The Ruin song might actually be called the history of all people.  It begins with the story of creation, progressing to the rise and fall of civilizations.  This cycle of ruin and regeneration parallels the course of human history - prehistoric times, the ruin of the Ice Age, the rise of dynasties such as the Roman Empire, and their demise through warfare, conflict, and death.  The times of ruin, which in the modern day can be compared to the World Wars and the threat of nuclear annhilation, are interspersed with periods of peace and calm.

I believe that the history in the book is called the Ruin Song because, as Kira noticed about the pattern, "each time the ruin was worse and the rebuilding more difficult" (Chapter 12).  It is the memory of the last ruin which remains foremost in the outlook of the civilization, which to the time of the story had not yet been able to recapture the "blue" of tranquility.