Roman numeral code: vi
Scale notes: 6, 1, 3
Attributes: peace, mediation, introspection, gentleness
Whereas 5 and 4 represented aspects of power, 6 tones down that power and smooths out high-energy harmonic transitions, and provides a resting place.
Like 5 and 4, 6 is a movement away from 1, but not a very far one. Unlike 5, there is very little energy involved in the transition either way. 6 is too 'close' to 1, too lacking in a natural return force, to serve as a strong affirmation of the tonic. Its harmonic function is something else: as a more introspective version, or a softening, of 1. It is used when we want to keep a sense of the base key but in a more subtle way, or when the music wants to temporarily 'rest'.
Music sometimes mitigates the forward 1 -> 4 motion by using 6 as an intermediary (1 -> 6 -> 4).