On the word and importance of coral, the OED states:
Historically, and in earlier literature and folk-lore, the name belongs to the beautiful red coral, an arborescent species, found in the Red Sea and Mediterranean, prized from times of antiquity for ornamental purposes, and often classed among precious stones.
This association with red coral seems to hold true in much of Shakespeare's writing, with numerous comparisons(such as Lucentio of Shrew, and lines of Venus and Adonis as well as Rape of Lucretia) of ladies' lips to coral. An example of such coral might look like:
In this case, however, there is no reason to believe Ariel is not referring to the white coral also present in the Mediterranian, which looks more like bones:
In either case, coral was regarded as a precious substance. It is both fragile and natural, and always built of dead things, making it particularly appropriate as part of Alonso's transformation.
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