Simple models to generate integer ratios between temporal intervals

Rhythm links the structure of music with sounds in nature, reflecting common patterns across species. An intriguing commonality found across diverse musical traditions and species is the categorical distribution of rhythms. Such categories often conform to small integer ratios: intervals whose relative durations can be expressed as a fraction of two integers. This thesis explores the generation of rhythmic patterns which display integer ratios, using three models: a Markov-chain, a spiking neural network, and a model inspired by crickets’ rhythmic stridulation. Each model uncovers key mechanisms behind the emergence of integer ratios in rhythmic behavior. The Markov chain model demonstrates how simple stochastic processes can generate these ratios and how the models' parameters control their presence and variation. The spiking neural network model shows that a great variety of rhythmic patterns related to integer ratios can emerge from intrinsic neural properties. Finally, the cricket model reveals how basic biological feedback loops can produce rhythmic categories and integer ratios. Our findings suggest that rhythmic patterns in music and animal vocalization may stem from shared, fundamental processes, providing benchmarks in the study of the evolution of rhythm and musicality.