Right now, it's not possible to Ascend the Stranger's Rifle due to the fact that it requires 25 Legendary Marks rather than Etheric Light. Legendary Marks can't be earned until September 15th, when The Taken King launches.
This got me thinking... what happens when we Ascend the Stranger's Rifle? Will it simply increase the Attack, or will it turn into the Exotic version, No Time to Explain?
Think about it; the Legendary version of Necrochasm (Eidolon Ally) couldn't be ascended at all. You had to find the Crux of Crota to upgrade it to Necrochasm to increase the Attack modifier.
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Just goes to 170 unfortunately :(