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Musicians' relationships with algorithms have deep precedents in the confluence of music and mathematics across millenia 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 18th century ars combinatoria, there is a rich background to 20th century rule-led music making. Robotic music too has its mechanical precedents, and the link from the great automata builder Vaucanson to early programmable weaving looms shows an interesting proto-computational thread. The likes of 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 later algorithmic music. Indeed, the world's musics as a whole 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.