Detriment rhymes with:
instrument, excrement, experiment, increment, instrument, sacrament, temperament, adamant, argument, armament, complement, condiment, diamant, disarmament, element, excrement, experiment, filament, impediment, implement, increment, instrument, integument, ligament, ornament, orpiment, parliament, predicament, rearmament, regiment, sacrament, sediment, sentiment, supplement, temperament, tenement, testament, tournament, vehement
Detriment sounds like:
darned, daydreamed, dearment, dearmond, deodorant, dermody, dermot, dermott, determent, determinant, determinate, determined, deterrent, dethroned, doormat, dorinda, dormant, drained, dreamed, dreamt, drenth, droned, dronet, drowned, drumhead, drummed, drummond, duramed, durand, durando, durant, durante, durrant