Which programming language do you use? I have created a mainly bug to bug compatible Scala parser for Mutabor (C++/Bison/Flex).
And there is a book “The Mathematical theory of tone systems” by Jan Haluška which countains lots of tunings.
Most tunings in western music can be (and were, historically) derived mathematically. You can not copyright mathematics.
You can certainly copyright a document containing mathematics (e.g. a math textbook) but the copyright is of the arrangement of the text on the page, not of the maths itself.
So IMO you can include any tunings you like in your software ...
From what I've read / heard, I believe Japan uses Chinese tuning, which if I recall correctly is essentially Pythagorean tuning, which would be reasonably approximated by 12tet. There is a heavy reliance on heptatonic and pentatonic scales obviously, which probably suggests a 12-tet or meantone kind of system.
Britannica Encyclopedia Page on Japanese Music