Lateralus

The harmony of Lateralus is secondary to its rhythmic and formal structure. It utilizes a D tonic center almost exclusively, shifting between D Aeolian, D Dorian, and D Phrygian modes to alter the emotional weight. The 'Spiral out' climax uses a Neapolitan-style bII-i movement (Eb to D) to create maximum dissonance and tension. While the chords themselves are simple power chords, their placement within shifting time signatures—moving from 9/8 to 8/8 to 7/8—creates a sense of mathematical expansion and contraction that mirrors the lyrical themes.

The song was developed following a four-year legal dispute between Tool and their label, Volcano Entertainment, during which the band avoided writing new material. In early 2001, the band misled file-sharers by announcing a fake album title, Systema Encéphale, and a tracklist of bogus song names before revealing the actual title and music.

The title track of Tool's landmark 2001 album, 'Lateralus' is famous for its mathematical construction and philosophical depth. It represents the band's peak transition from alternative metal into complex art rock, featuring intricate polyrhythms and evolving structures.