In an interview with The Quietus, Thorpe explained that the success of their second album Two Dancers enabled the band to be "dynamic and daring" on its successor Smother.
He said: "We had a few options, one being to get faster and louder... I heard someone coin the phrase, 'Make a Three Dancers'. But we wanted to be more dynamic and daring.
"We felt really empowered by knowing that people were listening, and if you know people are listening you can be a bit more subtle and a bit more collected."
Thorpe added that the band were "so frustrated by the non-adventure in British music" and "wanted to be heard" when recording their first two albums.
"In a sense that paid off because we proved a point that we don't have to prove again," he explained.
Wild Beasts will headline The Park stage at Glastonbury on Saturday, June 25.
They have also been booked to play at Field Day in London's Victoria Park this August and End of the Road festival in north Dorset this September.
The band's third album Smother is out this week.
> Wild Beasts: 'Something shifted for us'