Matt Groening’s Futurama (1999-2003) contains one of the more niche classical music references in popular culture. It turns out the show’s cycloptic heroine Leela is in fact called Turanga Leela, named for Olivier Messiaen’s Turangalîla-Symphonie. We assume on first meeting Leela that she is an alien, like many of the characters in the sci-fi cartoon, but it transpires she is a mutant and ultimately human after all.

She’s well named. Messiaen’s 80-minute orchestral spectacular, whose title comes from the Sanskrit word for love, is a wild mélange, and no less loveable for it. Its ten movements (rather than the customary four) have the bolts and rivets of traditional symphonic language (a scherzo here, a sonata-form development there) with a thick maquillage of other elements plastered on top: a wildly virtuosic role for solo piano, making it part concerto, and lengthy experiments with layered rhythmic patterns for percussion drawn from Indonesian music. Elsewhere, its lushness seems to come straight out of splashy Hollywood scores.

Messiaen the musical mutant: when Aaron Copland heard him play the organ in Paris in 1949, he wrote in his diary: ‘Heard him improvise at noon. Everything from the “devil” in the bass, to Radio City Music Hall harmonies in the treble. Why the Church allows it during service is a mystery.’ If Turangalîla resembles anything in the musical canon, it’s the genre-spanning oddities of Beethoven’s late period like the Choral Fantasia for piano, orchestra, and voices, or Mahler’s Symphony No.8, which sits somewhere between oratorio, symphony, and opera, in its gargantuan setting of Goethe’s Faust.

The piece, Messiaen said, is ‘a love song; a hymn to joy’. It is 75 this year – there is a dizzying new recording recently out from the Toronto Symphony Orchestra and Gustavo Gimeno – which is a great excuse to give the piece to students from the Royal College of Music, conducted by Jac van Steen, who performed it at the Royal Festival Hall on 1 May. A mainstay of the National Youth Orchestra of Great Britain, it’s a wonderful piece for young musicians with its relentless erotic and expressive churn and unembarrassed grandiloquence.

Gustav Mahler, of the 90-minute ‘Symphony of a Thousand’ fame, said such works should contain the entire world. ‘Why not the universe too?’, Messiaen asks in Turangalîla. Its fifth movement, the ecstatic scherzo ‘Joie du sang des étoiles’ (Joy of the Blood of the Stars), represents the union of two lovers cast on a cosmic scale; the Big Bang, so to speak. Its erotic impulses come from Messiaen’s fascination with Tristan und Isolde, with Turangalîla capping a trio of works that tried to bottle some of Wagner’s erotic smouldering.

At root, ‘Symphony’ means simply ‘sounding together’, implying grand consonance. In Baroque music the ‘sinfonia’ signifies the complete orchestral forces coming together; in Turangalîla it is the cosmos that vibrates with love, both human and divine (for the sensuously Catholic Messiaen there was no distinction), making Beethoven and Gamelan sound together. (One movement ends with three lashes on the suspended cymbal followed by a single dead stroke in the bass drum – a tongue-in-cheek reference, perhaps, to the opening of Beethoven five, perhaps?)

Isidore of Seville used the word ‘symphony’ to refer to a type of two-headed drum. Turangalîla is awash with percussion – I counted 12 players – and its battery is drawn from the world over: Provençal tabor, woodblock, temple blocks, glockenspiels, maracas, and lounge jazz vibraphone. The young percussionists found a remarkably disciplined groove – but special praise should go to the player on the maracas, who shook them aloft with shamanastic abandon at the climax of movement seven.

In German, ‘Symphonie’ was a generic term for keyboard instruments from the 16th century onwards, and Turangalîla has plenty of those, too, flanking the front of the Festival Hall stage from right to left, with more tuned percussion arrayed behind them. Along with the fearsome solo piano part and a twinkling celesta, there is the fruity ondes Martenot. The latter is a special fixture of Messiaen’s music, invented in 1928 by Maurice Martenot – it is played with a keyboard and a ring moved along a wire, which gives it an expressive wobble like a cello buzzed on amphetamines.

