Her prime example was, famously, music. "Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of [mathematical] expression and adaptations," Lovelace wrote, "the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent."
Lovelace's intuitive intermingling of science and art was a birthright. Her father was George Gordon, Lord Byron, the famous and infamous poet; her mathematically inclined mother, Anne Milbanke, left Byron when Ada was five weeks old. (Byron never saw his daughter again.) Her mother intended the mathematical emphasis of Ada's education as inoculation against her father's tendencies, but Ada never shared her mother's loathing of Byron, instead regarding that poetic legacy as integral to her holistic view of science. "I believe myself to possess a most singular combination of qualities," she wrote, "exactly fitted to make me pre-eminently a discoverer of the hidden realities of nature."
Music was a constant in Lovelace's education; as an adult, she toyed with a professional performing career — prompting mild disagreement with her husband, William Noel-King, Earl of Lovelace, who considered a musical wife an exclusively domestic virtue. But Ada's enthusiasm, and confidence, was considerable, announcing that "should I take seriously with 'undivided mind' to musical composition" it would be a "formidable rival" to her scientific pursuits. (Other enthusiasms were less benign; Lovelace's zeal for gambling led to substantial financial strain.)
Lovelace hinted at ambitions for a comprehensive synthesis of music and mathematics, but died, from cancer, at 36. The music she imagined emerging from the Analytical Engine would finally sound a century later, when composers and programmers began to coax synthesized sounds and algorithmically controlled compositions from early digital computers. It is impossible to calculate the exact probability, but one suspects that Lovelace, granted the time, would have gotten there sooner.