I am the rythm/lead/vocalist guitar player for my band and I was wondering if when I'm writing rhythms, it matters if each one sounds completely different from the others.

Ps. In case you didn't get it it's thrash metal. Like Heathen, Dark Angel, Exodus, Death Angel, Overkill
i would think it would help. my personal complaint against a lot of bands is that alot of their songs sound the same.
Within one song a lot of thrash bands sort of develop their riffs, starting with one thing and either just sort of extending it melodically or changing the rhythm for a measure when new riffs come about. It's not the best idea to have all your riffs stick to the same rhythm, but it's good to have it as a basic blueprint.
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im more of a social godzilla than chameleon

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Alright, I'll give them a try, Japanese Black Speed rarely disappoints.

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Hmm judging from your pic you'd fit in more with a fat busted tribute.