Swung rhythmic subdivisions have long been described in terms of their liminal character: jazz swing occupies a perceivable space between binary and ternary feels, and analogous phenomena have been documented in West African, Afro-Brazilian, and Afro-Cuban rhythmic traditions, among others. This paper takes swing as its theoretical starting point and proposes a systematic framework in which swing extends into higher-order, self-similar rhythmic structures. I show that when the mechanism producing a swung subdivision is iterated upon its own output, a small number of irrational proportions emerge as the only values compatible with a consistent swing character at every level of iteration. Specifically, three such proportions arise from three substitution rules that propagate the swing character across iteration levels: the golden ratio 𝜙 from the Fibonacci morphism; √2 from a second binary rule; and the plastic ratio 𝜌 from the corresponding ternary rule. Each proportion is the unique positive real solution to a consistency equation internal to its rule, imposed by the structural requirements of the substitution rather than fitted to empirical data. The resulting phenomenon — sequences whose internal proportions replicate at every scale of observation, within the range 1 < 𝑟 < 2 that characterises swing — is introduced under the term fractal swing. The triad emerges from the combination of the formal substitution framework with the perceptual constraints of the groove window, which act as a structural selector among the rules admissible in principle. I examine the properties that distinguish fractal swing as a structural category, discuss the perceptual limits that bound the depth of iteration musically accessible to a performer, and outline directions for future research. The accompanying concert Morph Congas, for piano and live electronics, is a practical realisation of the mirror effect examined in this paper.
Malcolm Braff (Thu,) studied this question.