All-Scalar Set Theory
This theory deals with the extended application of of combinatorics to microtonal set theory. These rules need to be established, as set theory-oriented interests and regular temperament theory-oriented interests have not overlapped as much as they could have yet. What does all-scalar set theory accomplish?
<> Allows for a more thorough understanding of set theory properties
<> Provides a more thorough categorization of scales in general
<> Answers open-ended questions such as, "How many kinds of scales are possible?"
<> Focuses on shuffling the objects themselves through permutation (meaning that it's not limited to MOS scales)
Originally, I wrote a paper for my Honors Thesis at Ball State University introducing the mathematical principles, and what I had figured out so far. Some of the mathematical ideas will likely be discarded in favor of enumerating all of the scalar class sets (or at least figuring out how that would be done). The paper can be found on the Ball State University website:
I've also lectured on the concept at Ball State, UnTwelve 2016, SCI Student National 2016, and Microtonal Adventures Festival 2018:
And finally, I also created a web series to walk a potentially interested theorist through some visual concepts: