Colour I could see is green...red and yellow are too close to Solar, Darker Blue is too close to Arc. Yellow? Not so sure. (i.e.: Enemy with Shield, Super Colour, etc.)
Call it Etheric or Soul, Aether or something else...etc.
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I see it as a bit of a triangle because of how the exotic swords work against against the same/alternate 'elements'. Kinetic is one damage type that could be fleshed out, but I believe it would be seriously week against shielded PvE enemies. Solar, Arc, Void... How about: Toxin? Precedent being the damage from Thorn and the damage from Khepri's Sting. Just an idea...