▁length ened ▁note . ▁This ▁and ▁similar ▁pass ages ▁by ▁R ame au ▁( in ▁his ▁first ▁G av otte ) ▁clearly ▁show ▁that ▁this ▁means ▁to ▁apply ▁an ▁even ▁greater ▁amount ▁of ▁inequality ▁to ▁d otted ▁e ighth – six teenth ▁note ▁pairs ▁than ▁to ▁e ighth – e ighth ▁pairs , ▁which ▁are ▁already ▁understood ▁to ▁be ▁played ▁une qu ally . ▁The ▁exact ▁amount ▁of ▁inequality ▁required ▁is ▁also ▁un spec ified , ▁and ▁most ▁of ▁the ▁treat ises ▁leave ▁this ▁detail ▁to ▁the ▁taste ▁of ▁the ▁perform er . ▁It ▁may ▁have ▁varied ▁from ▁double - d otted ▁to ▁minim ally ▁per cept ible , ▁depending ▁on ▁the ▁context . ▁Some ▁recent ▁papers ▁and ▁books ▁include ▁a ▁full ▁analysis ▁of ▁this ▁topic ▁as ▁well ▁as ▁practical ▁gu ides ▁for ▁the ▁perform er . ▁Also , ▁musical ▁clock s ▁have ▁been ▁discovered ▁from ▁the ▁period ▁that ▁show ▁the ▁dot ting ▁very ▁clearly ▁as ▁such ▁devices ▁have ▁" pres erved ▁performances ▁of ▁notes ▁in ég ales ▁that ▁are ▁often ▁as ▁subt le ▁as ▁a ▁ 3 : 2 ▁ratio ▁( i . e . ▁three ▁fifth s ▁of ▁a ▁beat ▁for ▁the ▁first ▁note , ▁two ▁fifth s ▁for ▁the ▁second ▁in ▁the ▁pair ), ▁as ▁well ▁as ▁the ▁more ▁obvious ▁ 2 : 1 ▁ratio ▁( tri ple ts ), ▁and ▁ 3 : 1 ▁( d otted ▁e ighth – six teenth ▁pairs ▁and ▁their ▁multi ples ). ▁ ▁There ▁were ▁situations ▁which ▁were ▁understood ▁to ▁be ▁ex empt