Fig. 4: Relationship of priors to integer-ratios.

a, Average distance from the nearest small-integer-ratio rhythm, for each participant group (split into two rows to make the figure more compact). This measure is small for a prior with all its mass at small-integer-ratio rhythms. The lines and shaded regions at the top plot the mean and 95% CI of a null distribution of the average distance from randomly selected points (this varies somewhat across groups as it depends on each group’s data distribution). The asterisks denote statistical significance relative to this null distribution, one-tailed (***P < 0.001). Here and elsewhere, P values are Bonferroni-corrected for multiple comparisons. All groups have a probability mass concentrated closer to integer-ratio rhythms than would be expected by chance. b, Categories exhibit small but systematic biases away from integer ratios. The grey dots plot the component means of the Gaussian mixture model computed for each of the 39 groups. The large black dots plot the average location over the 39 groups. The red crosses plot integer ratios. The asterisks denote biases that are statistically significantly different from integer ratios across groups (***P < 0.001; **P < 0.01). The results show that 9 of the 22 categories exhibit consistent biases.