"This is one of the best albums I've heard in a while", uses the present perfect and, as such, refers to a past action relevant to the present. "This is one of the best albums I heard in a while", uses the simple past and, as such, refers to an action that happened in the past.
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whatchadoinThis is one of the best albums I've heard in a while. This is one of the best albums I heard in a while.Only the first is natural in British English.
Ivanhr5jj is right. For past events useThis was one of the best albums I had heard in a while. (past perfect)This made me think.
FCarvThis made me think.But why can't you use the Past Simple?People will use it sometimes informally. In AmE, sentences like "She's the most beautiful girl I ever saw" are possible. In the original sentence, "in a while" indicates a period of time up to now, so Present Perfect is the natural choice.
FCarvWhat if I want to menti