Musicians’ relationships with algorithms have deep precedents in the confluence of music and mathematics across millennia and across cultures. Technological and musico-mathematical precedents in the ancient world predate the Arabic etymology of the term ‘algorithm’. From Guido d’Arezzo’s hand to rule systems in music theory and eighteenth-century ars combinatoria, there is a rich background to twentieth-century rule-led music making. Robotic music, too, has precedents, and there is an interesting proto-computational thread linking the automata builder Vaucanson to early programmable weaving looms. Ada Lovelace’s writing, Joseph Schillinger’s composition system, and John Pierce’s 1950 stochastic music science fiction article provide productive insight into the origins of algorithmic music. Indeed, the world’s musics reveal a panoply of interesting practices, such as campanology, Nzakara court harp music, time structures in Indian classical music, and many more examples of the rich combinations of music and mathematics often predating musical computer science.