Fundamental properties of rhythms sequences

Abstract

Fundamental mathematical properties of rhythm sequences are studied. In particular, a set of three axioms for valid rhythm indicators is proposed, and is shown that the R-indicator satisfies only two out of three but that the R'-indicator satisfies all three. This fills a critical, logical gap in the study of these indicator sequences. Matrices leading to a constant R'-sequence are called baseline matrices. They are characterized as matrices with constant w-year diachronous impact factors. This relation with classical impact factors is clarified. Using regression analysis matrices with a rhythm sequence that is on average equal to 1 (smaller than 1, larger than 1) are characterized.