Compositional Applications of Generalized Lead Structures, SP-Cycles, and Syntax Graphs and Hardscrabble for Wind Ensemble

Within the tradition of English change ringing, a specialized music theoretical framework developed to notate and perform long compositions from memory with one player per bell. The music theory and practice of English change ringing have elsewhere been used as a compositional tool by Peter Maxwell Davies, Robert Morris, and others. After reviewing and analyzing these representative works and compositional generalizations, such as Morris's SG(alpha) System, I explore the compositional scope and properties of change ringing leads, Gray codes, and SP-cycles. A unifying compositional principle that underlies the construction of each of these spaces is to partition a set of permutations into various kinds of equivalence classes and then chart a specific path through the sets.;The resulting technical guide to the composition of leads includes determination of factors that affect the periodicity of the lead and methods to check for the integrity of the Hamiltonian path within a traversal of all n! permutations. Defining a lead as an ordered multiset of operations, I show the minimal n for multiset members to create a Hamiltonian path through a given set of permutations. I demonstrate the musical use of a SP-cycle, a recently discovered generalized order structure that provides a flexible way to present Hamiltonian permutation sequences in a condensed or expanded fashion.;The final section of the paper is devoted to defining and applying syntax graphs, which condense information about musical sequences and aid in quantifying that information for analysis, thus addressing certain order-related phenomenological inquiries. Such quantified information can illustrate how and to what degree musical sequences differ. An analysis of Davies's Missa Super L'homme Arme is given, including discovery of the source material for the work.