A quick definition of terms. A tuple represents an intersection or slice of a cube, specified by a list of members. The list of members does not need to include all dimensions, but any dimension included must be represented by only one member.

In MDX, parentheses are used to denote a tuple. Sometimes this is optional, but I prefer to include them. The following are examples of valid tuples (from Sample.Basic):

([Jan])
([Jan], [Sales])
([Jan], [Sales], [New York])

A set is a collection of tuples sharing the same dimensionality. In MDX, braces are used to denote a set. Again, this is sometimes optional, but recommended for clarity. The following are examples of valid sets:

{([Jan]), ([Feb])}
{([Jan], [Sales]), ([Feb], [Sales])}

A Crossjoin is used to generate a set which is the “cross-product” of sets from more than one dimension. For example, if we want to reference all Sales and Expenses from January and February, we can use a Crossjoin like this:

Crossjoin({[Jan], [Feb]}, {[Sales], [Expenses]})

It produces the following set:

{([Jan], [Sales]), ([Feb], [Sales]), ([Jan], [Expenses]), ([Feb], [Expenses])}

But here’s the deal:

1. Though a Crossjoin can be used to construct a tuple, we only need it to construct a set.
2. We don’t need to nest Crossjoins for every dimension in the set, only those from which we are choosing more than one member. All other dimensions can be represented by a single tuple.

For example, if we want to reference January Sales (from Sample.Basic), do this…

([Jan], [Sales])

…not this…

Crossjoin({[Jan]}, {[Sales]})

And if, we want to reference January and February Sales for Actuals only, do this…

Crossjoin({[Jan], [Feb]}, ([Sales], [Actuals]))

…not this…

Crossjoin({[Jan], [Feb]}, {Crossjoin({[Sales]}, {[Actuals]})})