Hello!
As I understand, you've data at 12 samples per year, and you wish to interpolate 30 samples per two samples, considering I put that on a number line. Is that all, or you've additional information? What is the dimension of each sample?
Regarding methods:
From what it seems linear interpolation would give very coarse results on such a low resolution data. We could build a cubic spline (which again confirms that you've 1 D data, so above dimensionality hope doesn't hold) and see how it does. However variations between any 2 samples for any 2 months, would be very difficult. However, if you've data collected from various sources that is 1000 such 1D monthly data collected over 5 years, let's say, we are in good shape.
About me:
I use RStudio on Linux Ubuntu. I also have MATLAB/ Octave. We could do Python too. I'm research student and takes up work along my domain from time to time.
Kindly let me know if you're interested, and can message me whenever you are free. If I'm not online, shall reply you ASAP.
Thank you! Have a great day!!