In recent lore there was a guardian who originally live about 13000 years ago and had to learn modern language because their ghost didn't give them the knowledge.
Shaxx has a Scottish accent.
Saint is Greek or Russian
Osiris is possibly British
In Y3 there was some lore of fallen learning human language and speaking to the apprentice speaker.
Then you have Sjur Eido learning Eliksne while mithrax learns English from her.
English
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Shaxx doesn't have a Scottish accent and Saint imitates a Russian speaker while the lines recorded for Rasputin are genuine Russian spoken by a native.
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Shaxx certainly doesn't have an American accent, and he eats haggis which is a Scottish dish. So he's likely Scottish. Saint speaks with a poorly performed Russian or Greek accent. Thought I believe bungie did claim it was ment to be a Greek accent, it mostly comes down to the talent of the voice accent. Note, I'm talking about accents. Rasputin speaks actual Russian. If he spoke English, he'd likely sound similar to Saint. Remember accents occurs when you learn a second Language (or more) and pronunciation from your primary language spill over into you 2nd, 3rd, 4th language when you speak them.
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Shaxx is of Scottish heritage but the actor that records his lines doesn't use a Scottish accent. I live in the UK and I know what Scottish sounds like. Saint is imitating a Russian speaker speaking English. There's not the slightest hint of Greek.
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The problem is your trying to distinguish between the characters and the voice actors. You can't to that, since it's like comparing apples and oranges. Since the OP is talking in game lore, you have to go with the characters. You said it yourself that shaxx is ment to be of Scottish origin, the fact that the voice actor speaks more with a UK accent is on the lack of skill with the voice actor. As for Saint it's not just me, it's been a highly debate topic in the community if his accent is ment to be Russian or Greek and again this just comes down to the actor lacking in skill. As I recall Saint's VA is of Greek origin which is my most people now think it's ment to be a Greek accent.
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Shaxx doesn't have a Scottish accent and Saint imitates a Russian speaker while the lines recorded for Rasputin are genuine Russian spoken by a native.