SSAS: There is no such thing as an Attribute in MDX!

In MDX in SSAS the term "attribute" occasionally gets used interchangeably with "hierarchy" and "level", but it's not technically accurate.

In SSAS, MDX has concepts of Dimensions, Hierarchies and Levels, but not Attributes. Attributes and Attribute Relationships are design time concepts that are understood by the storage engine, but they are not directly exposed in the MDX language. Attributes actually map to levels (or properties) in MDX. I think the confusion comes about because, by default, an attribute generates a hierarchy with a single level in it that both have the same name as the underlying attribute. (I also think that some of this confusion comes about because of the way that SSAS coalesces different objects, but that is a topic for another time.)