3 syllables:
istical, listicle, mystical, mystikal, twistical

4 syllables:
artistical, baptistical, casuistical, deistical, eristical, juristical, linguistical, logistical, nastistical, papistical, patristical, phlogistical, poristical, puristical, sophistical, statistical, theistical

5 syllables:
agonistical, alchemistical, apathistical, aphoristical, atheistical, atomistical, belletristical, cabalistical, calvinistical, catechistical, ditheistical, egoistical, egotistical, eulogistical, euphemistical, hellenistical, nepotistical, optimistical, pantheistical, pessimistical, pietistical, rationalistical, solecistical, syllogistical, symbolistical, synchronistical, syncretistical, tritheistical, voyeuristical

6 syllables:
anomalistical, antagonistical, biostatistical, characteristical, dialogistical, monotheistical, philosophistical, polytheistical, semideistical

7 syllables:
materialistical

3 syllables:
silicle, whimsical, finical, synclinal, cynical, mispickel, cryptical, cyclical, mythical, tricycle, sinistral, physical, clinical, miscible, digital, rhythmical, critical, biblical, typical, biddable, bindable, binnacle, bridgeable, criminal, cystocele, drinkable, fictional, finagle, fixable, imbecile, integral, livable, liveable, minimal, miserable, mixable, pinnacle, pitiful, pivotal, principal, principle, printable, quizzical, risible, shrinkable, sinkable, syllable, synchronal, thimbleful, thinkable, tillable, trigonal, vincible, visible, visual

4 syllables:
elliptical, encyclical, uncritical, periwinkle, untypical, atypical, rabbinical, cylindrical, political, inimical, intrinsical, additional, admissible, admittable, admittible, antipodal, conditional, convincible, despicable, dissyllable, disyllable, divisible, divisional, duplicable, episcopal, equivocal, explicable, extricable, first principle, forgivable, formidable, hospitable, immiscible, indictable, invincible, invisible, in principle, life principle, medicinal, municipal, nonfictional, nutritional, original, permissible, pontifical, predictable, provisional, reciprocal, rescindable, resistible, school principal, traditional, transitional, transmissible, transmittable, trisyllable, unclimbable, undrinkable, unlivable, unliveable, unmixable, unprintable, unshrinkable, unsinkable, unthinkable, war criminal

5 syllables:
genotypical, impermissible, hypocritical, parasitical, jesuitical, analytical, hypercritical, antitypical, indivisible, archetypical, prototypical, apolitical, metonymical, aboriginal, apparitional, appositional, archepiscopal, archiepiscopal, basic principle, bitter principle, decasyllable, desperate criminal, diacritical, inadmissible, individual, inexplicable, inhospitable, irresistible, legal principle, monosyllable, moral principle, nonmedicinal, nonreciprocal, nontraditional, nontransmissible, octosyllable, pleasure principle, suppositional, unassignable, unconditional, unequivocal, unforgivable, unmedicinal, unoriginal, unpredictable, untraditional, vital principle, working principle

6 syllables:
stereotypical, apocalyptical, diethylstilbestrol, coenobitical, definite integral, exclusion principle, judicial principle

7 syllables:
fundamental principle, habitual criminal, indefinite integral, reality principle, uncertainty principle

8 syllables:
pauli exclusion principle