In our tradition we divide the year not only by eight solar and agricultural holidays, but also by the Kalends. We celebrate twelve months of the year by the common calendar, plus a special thirteenth month for Samhain. These month cycles are associated with different totemic spirits. Each month is assigned an animal, a bird (or other flying creature), and a tree. August's totems are Horse, Apple, and Swan.
The totemic associations are as follows:
Horse (Each) – travel, power, freedom, civilization
Apple (Quert) – beauty, choices, love, inspiration
Swan (Eala) - shape-shifting, love, grace, beauty
The Swan is often depicted with a silver or gold chain around the neck in Celtic legends -- possibly a carry-over from the Aphrodite tradition of the golden sash. Aphrodite was a water-bird Goddess in early Proto-Indo European practice, and the Swan is heavily associated with her in Greek tradition. This is hardly a surprising connection, given that the Swan is very prominent in love stories in Celtic lands, including the tale of Oenghus and Yewberry (who is a Swan Maiden).
In Celtic lore, Swan is associated with Otherworldly travel and migration of the Soul. The "swan song" speaks of both grace and beauty (because Swan's final song is said to be strikingly beautiful) and also of death and transition. Swan is often the poetic representation of the Soul itself in Celtic lore.
This bird's skin and feathers were used to make the bard's ceremonial cloak, according to Philip and Stephanie carr-Gomm's Druid Animal Oracle. This is another sign of grace and beauty -- the grace and beauty of word and song, which the celts understood to be very important to both art and magic.
Swans are intimately linked with shape-shifting in celtic lore, as well. Several tales speak of children and maidens who are changed (or can change themselves) into swans for one reason or another. Because of these shape-shifting characteristics, Swan is also further linked to Elphame and the realm of Faerie.
Swan is sacred to Oenghus, Lyr, Cuchulain, Aphrodite and Apollo.
Swan's connections to Horse and Apple:
Swan, Horse and Apple are a very potent feminine, Faerie Totemic set in relation to the White Goddess (known/shown to us as Goda).