The waltz was a common style of ballroom dance on Earth. In his sixth life, the Doctor met a woman named Becky, from whom he learned the dance. Some 80 years later in his own life, he met Becky as a teenager and taught her how to waltz, effectively meaning that he had taught himself the dance. (PROSE: Teach Yourself Ballroom Dancing)
The Eighth Doctor stated that he had not gone waltzing in ages. (AUDIO: The Silver Turk)
Later, while disguised as John Smith by the chameleon arch, the Doctor attended a local dance and attempted the waltz with a very forgiving Joan Redfern. (TV: Human Nature)