Myths and Psychology
Psychology describes a process called "projection", whereby inner experiences that are taking place in the unconscious are displaced into the outside world and appear there as having a life of their own. Unconscious projections can seem to have nothing to do with the individual who, unconsciously, does this.
Myths can be understood as projections of the unconscious. All those gods and goddesses playing out their roles may well be acting out for us not how gods behave but how we behave. They are inside our heads not up Mt Olympus.
For example, Venus, the goddess of love, has much to teach us about the way we behave in our intimate relationships. In psychology, these inner gods are called "archetypes" and they form the foundations of our personal identity, the way we think, feel and act.
In Greek mythology, which concerns us most here, there were nine Muses, daughters of Zeus, the head of the gods, and Mnemosyne, the goddess of memory. Memory seems to play a significant role in this as originally there were only three Muses who represented song or tune, practice or occasion, and - memory.
The Greeks performed poetry or metrical speech inspired by the Muses and accompanied by the notes of a lyre or cithera (plucked) or aulos (wind). This was called mousika, hence the English term, "music".
The sun god, the god of light, Apollo (Helios is Roman mythology), was the leader of the Muses. He is also the god of music and carries its symbol, the lyre with its seven strings.
Apollo is also associated with truth and prophecy, healing, plague, poetry, and more. In psychology he is described as the archetype of rationality and reasoning.
Hermes (Mercury in Roman mythology) is a "trickster". He is the god of communication and has power over commerce - and thieves. Greek myths have many tales of Hermes' unruly behaviour, including the theft of Apollo's sheep. To atone for this act, he made a lyre from a tortoise shell and presented it to Apollo.
As a trickster he is an annoying psychological force, always stirring things up and upsetting the smooth course of events. This may be a painful process but which can have a positive outcome. He mixes things up, introduces a little chaos and anarchy into what would otherwise be a stagnant, predictable situation.
Hermes, as the messenger god, can bring polar opposites into a relationship. In this process, he also, like Apollo, is a god of healing.
Orpheus and the Underworld
Not strictly speaking a god, Orpheus also has great musical powers and his attribute is also the lyre. Orpheus had the ability to charm all living things with his music, even stones.
Founder of the Orphic Mysteries, the most well known story about Orpheus is his journey into the underworld, the realm of the dead, ruled by Hades (Pluto in Roman mythology). His task was to charm Hades and Hades' consort, Persephone, with his music and thus persuade Hades to release his wife, Eurydice, from the underworld. This nearly succeeded but at the last moment Orpheus failed to follow Hades' instructions and looked back to see Eurydice following him before she had left the underworld.
Orpheus represents the great power and influence that music is capable of wielding.