My guildmates gifted me with this item. I can corroborate the 1.4 instrument mod. It's not the best thing in-game, but availability in a mid-30s LDoN mission (not sure which theme) wouldn't set my expectations very high.
OK, you are going to confuse everyone with your logic. If the mod is 1.4, then the % is 40%. Cause if you are doing 100 points without lute, then 1.4x100 is 140 cause (1x100=100 plus .4x100=40) = 140. So you are adding 40%. To get a 240% boost, the mod would be 3.4, not 1.4 You went the wrong way on the converson.
40%=1.4 140%=2.4 240%=3.4
Use a calculator if you are still do not believe me.