Today I was fortunate to be able to view a live feed of a discourse given by Swami Vidyadhishananda which he gave on the topic of the Taittiriya Upanishad. It is one of the primary Upanishads from the pre-Buddhist eras. The swami talked about the upanishad and how it relates to various Shanti (peace) mantras. Particularly why we say “Aum” followed by shanti three times.
Because there are three sources of joy and three sources of misery. He said never mind the three sources of joy because we can always stand more joy, but as for the misery, we protect ourselves from the three miseries of life, namely that which comes from 1) the natural phenomena, natural disasters, uncontrollable factors of the conditional world, etc. 2) other living things, other people, the unease that interactions with others might bring us, and 3) the discontent that can come from the battles that rage within ourselves.
We temper these three things by chanting “Shanti” thrice.
Aum Shanti Shanti Shanti!
Aum Jai Harihara!