Kerenyi gives another interesting perspective:
"The Italian name TARTARUGA keeps alive the a designation dating from late antiquity, according to which the tortoise holds up the lowest layers of the universe, namely, TARTARUS."
From: Jung, C G, and Kereneyi, C., Essays on a science of mythology; The Primordial Child in Primordial Times, 7. Hermes
The Tortoise has the qualities of:
PLUTO - in its associations with Tartarus and the Titans. This merely reflects Pluto as symbolic, in one sense of the Earth.
SATURN/KRONOS - in its connections with TIME, and:
Pillar of Mars in Memory Theatre
MOUTH OF TARTARUS, Purgatory
Hekate is called - "She who rules Tartaros" or "the Lady of Tartaros" [*] Therefore, by association, she is also the Ruler of the Titans - who were banished to live in Tartaros. Holding to Key to these realms, Hekate would then also be in possession of the Key to the Titanic propensities. She fits in very well with her Oriental form, as transmitted through the esoteric lineages of Tibetan Buddhism - where Hekate could be equated, archetypally with Mahakali. Thus, she would also have her roots in the spiritual homeland of India - where her forms were constellated around Kali, and related Goddesses.
[*] Johnston, Sarah Iles, Hekate Soterira, A Study of Hecate's Roles in the Chaldean Oracles and Related Literature, Scholars Press, Atlanta, Georgia, 1990. American Philological Association, American Classical Studies 21, . p.41.
THE TITANS AND ASH
"When ashes and sand have been timely heated in the fire, the Master makes therefrom a glass, which henceforth is always able to resist the fiery heat. In colour it resembles a transparent Stone and is no longer recognisable as ashes. For the unknowing this is a great and secret art; but not so for those who know, for it is their craft, attained through knowledge and experience... For the true Tartarus is concealed in the ashes and must be set free, and after its dissolution the strong Door of the royal Chamber can be opened."
Basil Valentine The Twelve Keys.
Wolf van Brussell, The Phoenix and Cinderella, The Hermetic Journal, pp.25-28
See Kontopoulos for the association of the Titans with Tartarus…