Microtonalis: A Systematic Approach to Microtonal Composition is a complement to existing (Western) microtonal practices, which usually focus either on the quality of tuning ratios, via the harmonic series, or the spectral analysis of sound-both very vertical in nature-with very little attention given to how microtones may or may not move and/or function on the linear plane. This study proposes and delineates a method, or technical structure, for the systematic movement of microtones in both melodic and harmonic spheres, bridging the gap between European and American microtonal practice by adapting well-known operations from tonal and post-tonal music. The main theory informing this study is my personal approach to pitch multiplication, wherein intervals of a previously existing parameter (i.e., a scale, mode, melody, or chord) are multiplied by decimal increments (0.5, 1.5, 2.5, etc.) to create microtonal (quartertone) contractions or expansions. These mutations of familiar structures form new parameters, each of which possess a novel character, and which retain the specific functions, be they tonal or serial, of the original version. After introducing this theory, I describe 1) the specific qualities of microtonal intervals-their unique character traits-and 2) how microtones can be applied to a host of tried-and-true techniques, such as serialism, neoRiemannian theory, the counterpoint of Bach and Brahms, and the modes of Messiaen. I then demonstrate how certain of these concepts are used in my own compositional work.