Many ballet dancers may automatically recognize waltz music for its ¾ time signature. Waltz began in Europe sometime during the 16th century. It was both a ballroom and folk dance. In contrast to ballet, it began among the peasant population and was later adopted by the aristocrats.
Since it is such a traditional dance, I would say the different types are basically related to the tempo of the song, which in ballroom we breakdown in three: (1) the Viennese Waltz (has the fastest tempo and it is the original), (2) medium Waltz, and (3) slow Waltz (these last two started only on the latter part of the 19th century when composers were written slower Waltz).
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