3 syllables:
graphical

5 syllables:
aerographical, autographical, biographical, cacographical, calligraphical, cartographical, cerographical, chirographical, chorographical, cosmographical, cryptographical, demographical, diagraphical, discographical, epigraphical, ethnographical, geographical, glossographical, holographical, hydrographical, hypsographical, ichnographical, lithographical, logographical, monographical, myographical, orographical, orthographical, pantographical, paragraphical, pasigraphical, pentagraphical, petrographical, phonographical, photographical, phytographical, polygraphical, scenographical, sciagraphical, seismographical, stenographical, stratigraphical, stratographical, stylographical, tachygraphical, telegraphical, topographical, typographical, xylographical, zincongraphical, zoographical

6 syllables:
agrostographical, bathyorographical, chromatographical, crystallographical, historiographical, iconographical, ideographical, idiographical, idolographical, lexicographical, oceanographical, paleographical, physiographical, prosopographical, pseudepigraphical, stereographical, uranographical, zoogeographical

7 syllables:
autobiographical, biogeographical, paleontographical, phytogeographical, psychobiographical

8 syllables:
paleogeographical

9 syllables:
semiautobiographical

3 syllables:
tropical, conical, hospital, popsicle, prodigal, follicle, dropsical, coccygeal, ossicle, chronicle, comical, logical, optical, amytal, bacchanal, calyceal, calycle, capital, capitol, classical, clavicle, fanciful, fascicle, hannibal, madrigal, magical, mandible, mannitol, panicle, practical, radical, radicle, sanicle, tactical, tragical, vatical

4 syllables:
methodical, field hospital, subtropical, symbolical, cupronickel, synoptical, ironical, illogical, inositol, botanical, climactical, climatical, didactical, dogmatical, dynamical, expandible, expansible, fanatical, fantastical, grammatical, impractical, irascible, mechanical, monastical, nonclassical, phlegmatical, pragmatical, sabbatical, schismatical, syntactical, theatrical, tyrannical

5 syllables:
chronological, phonological, theological, cosmological, pedagogical, synecdochical, neurological, microscopical, ecological, periodical, gastronomical, morphological, biological, psychological, semitropical, anagogical, tautological, mythological, homological, acrylonitrile, economical, oncological, astronomical, anatomical, rheological, pathological, apostolical, technological, ethnological, mental hospital, geological, paradoxical, parabolical, diabolical, autocratical, diplomatical, emblematical, enigmatical, hieratical, mathematical, neoclassical, nonmechanical, plutocratical, problematical, psychiatrical, puritanical, undogmatical, unmechanical, untheatrical

6 syllables:
archaeological, heterological, ideological, aetiological, toxicological, gynecological, gerontological, pharmacological, dermatological, immunological, hematological, uneconomical, archeological, entomological, physiological, etiological, genealogical, gynaecological, anticlimactical, apothegmatical, aristocratical, axiomatical, ecclesiastical, idiomatical, servomechanical, thermodynamical

7 syllables:
bacteriological, psychiatric hospital, epistemological, paleontological, meteorological

8 syllables:
epidemiological