The Song is the main focus of the Tuatha'an philosophy. They search for it throughout the world and hope to find it somewhere.
Age of LegendsEdit
In the Age of Legends, the Tuatha'an were part of the Dai'shan Aiel. They served the Aes Sedai of that time and worked on the fields. Here they used to song along the Ogier and the Nym to grow the crops and nature in it's whole using the song. The song had a magical effect on the world around the singers. It doesn't use the One Power. How it actually works is unknown.
When the Collapse began, the Dai'shain Aiel stood in the way of the armies of the Shadow, holding hands and singing their song. Because of their no-violence philosophy, they were slaughtered.
During the Breaking the song was lost. How it was lost is not known. The ancestors of the modern-day Tinkers split of from the Aiel to search for the song. They hope to find it somewhere in the world. Until this day, they have not found it. They even don't know how it goes or what the words are. When confronted with these facts, they reply they will know how the song sounds when they hear it. Their heart will recognise it. This makes a lot of people think they will never find the song and think the Tinkers are a strange lot.
The song is a very big part of Tinker daily life. When they meet someone, they ask if they know the song. When they say farewell, they say the song will be found by someone, sometime. They are confident it will be found.
It is unknown wether the song will be found before the Last Battle, or that it will play a part in it, if it's found.