The population of male horned whales is subjected to a "cultural revolution" every few years when the hymn changes, the study showed.
The study of 13-year-old whale song samples showed that the signature song of individual groups evolved gradually over time.
But every few years, the song of the population is completely replaced by an event described as a "cultural revolution".
When the revolutions return, the new song is always simpler than the one that preceded it.
Whale kits are known to have "dialects" unique to different populations. In addition, male whale groups have their "anthems", each member of the population singing the same sequence of the same sounds.
New research, focusing on 95 "singers" from Eastern Australia, found evidence that the gradual changes of the poem were the result of ornaments introduced by individuals and then taught them from the rest of the group.
Songs introduced in revolutions may be simpler because singers are harder to learn a whole new material, scientists say.
Dr Jenny Allen of Queensland University, Australia, said: "We've looked at two dimensions of song structure, complexity, and entropy [a tendency to become more disordered] in eastern Australia over 13 consecutive years.
"Complexity increased as the songs evolved over time, but they diminished when the revolutions emerged.
"No correlation between the complexity and the estimate of the entropy suggests that the complexity of the changes could be the delight of the song, which would allow men to stand out in the midst of population conformation.
"The constant reduction of complexity during the song revolution suggests a potential limitation of the social learning of new material in whale kits."
The study, which included British scientists at St. Andrews, was published in the Royal Society Proceedings B.