Singing Magic theory, and why there was - of course - no music.
Haliax seems to indicate that the Singers are a great threat to the Chandrian.
- "Who keeps you safe from the Amyr, the Singers, the Sithe?" And then Cinder, when his troupe was killed, “Someone’s parents,” he said, “have been singing entirely the wrong sort of songs.”
I think Singing (like "Naming", different from "naming") is one of the types of magic, and that he learns it in the Stormwal mountains.
- “I guess I’d to go to the Tahlenwald,” [Kvothe] said. “I heard a story once that said the leaders of their tribes aren’t great warriors, they’re singers. Their songs can heal the sick and make the trees dance.” I shrugged. “I’d go there and find out if it was true.” - WMF, ch 38, Kernels of Truth
- "The boy followed the road over the Stormwal to ask the witch women of the Tahl, but none of them could give him an answer." - WMF, ch 83, Lack of Sight (Hespe's infamous Jax story.)
The Tahl are known by the Adem, likely distantly related, and, as Penthe suggests, seem very knowledgeable aside from magic.
- “Then I would make the long trek over the mountains into the Tahl to be cured of it. Even if the trip should take two years and bring no money to the school. And none would think the less of me for that.” - WMF, ch 127, Anger
I could easily see Kvothe going there after his expulsion's suspension is revoked by new Chancellor Hemme, to expand his education of Naming and to search for the Chandrian. (Remember that it says his expulsion was suspended - not removed completely.)
- “Six lashes and expulsion,” the Chancellor said heavily. Expulsion, I thought numbly, as if I had never heard the word before. To expel, to cast violently away. I could feel Ambrose’s satisfaction radiating outward. For a second I was afraid that I was going to be violently ill right there in front of everyone.
- “Does any master oppose this action?” the Chancellor asked ritualistically as I looked down at my feet.
- “I do,” the stirring voice could only be Elodin’s.
- “All in favor of suspending expulsion?” I looked up again in time to see Elodin’s hand. Elxa Dal’s. Kilvin, Lorren, the Chancellor. All hands save Hemme’s. I almost laughed out of shock and sheer disbelief. Elodin gave me his boyish smile again." - NotW, ch 86, The Fire Itself
Since we know he won't give up on the Name of the Wind or his search for the Chandrian just because he is no longer in the University:
- “Arrogance,” the Cthaeh said. “You assume you know everything. You laughed at faeries until you saw one. Small wonder all your civilized neighbors dismiss the Chandrian as well. You’d have to leave your precious corners far behind before you found someone who might take you seriously. You wouldn’t have a hope until you made it to the Stormwal.” - WMF, ch 104, Cthaeh
We already know that it is possible to Sing a Name as much as you can speak it, from Kvothe's experience with Felurian.
- "But now, looking into Felurian’s twilight eyes, I understood her far beyond the bottoms of her feet. Now I knew her to the marrow of her bones. Her eyes were like four lines of music, clearly penned. My mind was filled with the sudden song of her. I drew a breath and sang it out in four hard notes." -WMF, ch 97, Blood and Bitter Rue
There's already lots of foreshadowing that he will go there.
- “I want to hear about the dry lands over the Stormwal,” one of the younger girls complained. “About the sand snakes that come out of the ground like sharks. And the dry men who hide under the dunes and drink your blood instead of water. And—” She was cuffed quickly into silence from a dozen different directions by the children surrounding her." - NotW, ch 26, Lanre Turned
And Bast mentions the white sisters, which seems to be the Fae's way of referencing the witch women of the Tahl:
- "It's just that you know so many things," Bast said. "You know all sorts of things you're not supposed to. You know about the Berentaltha. You know about the white sisters and the laughing-way. How can you not know about the Cthaeh?" - WMF, ch 105, Interlude - A Certain Sweetness
And his music already seems to have a magical quality about it. When he plays for the caravan on his way to the University:
- "I don’t know how long I played. It could have been ten minutes or an hour. But my hands weren’t used to the strain. They slipped and the music fell to pieces like a dream on waking.
- I looked up to see everyone perfectly motionless, their faces ranging from shock to amazement. Then, as if my gaze had broken some spell, everyone stirred. Roent shifted in his seat. The two mercenaries turned and raised eyebrows at each other. Derrik looked at me as if he had never seen me before."
In the Eolian getting his talent pipes:
- "A string broke. High on the neck of the lute it snapped and the tension lashed it across the back of my hand, drawing a thin, bright line of blood.
- I stared at it numbly. It should not have broken. None of my strings were worn badly enough to break. But it had, and as the last notes of the music faded into silence I felt the audience begin to stir. They began to rouse themselves from the waking dream that I had woven for them out of strands of song.
- In the silence I felt it all unraveling, the audience waking with the dream unfinished, all my work ruined, wasted. And all the while burning inside me was the song, the song. The song!"
And later, when he salvages the song with a broken string:
- "Then, waiting, I heard the silence pouring from them. The audience held themselves quiet, tense, and tight, as if the song had burned them worse than flame. Each person held their wounded selves closely, clutching their pain as if it were a precious thing.
- Then there was a murmur of sobs released and sobs escaping. A sigh of tears. A whisper of bodies slowly becoming no longer still.
- Then the applause. A roar like leaping flame, like thunder after lightning."
I think that, like Sympathy and Naming, Singing is another type of magic in Temerand that Kvothe, as Kote, hid from himself to help him hide from everyone looking for him as it was too dangerous for a simple inkeeper to know.
And that's my Singing Magic theory.