I would recommend a dual major between your current major and computer science. Computer science is going to be the main degree behind developing software as it involves how to break down a problem in to its constituent parts and form a program that solves that problem.
Adding to that the knowledge of music production will help understand the problem you are trying to tackle better. You may also want to take some courses on analog effects as part of your music program if they are available so that you can learn about how they impact sound and what they actually do. You will not simply need to know how the circuits work from an electrical engineering perspective, but rather how they impact the sound and how sound signals work, so you may want a signals and systems class thrown in their as well, particularly if there is a signals class available that focuses on audio.
I'm saying this as someone who is an electronic arts and computer science dual major. I ended up not going into working with audio/video software development as there were good jobs outside of that field in my area, but it prepared me pretty well overall to tackle those kinds of jobs.