Sufjan Stevens' "Eugene"

This morning I listened to Sufjan Stevens' Carrie & Lowell and noticed something about a recurring line in "Eugene."  It changes a bit every time it's repeated, but it's some variation of "I just wanted to be near you," "I wanna be near you," or "I just wanna be near you."  In all of them, there's the interval of a sixth between the "near" (F#) and the "you" (D#).  This interval does two things.  First, it implies distance between the singer/speaker and the "you."  Second, because of the musical distance covered in singing that sixth, it shows the effort that the singer/speaker is willing to exert in order to "be near you."