Are there emotions that motivate pattern completion? If so, where in the brain are they located?
This "tension" is actually called anticipation in neurobiology and related fields. Whole purpose of this is to get higher reward. This is generally happens because of dopamine release. Many musicians have utilized this 'anticipation' technique in their compositions. Famous example is Led Zeppelin's stairways to heaven in which audience is 'anticipating' third part of song where Page's guitar in high tempo. Anatomically distinct dopamine release happens during anticipation and one will experience of peak emotion to music. You can read this paper for experiments related to this. This paper's introduction has given reference to many of such research papers. Go through it's references.