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The doubly block is specific to augmented and diminished interval calculations. If an interval is cascaded through a doubly block, it is either increased or decreased by one semitone. When a perfect, major or minor interval are cascaded through the block, there is no change. When a non-interval block is cascaded through, the value is simply doubled (x2).

The problem is that doubly doubly does not work. The second doubly doubles the value of the interval rather than further incrementing it.