I'm sure someone is more qualified than I, but:
Depending on what you mean by "build," you might even think about EE. Here's my litle bit of experience: I took a DSP as an EE course (elective), where we often wrote computer code to process signals (many were sound files, and the processing was done using a MatLab platform but of course you could use others). DSP is definitely cool, but of course, you might also want to know about signal process in the analog sense...learning about the actual electronics that can make up certain types of filters ... and that decidedly falls more in the realm of an engineering curriculum. In my day, computer engineering REALLY new, and was in the department of EE anyways...
Many of the EE's I know consult on things like the design of lighting systems, security systems, etc. and hire contractors to install stuff. Sounds somewhat similar, if you want design systems for buildings, venues, or even for people's homes when they are pouring big bucks into a restoration or new build.
Of course... whichever you chose...you can always tailor extra coursework or a minor to include the classes that really relate. Something really fun...there are companies (although they are often small) that do that kind of thing... can you find a part-time job or an internship in this area?