The word excrucis is derived from the Latin: ex, meaning - out of, and crux, meaning - cross.  Excrucis is, literally, “out of cross” or “out of crossing.” This technique has to do with how important moments involving dissonances are treated. When voices in music, each of which is logically and expressively following its own inexorable path, come together in a crossing (dissonance) which then resolves in an elegant and beautiful manner, the moment is ripe for the excrucis technique. These moments, properly treated, produce some of the most "excruciatingly" beautiful effects of which music is capable.

    Perhaps the easiest way to think about this is by noticing how it is similar to the feeling one gets when deeply hugging (out of a crossing action) or being deeply hugged by one you love or who loves you intensely. It feels so good it hurts. Many times such moments in human interaction are heavily loaded with profound emotion of the most positive and spiritual kind. This is the cognitive effect of the excrucis technique. Making the most of those moments in which such voice crossings are found means temporarily slowing the action down, to the point that any casual observer can notice exactly what is happening, without causing a loss of flow, in order to create a "grinding" effect as the dissonances rub and grate against each other in the crossing process.

As heard in the example video, Beethoven has most skillfully created a 4 voice fugue with an almost impossible theme in order to create a piece of excruciatingly beautiful music that takes the excrusis technique to its most extreme expression.  Beethoven grinds the voices against each other to cause some of the most dissonant, yet beautiful, sounds composed before the advent of atonal music. Not only does he do this once, but he does it thrice, as the music is a triple fugue weaving three themes together in a fabric so dense and exquisite that it stretches the listener's feelings to the uttermost.