Wikipedia does not provide many details1 on how baleen whales produce 'whale song', saying it's still a mystery.
The linked Gizmodo article provides these paragraphs:
Humpback whales, for example, do not appear to exhale while singing, and yet their songs are believed to be produced by a phenomenon similar to how humans sing: by air flowing across internal membranes within the respiratory system. In a whale, air could be circulating back and forth between the lungs and another respiratory chamber during 20-minute dives, though this remains speculative.
The researchers argue that "ingressive" and "egressive" air movements may produce different sounds. They also posit that the shifting of the oxygen/carbon dioxide ratio (which must occur during a dive) could be changing the resonant frequency of the singing organ, by changing sound velocity in the gas in the organ.
Both of these physical constraints might contribute to the periodicity (and variability) commonly observed in whale songs. Compare this reading to a hierarchical interpretation of whale singing (which, you'll recall, involves naming the individual components of a song), in which qualities like periodicity and variability might be linked to some function of syntax, rather than physiology.
Mercado and Handel's "heterarchical" model could be empirically tested by linking subtleties of whale songs to their behavior, or their breathing patterns. For instance, this model would be well-validated if the scientists could predict the diving or breathing of a whale based on the spectrotemporal nature of its song.
But I'm not clear exactly what '"ingressive" and "egressive" air movements' these would be? Unlike for Odontocetes, in that wikipedia article, there's not cross section or diagram with any hint of explanation.
1. At least at time of access: 2021/09/23 17:40
