Last year saw the continuing rise of Muse as one of the most popular rock bands in the UK, and a few years ago guitarist/singer Matt Bellamy was hailed by Guitarist as the century's first new guitar hero. With sell-out gigs taking place as I write, this seems like a good moment to take a closer look at the band's music. The three-piece Muse have released three albums to date: Showbiz (1999), Origin Of Symmetry (2001) and Absolution (2003) (not counting the Hullabaloo live album/B-sides compilation), which have given them a number of hit singles.

Muse juxtapose a pop sensibility with a dollop of guitar noise and slightly histrionic vocals recalling Jeff Buckley in their extended range. If Bellamy is a new guitar hero then he demonstrates how much the whole concept has been deconstructed during the nineties. Listen closely to these albums and you will hardly hear a single pentatonic/blues-rock phrase. The solos are short, not especially melodic, definitely un-rock 'n' roll, and use effects and noise to paint with sound. Think of Jonny Greenwood and Billy Corgan. Bellamy is fond of tremolo picking - where the string is strummed rapidly as on a mandolin - as tracks like Sunburn, Showbiz and Citizen Erased attest. He also uses octaves, as on the intro of Sober and in Fillip.

Despite Bellamy's expressed admiration for Tom Morello and Rage Against The Machine, Muse sound thoroughly European. There are concrete musical reasons why this is so that go beyond the rippling keyboard arpeggios found on Bliss. Muse's nervy, solipsistic angst (in contrast to the listless resignation of much Brit rock) is partly expressed through their liking for writing songs in minor keys. Em, Dm and Gm seem to be favourites. The songs avoid predictable blues-influenced progressions heard elsewhere. For example, a common rock songwriting trick is to take a pentatonic minor scale - say E pentatonic minor, whose notes are EGABD - and write with the major chords on these root notes (this happens in quite a few Rolling Stones songs).

Muse, however, show a pop sensibility in their combinations of major and minor, and in their fondness for the minor chord IV (Fm in C). Normally chord IV in a major key is a major chord. But you can turn it into a minor (an example of what I term a 'reverse polarity' chord in my book The Songwriting Sourcebook) for an explicitly romantic effect. A IVm-I change makes for a touch of melodrama, especially in an amped-up rock context. Played more delicately it creates a feeling of an almost painful tenderness, as in the case of Radiohead's No Surprises. Hate This ends Gm-D like Radiohead.

Another songwriting signature of Muse is their willingness to put other notes in the bass than the root note. At times their progressions sound almost baroque. The reason for this is the first and second inversions above bass lines that move in ascending or descending semitones. You can hear this in Falling Down, Micro Cuts and the guitar break at the end of Cave, which is played over the progression Bm Bb D/A E/G# G7. Muse songs feature an above average number of chromatic chord changes like Gm-F# or the sequence Gm F# Fm E Fm E Em from Fillip, and changes from major to minor (or vice versa) on the same root note. Consider Plug In Baby's chorus of G Bm F#m G Bm F#. As well as inversions, progressions are also spiced up with diminished seventh chords. Most significant is Muse's use of the harmonic minor scale.

In rock, blues and folf, the most common minor scale is the natural minor or Aeolian mode. For example, the A natural minor scale is ABCDEFGA. Notice that it finishes with a tome between G and A. If you build a chord on the 5th note, you get E G B which is E minor. By contrast, the A harmonic minor scale sharpens the 7th note: ABCDEFG#A. Chord V becomes E G# B, which is E major. This G# gives a more 'classical' sound. You can hear E harmonic minor on Sunburn and New Born, F# harmonic minor in Muscle Museum (its E# clearly heard at 1:54-2:00), and D harmonic minor in the solo on Micro Cuts (2:42-3:06) and in Dark Shines. The chord sequences often imply the harmonic minor by having the major chord V in the minor key. Feeling Good, for example, is Gm Gm/F Eb Dsus4 D implying G harmonic minor.

Current pop influences occur in Screenager, with its opening Gm/maj7 chord to give a Bond feel, and the early sixties clean guitar break in Uno. Escape has the grunge trick of the vocal line plus single note guitar phrase stuck between power chords on the chorus. From earlier on, the ghost of Hendrix is felt in the riffs for Uno, Hyper Music and the Purple Haze rhythm of Sober.

At their best, Muse sound like the inspired offspring of the Smashing Pumpkins, but these 'classical' harmony touches sometimes nudge them close to the pomp of Ultravox and Yngwie Malmsteen, however different the execution of the music. The harmonic minor does not sit easily with rock, being at odds with its roots in blues, and more than offsets the 'aural terrorism' touches.