Technomic rhymes with:
autonomic, economic, ergonomic, gastronomic, macroeconomic, microeconomic, noneconomic, socioeconomic, uneconomic, adamec, adamik, atomic, autonomic, comic, diatomic, economic, ergonomic, gastronomic, islamic, macroeconomic, microeconomic, monatomic, noneconomic, romick, socioeconomic, subatomic, tomich, tragicomic, uneconomic
Technomic sounds like:
tacking, tacoma's, taganka, tagging, takanashi, taking, takings, tasking, taxiing, taxing, teaching, teachings, teasing, technic, technics, technique, techniques, tecumseh, texan's, texans, thesing, thickening, thickens, thickness, thyssen's, ticinus, ticking, tokens, tokunaga, toscanini's, tossing, touching, toughening, toughens, toughness, toxins, tsang, tseng, tsiang, tsongas, tsongas', tsongas's, tucking, tudjman's, tugging, tusing, tussing, tweaking, twitching, tycoon's, tycoons, tyson's, tysons