Erika's Bloglet dismisses modern music and specifically, John Adams' Gnarly Buttons:
Although [it] isn’t atonal, it still manages to sound incoherent, and his borrowings from popular styles only make it sound twee.
She does speak positively of Philip Glass.
For myself, I never much liked the banjo in Gnarly Buttons although how many CD covers have a cow? William F Olive III on Amazon calls the piece "goofy."
I'll have to ponder if Adams' music tends toward "twee-ness." Eros Piano, a "gloss" on Toru Takemitsu, has some of that quality and is one of my least favorite Adams works; Grand Pianola Music is bombastic but yet still refined; El Dorado, Shaker Loops or maybe Harmonium are good representatives of the "non-twee."
Interestingly, Peter Gutmann points out that the work has a poignant context despite its surface. Adams wrote it in tribute to his clarinet-playing father, who ultimately suffered from dementia. Here's Adams'
overview of Gnarly Buttons:
I. "The Perilous Shore": a trope on a Protestant shape-note hymn found in a 19th century volume, The Footsteps of Jesus...
The melodic line is twisted and embellished from the start, appearing first in monody and eventually providing both micro and macro material for the ensuing musical structures.
II. "Hoedown (Mad Cow)": normally associated with horses, this version of the traditional Western hoedown addresses the fault lines of international commerce from a distinctly American perspective.
III. "Put Your Loving Arms Around Me": a simple song, quiet and tender up front, gnarled and crabbed at the end.
Boosey & Hawkes samples in Real Audio.