Although music of the twentieth and twenty-first centuries makes frequent use of non-isochronous meter (meters involving beats of different length, such as 5/4 and 7/8), most studies on meter and metric dissonance focus on isochronous meters (meters involving beats of the same length, such as 4/4 and 9/8). This dissertation bridges this gap by developing two methodologies to account for metric dissonance involving non-isochronous pulses: modified ski-hill graphs and the composite beat attack point system. Modified ski-hill graphs, adapted from Richard Cohn's ski-hill graphs, illustrate metric states involving non-isochronous pulses and reveal degrees of dissonance in musical passages that share time spans, as in 5/4 grouped 3+2 vs. 5/4 grouped 2+3. The composite beat attack point system uses rhythmic notation to illustrate metric states involving any pulse duration or time span, revealing specific points of dissonance and consonance, relative strength of dissonance and consonance, and patterns of dissonance and consonance. The methodology is used to closely examine the treatment of metric dissonance in Holst's "Mars," from The Planets, Ligeti's Hungarian Rock (Chaconne), and Ligeti's Désordre. The analyses focus on passages where the metric dissonance becomes ever more pronounced and ends up obliterating any sense of meter.