I've heard that it's common for INTPs to use music and art as an outlet for the feelings that we don't necessarily (want to) understand. I'm an english education major with a music minor, and I studied art all throughout high school. INTP.org provides a very comprehensive analysis of the type. Here's an excerpt regarding our affinity for music:
"Another area of interest common to INTPs, where Si has a strong influence, is Music. INTPs are usually fascinated by music and may have deep and wide-ranging tastes. Indeed, each of their three main functions (Ti, Ne, Si) plays a role in the enjoyment of music, and indeed music is a key interest for bringing out the feeling shadow of the INTP. Si itself brings a fascination for mood and atmosphere in music as well as for a strong sense of personal nostalgia. INTPs are therefore often keen on melancolic minor-key music in which an introspective and/or esoteric mood is conveyed. Equally, INTPs enjoy hearing music that they heard and enjoyed when younger (provided they can still appreciate it now) and yearn for the sense of nostalgia that it yields. INTPs are also drawn to complexly structured music, thanks to their Ti core. An appreciation of modern classical music, as well as perhaps contemporary jazz, is therefore common with them. Such music types are usually too complex to be understood after a single hearing, which hence provides excellent material for analysis, exciting the INTP no end. Once the basic developmental structure of the music has been assessed, Ne provides the impetus to derive a general meaning of the piece. What does the composer wish to convey, for example? Why was that particular development chosen? Indeed, the Ne is usually hard at work during listening sessions, trying to grasp the meanings behind the often fascinating combinations of sound-world evocations, structural developments and nostalgic impressions."