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Have Santiago Calatrava's soaring architectural aspirations peaked? And are they perhaps on the verge of a cataclysmic crash? Such an irreverent thought is hard to banish when confronted with the Spanish architect–engineer's latest work, a concert hall in Tenerife that appears on the point of being engulfed by an immense concrete tidal wave cresting directly above it.

The hall, which held its inaugural performance last week, is a bombastic attempt to bring high culture and world-class architecture to the beaches and nightlife of the Canary Islands. It is also Calatrava's first performing arts building, yet it still manages to exhibit the sweeping, wide-span forms of the bridges and railway stations with which he made his name.

The spectacular cantilevering arch, which is there solely for sculptural effect, rises to a height of 58 m. Calatrava himself avoids marine references – he describes it as the wing of a bird, and says its curvaceous geometry derives from essays in sculptural form carried out early in his career. Following in the footsteps of his great hero, Antoni Gaudí, these early explorations were inspired by the natural forms of plants, birds and the human body – not just in imagery but also in underlying structure.

Nearly everything about the building breaks the rules for concert hall design. Instead of a shoebox or fan shape, the main 1668-seat auditorium is a concrete cone beneath the Crest of the concrete wave. Two outer concrete shells, or "sails", encircle it, enclose the lobbies and provide an acoustic buffer. A second flat-floored hall seating 410 is intended to be used for chamber music.

A section through the building reveals another of Calatrava's natural inspirations – the human eye – with the cone-shaped auditorium representing the pupil and the arching wave the eyelashes.

The interior of the concert hall is lined with giant, leaf-shaped arches, which vault up and over from front to back to diffuse sound waves. Acoustic reverberations in the hall are modified by opening or shutting a series of shutters faced in solid wood on one side and fibreglass on the reverse.

The interlocking structural shells that make up the building were constructed using a combination of precast and insitu concrete totalling 2000 tonnes in mass. The overhanging wing was precast in Seville in 17 hollow sections, the largest weighing 60 tonnes, and lifted into place by a crane with a bearing capacity of 2400 tonnes. Once fixed in place, the internal cavity was filled with insitu concrete.

The external surfaces of the shells, some 18,000 m2 in area, were covered in another of Calatrava's favourite materials – broken shards of white ceramics, or "trencadis", shipped from Valencia. The polished white surfaces set the building off against the dark crags of the Canary Islands and blue Atlantic ocean.

Calatrava has since moved on to design two more concert halls for Atlanta, USA, and his home city of Valencia, both of which are due for completion next year. The big question is how on earth this structural magician can top the crashing wave of his spectacular Tenerife design –without falling flat on his face.