'Decadence' is Latin for 'falling away' — kin to 'cadence,' 'cascade,' and 'accident.'
Moral or cultural decline, especially after a period of prosperity; luxurious self-indulgence.
From French 'décadence' (cultural decline, luxurious deterioration), from Medieval Latin 'decadentia' (a falling away, a sinking decline), from the Latin verb 'dēcadere' (to fall down, to sink, to deteriorate), compounded from 'dē-' (down, away from — an intensifier of downward motion) and 'cadere' (to fall). The root 'cadere' traces to PIE *ḱad- (to fall) — one of the more generative Latin roots in English vocabulary. Its descendants include 'accident' (that which falls upon you), 'occasion' (that which falls as an opportunity), 'incident' (that which falls in your path), 'case' (what has fallen out, what has happened), 'coincide' (to fall together), and 'chance' (what falls by lot). The noun
'Decadence,' 'cadence,' 'cascade,' 'accident,' 'incident,' 'occasion,' and 'coincidence' all come from Latin 'cadere' (to fall). Decadence is falling-down. A cadence is a falling of musical pitch. A cascade is a waterfall. An accident is something that falls-upon. An incident is something that falls-into. An occasion is something that falls-toward. A coincidence is a falling-together. All falling, endlessly.