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I need to find out the trop for the book of Ruth fairly soon because our Rabbi has developed a minor illness and I'll have to do the reading on Shavuot. Surely there is something on the web with the melody?
As noted by Dr. Shmuel in a comment, here are two recordings using the traditional Ashkenazi melody:
Modern Hebrew pronunciation - Cantor Moshe P. Weisblum, PhD
Ashkenazi pronunciation Part I Part II Part III Part IV - Rabbi Jeremy Wieder