It was all nice and perfect. A warm evening of the ending summer. They were on top of a hill, outside Ba Sing Se's inner walls, watching the beautiful sunset. He had her head on his lap. There was nobody else around - especially Sokka, who certainly wouldn't approve. They just watched the burning sky in silence. Everything was perfect.
And then Aang heard it.
Katara noticed him getting tense, with her supernatural skills of always knowing when Aang was in distress. "Aang-?"
"Sshh!" He hissed, bringing his finger to his lips. He looked around, eyes darting everywhere, to see if they were truly alone. They were. Only when he was sure about this, he whispered: "Can't you hear it?"
"Hear what?"
And then she heard it too. A faint, silent sound of a certain musical instrument - a guzheng, most likely. It went, "Ding, ding ding, ding ding ding, ding ding ding".
"Oh. Okay, that's... Kinda scary."
"Tell me about it," he looked at her. "It's a weird little thing. I sometimes hear it when we're together. Heard it in the Cave of Two Lovers, for the first time. Kinda beautiful, but also scary."
Ding, ding ding, ding di-
Silence.
"It stopped," Katara said slowly, silently.
"Yeah. Never done that before. Weird."
They never heard it again. Aang wondered, sometimes, if it had been some spirit's work. "Maybe some outer forces want us to stay together," Katara responded, when he told her about this.
Later, Aang made a journey to the spirit world, and learned that there indeed was one particular little spirit who had played a guzheng whenever he and Katara were together. Why? Because he had thought they were a cute pairing. Sometimes, the spirits would play music to the couples they really approved: This was rare, and it was even rarer for the mortals to notice anything. But once they did, the spirits had to stop playing. It was the rule.
Some weeks later, when the group had separated, to go their different ways, Aang purchased himself a guzheng. And at night, whenever he really missed Katara, he would play their tune with it. It didn't make his longing for her any lesser, but it did make him feel a little better.