The ondes Martenot appears in numerous works by Messiaen – his opera Saint François d’Assise features three of them, which makes it difficult to programme, given that there are only a handful of players and instruments in the world. The instrument counts among its champions Radiohead’s Jonny Greenwood (who used it on Kid A and in his score for There Will Be Blood) and Thomas Adès, in whose opera of Luis Buñuel’s The Exterminating Angel it represents the supernatural force confining the aristocratic party guests. At the Festival Hall, Messiaen’s sprite-like writing was performed with balletic nimbleness by composer and ondiste Imsu Choi, who also found some brilliantly eerie Hammer Horror effects in the third movement.

A work so extravagant could only have been premiered by the young Leonard Bernstein, who served it up with Messiaen’s wife Yvonne Loriod and the Boston Symphony Orchestra in 1949 along with Ginette Martenot, co-inventor of the eponymous instrument. The original commission expressed no limitation when it came to instrumentation or forces, which must’ve been a salutary lesson to the management of the Boston Symphony. When it made landfall in the UK five years later at the Royal Festival Hall in a concert mounted by the BBC critic Eric Blom said its sensuous gardens recalled ‘the plant in Edward Lear’s botany which he calls “Nasticreechia Crawluppia”’.

He’s not exactly wrong – the chirruping melodies of the fifth and final movements are like tendrils that crawl into your ear, and, like poison ivy, prove remarkably difficult to extract. ‘Supremacy to melody!’, Messiaen wrote in The Technique of My Musical Language. In Turangalîla they are concentrated, motivic, and constructed of the simplest elements – not the achingly sophisticated endless melodies of Schumann or Chopin, but rather musical jelly beans. The ‘flower’ theme, a four-note gesture on a pair of clarinets, sounds like a radio jingle or something you might hear before an announcement in an airport terminal. If you can get past the sheer embarrassment it is nothing but full-fat musical pleasure.

Pierre Boulez called it ‘brothel music’ and ‘vomit’; for many listeners its sugary swooping and B-movie warbles are simply indigestible. When conductor Kent Nagano was asked for a scurrilous story about Messiaen in an interview, all he could come up with was the recollection that the composer and his wife once ate an entire pear tart in one sitting; an experience, one imagines, a little like sitting through Turangalîla’s syrup-soaked span.

At the Southbank Centre, Jac van Steen’s unfussy, brisk conducting, helped a great deal – taut, secco cut-offs provided vigorous dramatic punctuation; in slower movements he never allowed the endlessly circling layers of birdsong and melodic fragments to drift into torpor.

Focus was intense from the RCM Symphony Orchestra – it has to be for a work of such duration and complexity in ensemble playing, which hardly faltered – but perhaps at the cost of a little wildness. The opening brass chorale could’ve done with more brash, hieratic swagger; the strings were certainly sweet, but never quite ferocious enough (it’s a dance of death as well as a love song, for Messiaen). By the end, though, and the enormous restatement of the love theme, the whole stage was vibrating. The final F-sharp major chord – a key in which Messiaen sees the face of God – found its cosmic incandescence.

At the piano, Thomas Kelly represented the many faces of the instrument in the piece with fierce devotion: one moment, a spectacular, roaring Lisztian cadenza, the next folding into the clamorous percussive passagework with his colleagues on xylophone and vibes; the birdsong that perks up movement six’s languorous ‘Jardin du sommeil de l’amour’ was all springlike, wide-eyed attack.

Despite finding the piece almost unendurable in 1954, Blom felt that the sheer force of Messiaen’s ‘sincerity’ meant the BBC should be applauded nonetheless for mounting such a monstrosity. ‘Besides’, he noted, ‘someone or other is sure to have adored this symphony.’ Like Godzilla stomping on Tokyo, whose own prehistoric musical trudge Messiaen’s ‘statue theme’ oddly presages by a couple of years, one can only look on awestruck as the piece unfolds. You can applaud them again this summer – on 30 July Nicholas Collon and the BBC Philharmonic give the piece at the Proms with Cynthia Millar, the defining ondes Martenot player of her generation, and Steven Osborne, a renowned exponent of Messiaen’s piano music.