enberg ' s ▁death , ▁Ig or ▁Stra vin sky ▁used ▁the ▁twelve - t one ▁technique ▁. ▁I ann is ▁X en ak is ▁generated ▁pitch ▁sets ▁from ▁mathematical ▁formula e , ▁and ▁also ▁saw ▁the ▁expansion ▁of ▁t onal ▁possibilities ▁as ▁part ▁of ▁a ▁synth esis ▁between ▁the ▁hier arch ical ▁principle ▁and ▁the ▁theory ▁of ▁numbers , ▁principles ▁which ▁have ▁domin ated ▁music ▁since ▁at ▁least ▁the ▁time ▁of ▁Par men ides ▁. ▁ ▁Free ▁at on ality ▁The ▁twelve - t one ▁technique ▁was ▁preced ed ▁by ▁Sch o enberg ' s ▁freely ▁at onal ▁pieces ▁of ▁ 1 9 0 8 – 1 9 2 3 , ▁which , ▁though ▁free , ▁often ▁have ▁as ▁an ▁" integr ative ▁element ... a ▁minute ▁inter v all ic ▁cell " ▁that ▁in ▁addition ▁to ▁expansion ▁may ▁be ▁transformed ▁as ▁with ▁a ▁tone ▁row , ▁and ▁in ▁which ▁individual ▁notes ▁may ▁" function ▁as ▁p iv otal ▁elements , ▁to ▁permit ▁over la pping ▁statements ▁of ▁a ▁basic ▁cell ▁or ▁the ▁linking ▁of ▁two ▁or ▁more ▁basic ▁cells " ▁. ▁ ▁The ▁twelve - t one ▁technique ▁was ▁also ▁preced ed ▁by ▁n ond ode cap h onic ▁serial ▁composition ▁used ▁independently ▁in ▁the ▁works ▁of ▁Alexander ▁S cri ab in , ▁Ig or ▁Stra vin sky , ▁Bé la ▁Bart ók , ▁Carl ▁R ugg les , ▁and ▁others ▁. ▁" E ss entially , ▁Sch o enberg ▁and ▁H auer ▁system at ized ▁and ▁defined ▁for ▁their ▁own