A Harmonic minor the III+ chord is C+.
We can build chords using other intervallic schemes, such as 4ths [quartal], but we don't typically call them triads. We reserve the term triad for 3 tone chords built by superimposing 3rds.[separator]