My friends are learning about my current obsession with tuning systems, and starting to ask questions I don't know the answers to.
Last night Michael Fourman asked: if harmonies coming from simple fractions are so natural, do any bird or whale songs feature such harmonies?
So I looked around. It turns out an Australian bird called the pied butcherbird has long been a favorite of many composers! Jean-Michel Maujean figured out the frequency ratios that appear in the songs of this bird. He found the 4 most common ratios are close to
0.607, 0.745, 0.815, and 1.34
He notes that
0.607 is close to going down a major sixth (3/5),
0.745 is close to going down a major third (3/4),
1.34 is close to going up a perfect fourth (4/3),
0.815 is kinda close to going down a major third (4/5).
His work looks good - but he shouldn't have bothered comparing the ratios to 12-tone or 18-tone equal temperament. Equal temperament is a system developed for keyboard instruments in the late 1700s. It would be amazing if the birds used this!
Maujean also has a nice review of the literature on harmonies in bird songs, so I should dig into it:
@johncarlosbaez Would I be right in saying that many birds never encounter polyphony*? There must be some that sing together, I guess. I wonder if there's a connection there. Strict rules about harmony are only really necessary if you are modulating keys a lot, or doing polyphony - whether unison, or harmony.
*edit - I mean intentional polyphony. As opposed to the cacophony of birdsong I mention later.