Here's today's crazy shakuhachi origin theory: in short, that they are imitation monkey bones. This is reportedly from TOYOHARA Muneaki 豊原統秋's 16th-century encyclopedia of Japanese music, the Taigen shō 體源抄, although my translation below is based on the transcription in SAITŌ Eisaburō 斎藤栄三郎's Shakuhachi: Sankyoku no sekai 尺八：三曲の世界 ("Shakuhachi: the world of sankyoku").

Incidentally, this is the Saitō Eisaburō, author of "The Secret of Jewish Power that Moves the World" (世界を動かすユダヤパワーの秘密).

It is written in one source that long ago the shakuhachi was an imitation of the marvelous sounds of the monkey's cries in the west of China. At that time, the monkeys in the mountains there had such miraculous voices that those who hear them are not only moved to tears but also find themselves with new resolve to stay on the path of righteousness. The prince left his palace to retire to a mountain temple, and all the administrators in the surrounding villages went with him, until finally hundreds of people, from monks to merchants, had awoken to the principle of impermanency in this way. Finally the emperor, thinking that this was no way to run a country, sent his soldiers out to kill the monkeys and put a stop to it all.

The results were pitiful beyond imagining. Dozens of those who had entered into the way of righteousness after hearing the cries of the monkeys now mourned and lamented the passing of their teachers, and among them was one whose grief was so deep that it did not abate though the years and months passed, and eventually he began to dig in the earth, wanting to at least see the bones of the fallen monkeys. He found an arm. It was hollow, and when he held it to the wind and listened, it sounded like the call of the monkey itself. Struck by the pitifulness of this, he took it home with him, and one day remembered he had it, put it to his mouth, and blew into it so that it would sound.

Later, a certain musician tried cutting bamboo to that length and blowing into it, but the sound was not the same. However, when he bore one hole in the bamboo and tried again, it began to sound slightly similar. As he bored hole after hole, the aural similarity grew, until finally the bamboo had four holes in the front and one in the back, and sounded exactly the same. The original bone having been one shaku eight sun long, the instrument was given the shortened name shakuhachi [literally "(one) shaku, eight (sun)"].

This is a great story, but let me note for future Googlers that the only part of it that is true is the etymology of the word shakuhachi.