Muse, Meadowbank Stadium, Edinburgh <img src="http://www.independent.co.uk/template/ver/gfx/fourstar.gif"></img>

Many of Muse's lyrics mention revolutionary rhetoric and fashionable scientific concepts. This suits the band's image, with any comparison to a trio of glammed-up supply teachers being not entirely unmerited.

This year's Black Holes and Revelations album - their fourth since 1998 - takes such allusions a step further. Its very title mixes the purely scientific with the biblical, yet the band's singer and lyricist Matt Bellamy says he's dealing in personal concepts - the revelations are moments of personal discovery, the black holes represent those things that an individual doesn't know about themselves.

It is, most definitely, not the stuff of your average pop music, nor even the province of more well-educated guitar bands. Although stadium success came much later in the day for Bellamy, bassist Chris Wolstenholme and drummer Dominic Howard, a close comparison may be made to their relative contemporaries Radiohead.

While Radiohead manage to smuggle glitch electronica and avant-garde rock to a populist audience, Muse's influences begin with progressive rock and classical music, and worm their way into populist acceptance through the band's glossy stylings and deferences to contemporary rock, be it goth, grunge or stadium.

The effect, when played in an arena alongside a big-budget light show, is startlingly good. Bellamy, hair artfully tousled and clad in a zippered black leather jacket, makes a great 21st-century rock star. His voice is otherworldly but immaculate, alternating between a spine-tingling falsetto and a nerve-jangling shout. He employs a similar diversity of musical styles, his guitar-playing flitting between occasionally ragged surf-inspired riffs and histrionic, elegant solos.

When set against the powerful musicality of Wolstenholme and Howard's rhythm section, his virtuoso attention to detail is mesmeric. From the uproarious introduction to "Hysteria", the second song played here, they achieved a level of excitement mixed with attention-grabbing diversity that defines the best large-scale bands.

Similarly, the recent singles "Supermassive Black Hole" and "Starlight" stood out as passages of acutely constructed intensity, while "Plug in Baby" and "Time is Running Out" are more traditional, fiery rockers.

Yet, highlights aside, there was really not a moment of boredom throughout, as Muse demonstrated that blending massive appeal and an intellectual approach to rock is entirely possible.