Randomness plays a pivotal yet paradoxical role in computational music creativity: it can spark novelty, but unchecked chance risks incoherence. This paper presents a thematic review of contemporary AI music systems, examining how designers incorporate randomness and uncertainty into creative practice. I draw on the concept of structured uncertainty to analyse how stochastic processes are constrained within musical and interactive frameworks. Through a comparative analysis of six systems - Musika (Pasini and Schl\"uter, 2022), MIDI-DDSP (Wu et al., 2021), Melody RNN (Magenta Project), RAVE (Caillon and Esling, 2021), Wekinator (Fiebrink and Cook, 2010), and Somax 2 (Borg, 2019) - we identify recurring design patterns that support musical coherence, user control, and co-creativity. To my knowledge, this is the first thematic review examining randomness in AI music through structured uncertainty, offering practical insights for designers and artists aiming to support expressive, collaborative, or improvisational interactions.

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