FOUR AXIOMS FOR A THEORY OF RHYTHMIC SETS AND THEIR IMPLICATIONS

Abstract

In a recent article (Lugos Abarca, 2023) an equation was proposed that allows us to know the number of measures that a song has μ_mar from the musical variables of tempo Τ, song duration t and time signature β. Also, it was found that that by solving the equation μ_mar for the variable t yields a formula capable of expressing the duration in minutes of any rhythmic figure. Proceeding with this line of research, four axioms are presented whose purpose is to function as a basis for the construction of a set theory for rhythmic figures, during this process the consequences of the third axiom that establishes the non-commutativity in the sum of certain sets that have the same elements but with different order are studied, and whose most relevant consequence is to introduce the theorem that determines the existence of different types of empty sets.