6ths are upside down 3rds.
Musical math tells us that 6+3 = 8, which means that when you add a 6th and 3rd together, you get an octave. It also means that EC, the interval, is the inversion of CE.
6ths complete all major and minor chords that are not in root position, and they are the outside of augmented chords and diminished seven chords.There are three kinds of 6ths that are regularly used:
- #6 = aug 6
- b6 = m6