The ash is associated with prophetic dreams and spiritual journeys.
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The Celtic Tree Calendar is a calendar with thirteen lunar divisions. Most contemporary Pagans use fixed dates for each "month," rather than following the waxing and waning lunar cycle. If this was done, eventually the calendar would fall out of sync with the Gregorian year, because some calendar years have 12 full moons and others have 13. The modern tree calendar is based on a concept that letters in the ancient Celtic Ogham alphabet corresponded to a tree.
Although you don't have to follow a Celtic path to celebrate the Celtic tree calendar months, you'll find that each of the themes in the Celtic tree months ties strongly to Celtic culture and mythology.
It's also important to note that there is no proof that the Celtic tree calendar actually originated with early Celtic peoples. Joelle of Joelle's Sacred Grove says,
"The lunar tree calendar of the Celts has long been a source of controversy among Celtic scholars. Some even claim it was never a part of the old Celtic world, but was an invention of author/researcher Robert Graves. The Druids are generally given credit by other researchers for creating this system. There seems to be no scholarly evidence to prove otherwise, yet many Celtic Pagans feel that the system pre-dates the time of Druidic influence over Celtic religious matters. It is probably reasonable to believe that the truth lies somewhere in between these three extremes. It is most likely that the tree system was in place, with minor regional variations before the time of the Druids who experimented with it, discovered the magical properties of each tree, and codified all the information into the system we have today."
In the Norse eddas, Yggdrasil, the world tree, was an Ash. The spear of Odin was made from the branch of this tree, which is also known by the Celtic name Nion, pronounced knee-un. This is one of three trees sacred to the Druids (Ash, Oak and Thorn), and this is a good month to do magic that focuses on the inner self. Associated with ocean rituals, magical potency, prophetic dreams and spiritual journeys, the Ash can be used for making magical (and mundane) tools -- these are said to be more productive than tools made from other wood. If you place Ash berries in a cradle, it protects the child from being taken away as a changeling by mischievous Fae.
Wigington, Patti. "Celtic Tree Months." ThoughtCo, Oct. 16, 2018, thoughtco.com/celtic-tree-months-2562403.