Tom Johnson and a rational theory of harmony

In this article, I present a theory of harmony on the structure of conjunct connected sets in harmonic space. The theory is a product of the combined influence of Tom Johnson, James Tenney, and Larry Polansky. The title of the article is a respectful nod to James Tenney's seminal text “John Cage and the theory of harmony” which demonstrates how the ideas of Cage, who often remarked that his music had nothing to do with harmony, actually could serve as the basis for a new theory of harmony. Similarly, in this article, I aim to show how the ideas of Johnson, who claimed that he did not have much interest in tuning beyond equal-temperament, can form the basis of a rational theory of harmony.