Diatonic Set Theory
I've been reading up on diatonic set theory, using Timothy Johnson's Foundations of Diatonic Set Theory and various scholarly papers (thank God for Google!). It all seems to be based firmly on the syntonic temperament (that is, on stacks of tempered perfect fifths, in which the syntonic comma is tempered to unison).
This is absolutely the right simplifying assumption to make initially. Now, however, it seems reasonable to explore the application of its findings to other temperaments (such as Magic). Presumably, it will be discovered that some the "global" rules apply across a well-defined subset of all possible temperaments, and that each temperament has its own "local" rules.
Knowing which rules are global, and which local rules exist in any given temperament (such as Magic), could go a long way towards defining the intrinsic music theories of these alternative temperaments -- temperaments that now have, for the first time ever, the possibility of local consonance and dynamic tonality.
This is absolutely the right simplifying assumption to make initially. Now, however, it seems reasonable to explore the application of its findings to other temperaments (such as Magic). Presumably, it will be discovered that some the "global" rules apply across a well-defined subset of all possible temperaments, and that each temperament has its own "local" rules.
Knowing which rules are global, and which local rules exist in any given temperament (such as Magic), could go a long way towards defining the intrinsic music theories of these alternative temperaments -- temperaments that now have, for the first time ever, the possibility of local consonance and dynamic tonality.
Labels: alternative tuning, diatonic set theory, Magic temperament, syntonic temperament


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