Most would agree it's fair to say APC is the most accessible of Maynard James Keenan's musical projects.
Even though Keenan is the frontman, the group is definitively guitarist Billy Howerdel's brainchild. Howerdel and Keenan co-founded the band in 1999 after Keenan was impressed by Howerdel's demos and basic lyrical concepts. They are the only two consistent members of the history of the band's lineup, and between the two of them write all of A Perfect Circle's original lyrics, and nearly all of the musical composition. The current absolute lineup only consists of Keenan (vocals), Howerdel (guitar), and Josh Freese (Drums and Percussion).
The music of A Perfect Circle can be likened to Tool's in the atmosphere it creates, and the perpetual sense of frustration the lyrics suggest. But from a musician's standpoint, the structure is somewhat different. While Tool's music is very technical and very unelaborate, APC's music involves more instruments and yet is much less excessive. Tool's music tends to go through multiple vamps and interludes, and makes use of dissonance, and APC's music has a greater tendency to follow a verse-chorus format in a major key tonality, making it more accessible and much less intense. Less intense musically, anyway.
A Perfect Circle is also like Tool in that their album cuts are few and far between, and the group takes many extended breaks for the sakes of breathing room and for the opportunity to focus on other things. Their discography as of this writeup:
Mer de Noms, Virgin Records, 2000
Thirteenth Step, Virgin, 2003
Emotive, Virgin, 2004
Deep Cuts EP, Virgin, 2009
The band had gone on hiatus from 2004 - 2008, leaving many wondering about the future of the band. More recently, Keenan has confirmed the future of A Perfect Circle, and that new material was in development.
Highly notable songs:
Judith
3 Libras
Sleeping Beauty
The Noose
The Outsider
Passive