In the new study, Massey PhD researcher Sam Hill helped analyse the songs of 78 different songbird species from around the globe, including tui and hihi.
"We found a weak, but significant correlation between the percentage of chicks fathered by extrapair males and how complex that species' songs are," he said.
"This suggested that those species that have more complex songs are perhaps more likely to father lots of chicks outside of the social nest."
The researchers also looked specifically at tui, which are endowed with two voice boxes and are renowned for their wide repertoire of songs - it's been estimated at more than 300.
Hill explained how tui sing two main classes of song - "broadcast song", which are sung from a high vantage point, and "interactive song", which are sung at close range to other males and females, often aggressively, and sometimes even culminating in song battles where males attempt to out-sing each other.
"We found that tui broadcast songs are more complex than their interactive songs - they're longer and contain more different syllables and a greater proportion of trills," he said.
"The results together could provide some evidence that broadcast songs in songbirds are designed for, among having many other functions, attracting as many mates as possible."
The study follows other recently-published work by Hill that demonstrated how the plucky native bird's song is more complex in forest areas where there's plenty of plant species, and perhaps more competition.
That study found how birds in more wide open areas with less plant biodiversity sang simpler tunes, while those in dense, complex forest squeezed much more into their melodies.
Another 2015 Massey University study also found how urban tui songs typically had fewer syllables and trill components, but a higher proportion of harsher elements which enabled their calls to cut through the noise.
Hill expected there was "loads" still to be learned about our charismatic tui.