representing that dance style. The actual "Half and Half" dance was done to Waltz Music, but realistically could be any partner dance or Music.
Burlesque and Vaudeville would soon start playing with this 'Half-and-Half idea with many female dancers designing whole skits/acts around this idea.
... Just a note:
People have always been mixing dances together, whether because of lacking in knowledge, such as being weaker in one dance and stronger in another or would mix dances just because it was fun or just plain out of boredom. Plus there was a huge need for the Dance Masters of America to create new dances which helped fuel this form of mixing dances for something new. Music changes can make a dancer go from one dance to another as well within the same song. The castles probably noticed this and capitalized on it or just thought they were original, who knows?, but the costume idea was certainly an original one as well as dancing with oneself.