▁lower ▁note . ▁ ▁On ▁instruments ▁str ung ▁with ▁metal ▁wire , ▁however , ▁neither ▁of ▁these ▁assumptions ▁is ▁valid , ▁and ▁in harm onic ity ▁is ▁the ▁reason . ▁ ▁In harm onic ity ▁refers ▁to ▁the ▁difference ▁between ▁the ▁theoretical ▁and ▁actual ▁frequencies ▁of ▁the ▁harm on ics ▁or ▁over ton es ▁of ▁a ▁v ibr ating ▁t ine ▁or ▁string . ▁The ▁theoretical ▁frequency ▁of ▁the ▁second ▁harm onic ▁is ▁twice ▁the ▁fundamental ▁frequency , ▁and ▁of ▁the ▁third ▁harm onic ▁is ▁three ▁times ▁the ▁fundamental ▁frequency , ▁and ▁so ▁on . ▁But ▁on ▁metal ▁strings , ▁t ines , ▁and ▁re eds , ▁the ▁measured ▁frequencies ▁of ▁those ▁harm on ics ▁are ▁slightly ▁higher , ▁and ▁proportion ately ▁more ▁so ▁in ▁the ▁higher ▁than ▁in ▁the ▁lower ▁harm on ics . ▁A ▁digital ▁em ulation ▁of ▁these ▁instruments ▁must ▁re create ▁this ▁in harm onic ity ▁if ▁it ▁is ▁to ▁sound ▁convin cing . ▁ ▁The ▁theory ▁of ▁temper aments ▁in ▁musical ▁tun ing ▁do ▁not ▁normally ▁take ▁into ▁account ▁in harm onic ity , ▁which ▁var ies ▁from ▁instrument ▁to ▁instrument ▁( and ▁from ▁string ▁to ▁string ), ▁but ▁in ▁practice ▁the ▁amount ▁of ▁in harm onic ity ▁present ▁in ▁a ▁particular ▁instrument ▁will ▁effect ▁a ▁modification ▁to ▁the ▁theoretical ▁temper ament ▁which ▁is ▁being ▁applied ▁to ▁it . ▁ ▁V ibration ▁of ▁wire ▁strings ▁▁ ▁When ▁a ▁stretch ed ▁wire ▁string ▁is ▁excited ▁into ▁motion ▁by ▁pl uck ing ▁or ▁striking , ▁a ▁complex ▁wave ▁travel s