Polymetric writing is an integral technique in contemporary compositional practice. Dan Welcher and Yo Goto are principal employers of this practice in the wind band medium. Their methods endure even the results of modern scholarship showing limited human perception of polyrhythmic events. This dissertation provides a comprehensive metric analysis of excerpts from the music of Welcher and Goto. Five examples are explored from major band works of each of the two composers. The analytical process in the study utilizes the metrical concept set forth by Maury Yeston, so that a comparison can be made between the rhythmic components of the competing meters. The results of the study show that both Welcher and Goto, in all ten excerpts, create polymetric sections containing elements that surpass the aural limits proposed by modern scholarship. Additionally, through identification of the misaligned metric layers causing each polymeter, pedagogical considerations are offered to aid performance of each identified excerpt.