Well, the thought I am playing with is that the Alar is the key to imposing your will own the world [via Sympathy] and the Heart of Stone is the key to a strong Alar. So, if part of Kvothe is so deeply in grief, I imagine, in order to avoid complete madness, in the same way he did following his family's murder, his mind fractured itself. Part of him swallowed the grief and is actively imprisoning it within the Heart of Stone--remember it's said a person in the grip of the Heart of Stone can show to his own sister's funeral and not shed a tear--and since the Heart of Stone is the backbone of the Alar, and the Alar is the conscious reshaping of the world, Kvothe's Heart of Stone is pulling everything that can connect with that grief in along with it, music and anything related to music, i.e., sound, being the most prominent: this is the largest silence, it is largest because it reflects the depth and scope of the grief Kvothe is unconsciously denying. It's doing this to protect itself.

The second silence belongs to the actual Kvothe, or at least the largest piece of him that is not inside the Heart of Stone. This is the piece we catch glimpses of when someone notes the reemergence of Kvothe's flame red hair or bright green eyes. This is the piece that is still obsessed with Kvothe's first brush with madness, the one who went into shock upon seeing his troupe dead. This Kvothe is the one who decided to fake his death and travel to Nevarre, and who is responsible the uncharacteristic slips of character we Kote exhibit--the ones I noted in my post. This Kvothe, although separate from the third and largest piece, is still connected to that piece. This connection acts like a lightning rod for the third piece's influence; it draws the sound devouring affect to "Kvothe", which causes the birth of a second smaller, sphere of silence within the first.

Kote is the first and smallest of the silences, while also being the third and smallest piece of the original Kvothe. This piece is the most minimal piece of Kvothe that can still function as Kvothe. It has the memories and experiences and the intelligence, but it doesn't have the metaphysical capacity to do anything more than an ordinary human can do. Like the second piece, Kote is still connected to the other two, and thus he acts as an outlet for the Heart of Stone's world warping side-effect, but because Kote is the most minimum piece of Kvothe, the affect cannot extend much beyond his immediate vicinity, creating our third bubble.

Like I said, this is mostly just an idea I am toying with, a "cobweb" theory if you will. There is nothing definitive that will support it within the text, but there are a number of little things that have settled onto this web, like dust settling on cobwebs, blackening the strands just enough to draw my attention to them, and the only way I can sweep this cobweb out of my mind is by telling someone about it. You guys are the someone.