I am using the same melody for 2 instruments and I half-sharpened every D note on the second one, and left the first as C major. Does this have a name? Or is it used anywhere?
A scale that comes close to it is mentioned as a vertex tetrachord but it is not exactly a D with 50 cents but a D+33 cents and an additional A+33 cents: https://mizzan.de/archive/src/scala/vertex_diat2.html. If you are interested in microtonality you could drill here https://mizzan.de/scales