Answer: You actually don't have to raise it at all if the area is not a low spot and the soil drains well. However, for aesthetic reasons, in order to build up the soil with an improved mix, or for drainage purposes build a raised bed from 6 to 10 inches high.
If you are building a large bed that covers a great deal of the area beneath the tree canopy, I suggest staying at the lower end of the depth range. This is to prevent stressing too much of the tree's root system by covering it with a deep layer of soil, thereby reducing the oxygen levels in the upper root zone. Also, avoid piling lots of bed mix up against the tree trunk as this will promote decay organisms and other such problems.
Thanks for the question!
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