“I’m looking for perfection of form. I do that with portraits. I do it with cocks. I do it with flowers. It’s no different from one subject to the next. I am trying to capture what could be sculpture...”

Robert Mapplethorpe’s description of his art dictates the direction of this new show. By displaying 100 of his works in the Accademia Gallery, home to Michelangelo’s David, the aim is to show that the photographer still best-known as the chronicler of New York’s S&M scene in the 1970s was actually the heir to the classical tradition.

Taut poise: ‘Thomas’ (1987)

A similar re-evaluation occurred four years ago when the New York Guggenheim juxtaposed his pictures with Flemish Mannerist engravings. According to reports, that show dazzled not only because the images of flamboyant, muscular bodies mirrored each other but also because there was one 16th-century print for every two Mapplethorpes, creating a theatrical mix-and-match voyage through past and present.

The curators in Florence lack such conviction. A small number of works by Mapplethorpe are juxtaposed with Michelangelo’s statues in the main hall but the bulk of the exhibition, held in a screened-off space, hosts just four sketches and a miniature wax sculpture by the old master.

Such an impoverished comparison merely teases at the possibility of a shared aesthetic. Equally diffident is the attempt to situate Mapplethorpe within the modern era: an etching by minimalist Bruce Marden, Andy Warhol’s Electric Chair series and a photograph of a sculpture by Italian modernist Ettore Spalletti feel incongruous among the unflinching realism of Mapplethorpe’s oeuvre.

The only two works not by Mapplethorpe that seem at home are a photograph of a nude female torso rippled with shadows and a trussed, armless female sculpture. Both are by Man Ray, whom Mapplethorpe exalted as the most important 20th-century photographer.

Undoubtedly, Man Ray’s surrealist kinkiness also appealed to the New Yorker whose close-up images of male genitalia and elaborately staged S&M scenes resulted in accusations of obscenity. Here, the absence of sex shots haunts the show like Banquo’s Ghost. The only one to creep in, “Jim, Sausolito” (1977), a crouching, leather-masked man clinging to the rungs of a litter-strewn fire escape, feels more desperate than dangerous.

To be fair, the erotic pictures have always occupied a disproportionate importance in Mapplethorpe’s canon. By the early 1980s, he had ceased to take them, saying: “I’ve already recorded that.” For the rest of the decade, until his death from Aids in 1989 aged 43, he concentrated on nudes, portraits and still-lifes. Icy and idealised, these are the images that take centre stage here.

Aiming to highlight Mapplethorpe’s sculptural tendency, the show opens with a head and shoulders of a male model with his eyes shut. Depriving the face of its most expressive feature, the image embodies Mapplethorpe’s desire to “transcend the subject”.

Emphasising Mapplethorpe’s democratic formalism, figure studies are mounted next to inanimate objects. A woman’s naked torso arches back to mirror a sensuously curled lily petal; a man with his back to the camera clasps his hands to one side of his head, the bulge of his muscles echoed by the mottled shimmer on a bunch of black grapes.

One section concentrates on body fragments: two breasts shot from below in a sumptuous, unnatural diagonal; a close-up of a male torso, revealing the weft of taut, wispy lines etched on to the skin. Other images feel like calculated exercises in geometric form – in one a woman’s leg bisects a white triangle.

Mapplethorpe took many celebrity portraits, most famously of Patti Smith, who was briefly his lover in the early 1970s and went on to be one of his closest friends. Here, she is immortalised in a video, “Still Moving/Patti Smith” (1978) and a 1975 portrait. Smith’s physical oddness and intimate rapport with the artist ensure she retains a defiant individuality. But other sitters, such as Andy Warhol and David Hockney, are reduced to elements in an assemblage of shape, light and line by the rigorous angles and shadows of the backgrounds.

Consequently, the Renaissance artist who springs to mind as Mapplethorpe’s forerunner is less Michelangelo than the Quattrocento painter Piero della Francesca, who was famed for his geometric compositions and radiant light effects. With the emotional drama supplied not by the impassive protagonists but by the spectacular play of light, his “Flagellation of Christ”, which resides in the National Gallery of the Marches in Urbino, sets a fascinating precedent for the theatrical yet curiously soulless choreography that defines Mapplethorpe’s S&M images.

That Piero retired from painting to concentrate on mathematics is proof of his cool, measured sensibility. It also makes him, and by extension Mapplethorpe, the antithesis of Michelangelo, whose passionate nature is evident in his sculpture. Here, his unfinished statues of the four prisoners, struggling to liberate their limbs from the marble block, are giddy with anguish. In contrast, Mapplethorpe’s images of Thomas, a nude model pressing his hands and feet against the edges of a circle, possess a taut, deliberate poise that is mannered rather than moving.

Mapplethorpe was undeniably influenced by classical and Renaissance sculpture. But his pursuit of flawlessness has more in common with the neoclassicism embodied by Canova’s pristine nudes. As David’s seductively gauche proportions illustrate, Michelangelo never sacrificed nature for perfection.

‘Robert Mapplethorpe: The Perfection of Form’ runs until September 27