Relating to or characteristic of rope-walking or tightrope-walking; used for or involving funambulation.
From Latin funambulatorius, derived from funambulus (rope-walker). The suffix -atory indicates the adjective form relating to the action or practice. This scholarly term entered English through scientific and theatrical literature in the 18th-19th centuries.
Funambulatory describes anything related to tightrope-walking—so a 'funambulatory performance' would be a show featuring rope-walkers. It's the adjective form that adds sophistication when discussing the art form!
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