High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! Duncan Falls is an unincorporated community in southeastern Wayne Township, Muskingum County, Ohio, United States, located on State Route 60 south of the city of Zanesville. Although it is unincorporated, it has a post office, with the ZIP code of 43734. According to the Census Bureau the population for zip code 43734 is 1200.