If you do a two year CTI program you will have most of your basic math, English, history etc. classes when you graduate. So really your only adding a years worth of aviation classes. You could always major in music and minor in at-CTI as long as you have all the aviation classes, and core classes required for your two year degree you can be refered to the FAA.
So my two sence go to a college with a two year CTI program and a four year music program, all in one