I was just looking at Luke's dance and realized there is a big problem with gyre: it both starts and ends with a soft sound, with no hard consonants in the middle.  I can't think of a single other figure with that quality, and believe it will become slurred in execution.  Try enunciating it clearly yet musically, in context with other words, and you'll see what I mean.

For example, 'ladies gyre right' will likely be said as "ladies gyright" and be heard as "ladies gyrate."

Or, almost as bad, 'look at a new neighbor and jeer.'

Not the intended goal, in either case.

Neal