Why is this
transcribed like this
It seems much more obvious to me to fit it into 3/2 time:
Maybe the clue is in the 'split common-time' symbol? But perhaps it didn't have the same meaning in those days?
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This is an example of mensural notation, common in the 14th and 15th centuries. You are correct that the clue is the split common-time symbol, which was one of the symbols (along with the common time symbol) that carried over into modern notation. (By the way, this wasn't a "c" for "common," rather it was an open circle for "imperfect" time, meaning a breve divided into two semibreves instead of three.)
Imperfect time is generally translated into 4/4 time, whether there's a line through the C or not. While this particular tune may work as a 3/2 melody, that isn't the intent given by the notation. If it were intended as 3/2, the time signature would be a circle, optionally with a line through it.