In 1968, Richard Strauss entered pop culture with the release of 2001: A Space Odyssey. The ominous fanfare that begins the composer’s Also Sprach Zarathustra, ingeniously purloined by Stanley Kubrick, speaks of a universe entire. Turn to Strauss’s 1919 opera Die Frau ohne Schatten, performed at the Royal Opera House this month, and you’ll discover the same flair for the gargantuan. Strauss is the go-to composer for maximalism. But if you look beyond the decibel-busting surface of his music, you will find sensitivity at the core of everything he wrote.

2014 marks the composer’s 150th birthday. Born in Munich in 1864, he died shortly after the downfall of Nazi Germany. Strauss completed 15 operas, numerous songs and several orchestral works, evoking themes as diverse as Alpine landscapes, Don Quixote and the biblical nympho Salome. Lauded in Europe and performed around the world, he was one of the 20th century’s most prosperous composers.

Yet Strauss’s success has always been tainted by perceptions of him as a hard-hearted opportunist and this anniversary year has given his detractors a fresh chance to sling familiar mud, particularly when it comes to his involvement with the Nazis. Strauss notoriously became the first president of the state music bureau, the Reichsmusikkammer, and penned a hymn for the 1936 Berlin Olympics. Yet his insistence on working with the Jewish writer Stefan Zweig ran foul of the regime and the composer’s associations with Hitler and his cronies soon soured.

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Putting aside these reheated controversies, there is a more intriguing account of the composer to be drawn out. Meditative, even contrite, Strauss displayed great heart and insight in his final works, such as Metamorphosen, a 1945 threnody on humankind’s bestial nature, and the Four Last Songs of 1948.

The empathy that courses through these late works is likewise evident in Strauss’s earlier output. Even bloodthirsty operatic rollercoasters such as Salome and Elektra have disarmingly warm moments. And in spite of the inventory of over 120 instruments required to perform Die Frau ohne Schatten, including glass harmonica, thunder machine and organ, it too has a meeker soul than is frequently suggested.

This most sumptuous of Strauss and his librettist Hugo von Hofmannsthal’s stage works revolves around a half-mortal Empress, whose inability to cast a shadow renders her infertile. Keikobad, her father and the master of the spirit world, gives the Empress three days to find one, or else her husband will be turned to stone. Emboldened by a scheming nurse, she descends to earth, intent on stealing the shadow of a humble dyer’s wife. But the Empress quickly realises she could jeopardise an already precarious marriage and abandons her plan. Keikobad acknowledges his daughter’s compassion and both the human and spirit couples are reunited, greeted by the voices of their unborn children.

Knitting together elements from Mozart’s Magic Flute, the Brothers Grimm, Goethe and the Italian dramatist Carlo Gozzi, von Hofmannsthal’s exaggerated fairytale prompted Strauss to insist that it should be their “last Romantic opera”. Indeed, the opera came to mark the end of an era. Conceived before the First World War and composed during the hostilities, Die Frau ohne Schatten finally saw the light of day in Vienna in 1919, when the Austro-Hungarian Empire had been demolished and stories of Emperors and Empresses seemed old hat.

But while the opera has been known ever since for its symbolism and swagger, its simple, underlying tenderness has often been overlooked. Given the brooding Marschallin at the centre of Strauss’s Der Rosenkavalier or the touching tones of his Four Last Songs, that sensitivity should come as no surprise. And indeed, for all its fantastical qualities, Die Frau ohne Schatten features a decidedly lifelike couple, the dyer Barak and his wife, conceived by Hofmannsthal to mirror Strauss’s own troubled marriage.

Their relationship draws from Strauss music of incomparable beauty, not least in Act I when Barak calmly tells his irascible wife that he feels nothing but hope for their future together, accompanied by a quiet but intense lullaby. Barak’s wife responds curtly, unhappy at her lack of children, though he simply reassures her of “the blessings which are to come”. Given the potency of such passages, it is little wonder the stone-hearted Empress craves their co-dependent domesticity.

Claus Guth’s new production for the Royal Opera House, first seen at Milan’s La Scala in 2012, unfolds in a psychiatric clinic, where the Empress is undergoing treatment. Interpreting her predicament in these terms validates the opera’s duality between our world and the beyond. It likewise underlines the innate intimacy and warmth of Strauss’s music and grounds Hofmannsthal’s lofty symbolism in the Freudian concepts to which he so often turned. During the Empress’s last stand, introduced by a spellbinding violin solo, she faces her father’s wrath and, in Guth’s sometimes subversive account, bridges the gap between the conscious and the unconscious.

Despite Strauss’s inherent skill at illuminating such an interior drama, he continues to be dismissed as second-rate. Certainly, by concentrating on the outer dazzle of his work, it is easy to frame him as a braying manipulator. Yet while Strauss can be Zarathustra-like in his grandeur, pursuing self-mastery at any cost, he is also a romantic, the hapless Don Quixote, as featured in another of his tone poems. It’s an uneasy personality match, but one Strauss effectively acknowledges by ending his musical evocation of Also sprach Zarathustra with two harmonically exclusive chords, forever unresolved.

Die Frau ohne Schatten is similarly hard to reconcile. The insistence on the redeeming power of procreation jars with modern sensibilities, yet only a callous spectator could fail to be moved by its characters’ self-sacrifice. So while the ornamental and sometimes ear-splitting trappings of Die Frau ohne Schatten may not offer the most digestible opera, the work’s self-awareness and consequently profound shifts in perspective make it Strauss’s truest and, for that, perhaps his greatest opera.

‘Die Frau ohne Schatten’ is at the Royal Opera House from 14 Mar to 2 Apr