Even though teachers often ask for a ‘waltz’ for pirouettes on a 3, sometimes (in fact, most times) what works much better is a mazurka. Not the character-type mazurka that you get in Swan Lake or Coppélia, but the ballroom type that is slower than your average waltz, and has a more marked three-in-a-bar as opposed to the swaying feel of the late Viennese waltz. In particular, a mazurka for pirouettes works much better if there are any balancés involved.
Don’t look to Chopin for this type, or to many of the early 20th century composers who wrote ‘exotic’ mazurkas on the model of the folksy ones, because these are fast, and have a hold on 2, they’re not very triple. You have to look to the popular sheet music of the 19th century, where ‘mazurka’ meant the ballroom kind by default. ‘Polka mazurka’, while a different dance, has the same kind of feel. It’s closer to the three-step ländler type of waltz that you find in Giselle.
It’s a curious thing, this, the way that a long-forgotten dance form gets embedded in the conventions of a contemporary dance class. I discovered this trick by accident, by playing one of these that I’d found online for class one day. Try some of the 1062 mazurkas listed at the American Memory Sheet music collection for your next pirouette exercise and I think you’ll see what I mean. Go to the search page, and type in ‘mazurka‘. You’ll get a bunch of pieces back, some will be the folksy type with the held second beat – ignore those. Go for the ones called ‘polka mazurka’ or the ones which are rhythmically close to the polka mazurka, like the Falling Dew Mazurka for example.