Turrets make little sense unless they were higher than the curtain wall to which they were attached. Parallels from other contemporary Roman fortifications show square towers at gates, corners, and at intervals between those key points rising above the curtain walls of forts and fortresses. When reconstructing them, scholars have generally favoured only one additional storey, although differing over whether they had a flat-topped roof or a peripheral balcony.
Further reading: Symonds and Mason 2009
Per Lineam Valli 
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