The Trajectory Hymn appears as cascading waves of crystallized sound, each frequency rendered visible as geometric patterns that flow like living sheet music through dimensional space. In the Primal Schism, it manifests as predatory harmonics—the perfect pitch of a hunting cry that guided evolution itself. Within the Clockwork Schism, it becomes mathematical ratios made audible as crystalline tones. In the Hollow Schism, it exists as silent vibrations, a song defined by the spaces between notes. Where these three expressions intersect, the patterns achieve perfect synchronization—creating a white radiance that resonates directly with a Linewalker's consciousness, allowing them to hear colors and see sounds, all converging on a single melody that feels older than the schism itself.

It acts as the cosmic tuning fork that all three dimensions unconsciously harmonize with when manifesting the Perfect Line. Linewalkers who learn to perceive even fragments of its eternal song gain the ability to sense when their trajectories approach universal truth, as the Hymn grows louder and more coherent the closer a throw comes to perfection. Only those who can hear all three of its movements simultaneously—predatory chorus, mathematical harmony, and silent intervals—prove they've transcended their home dimension's limitations.