Encyclical rhymes with:
cyclical, cyclical, diabolical, evangelical, helical, umbilical, acoustical, alphabetical, analytical, antithetical, apolitical, archaeological, archeological, astrological, astronautical, astronomical, asymmetrical, atypical, autobiographical, barnicle, bicycle, biographical, biological, biomedical, biopharmaceutical, biotechnological, botanical, carmical, carmickle, categorical, chronicle, chronological, classical, comical, commonsensical, conical, critical, cubicle, cyclical, cylindrical, cynical, demichele, dermatological, diabolical, dialectical, ecclesiastical, ecological, economical, ecumenical, egotistical, electrical, electrochemical, electromechanical, elliptical, empirical, epidemiological, eschatological, ethnical, evangelical, fanatical, floptical, galenical, geographical, geological, geometrical, geopolitical, graphical, grossnickle, gynecological, helical, heretical, historical, hypercritical, hypocritical, hysterical, icicle, identical, ideological, illogical, immunological, inimical, ironical, lackadaisical, lexical, liturgical, logical, logistical, lyrical, magical, maricle, mathematical, mechanical, mericle, metallurgical, metaphorical, metaphysical, meteorological, methodological, metrical, monical, morphological, morrical, mosaical, musical, mystical, mythological, neoclassical, neurological, nonelectrical, nonliturgical, nonpolitical, nonsensical, nonsurgical, nontechnical, obstetrical, ontological, optical, ornithological, paradoxical, parenthetical, pathological, pedagogical, periodical, petrochemical, pharmaceutical, pharmacological, philosophical, phonological, physical, physiological, popsicle, preclinical, problematical, prototypical, psychical, psychological, puritanical, rabbinical, radiological, rhetorical, sabbatical, semiclassical, semicylindrical, semitropical, senecal, senechal, serological, sociological, spherical, statistical, stereotypical, strategical, surgical, symmetrical, tactical, technical, technological, teleological, testicle, theatrical, theological, theoretical, topological, toxicological, tricycle, tropical, typographical, tyrannical, umbilical, uncritical, uneconomical, unethical, untypical, vehicle, vertical, vesicle, viatical, virological, whimsical, zoological