Sanctified by history (it has been held every year since the Academy was founded in 1768), it yet straddles past, present and future, and this year includes at least one Young British Artist from the Sensation show, Gary Hume. It may not be on the cutting-edge of contemporary art, but it is no longer a bunker for ageing reactionaries.
Take Norman Ackroyd (born Leeds 1938), who was elected to the Royal Academy ten years ago. He is a printmaker, renowned for his atmospheric landscape etchings. This year he has been on The Hanging Committee, with special responsibility for the prints.
When I interviewed him, the multi-part sculpture by Antony Gormley - 60 cast iron figures in various postures, some strung up from the facade of Burlington House and adjacent buildings - was being dramatically re- located by crane and hawser in the courtyard.
"This is a great idea. We could have it being installed for the entire two-and-a-half months of the exhibition as a kind of happening, a performance piece. People are probably watching it more now than they will when it's in place."
"Sculptors will covet this courtyard as a great place to show. I think this is one of the ways the profile of the exhibition will change. Similarly with the print room: everybody wants to be in there. The submission of prints this year was phenomenal, and we selected more than we could hang in one gallery, so they are spread out through the other galleries amongst the paintings."
On our tour we started with the gallery of prints Ackroyd has hung - the Large Weston Room. "Of the older techniques there are some wonderful wood engravings by Colin See-Paynton, and very good mezzotints by Leonard Merchant and Sharon Avaliotis, as fine as anything done in the 18th century. There are also lots of new ways of making prints, like this beautiful woodcut by Christopher LeBrun on Japanese paper. Then you get someone like Anthony Eyton, who at 75 does his first etching, in classic soft-ground and sugar-lift technique, but with the freedom of all his wonderful big pastel drawings."
Ackroyd points out a woodcut of a father and child. "I don't know who it's by - that's one of the great excitements of the show. It's a privilege to actually discover these things."
But isn't there a lot of dross to be filtered out? "That's inevitable, but you really get to see what's going on from Land's End to John o'Groats. Sometimes your eyes can't believe what they're seeing."
What characterised the send-in this year? "There are more people interested in the finish of what they do, with a sheer desire to make the thing sing on the wall."
Two themes stood out in the initial submission: pictures of Diana, Princess of Wales, and work done in the manner of the YBAs. The selectors have to be rigorous. "There are ten pairs of eyes looking at each picture, but I pay especial attention to all works under glass - water-colours, drawings and all types of prints."
Looking round the print room, everything on the walls, except one large image of a tower by Maria Stroka-Robinson, is in fact under glass.
We talk of the tower. "That's not just a photograph on panels, it's an etching printed on to paper and then mounted on to linen in the way that the old maps were. I saw it when it was just a lot of pieces of paper on the floor at the Royal College and thought then what an ambitious piece it was. It's printed from 24 sheets of metal. That's an incredible amount of physical work: apart from the burnishing and scraping, it takes about three days to print."
Norman Ackroyd approves of showing sculpture with the prints. He is so impressed with one object, The Book by Carl Danby, that he is seriously considering buying it. "It's two pieces of steel held together with wonderful big bolts, the kind you have on etching presses, with a burnt book in between the plates. I'd love to open it up and see what the text is, but that would destroy the mystery."
How different is this Summer Exhibition from any other? As Ackroyd stresses, a lot depends on the personalities of the members hanging the galleries.
For example: "Bryan Kneale and Phillip King, both of whom have an incredibly good eye for colour and materials, hung the two corner sculpture rooms very beautifully. And I think that one of the great things that we did last year was to move the architecture models out of Gallery VI which interrupted the long run of five galleries right down the north side."
Amongst the works that Ackroyd points out are the memorial groups to Carel Weight and Victor Pasmore (in Galleries I and II), and Patrick Procktor's version of Perseus and Andromeda, hard by Krakatoa, east of Java, in Gallery III. In Gallery IV, Ackroyd memorably describes the yellow figure sculpture by Malcolm Poynter as "a human barley-sugar stick".
A number of students have work on display. I ask Ackroyd whether they don't have enough exhibiting opportunities elsewhere; shouldn't the Summer Exhibition be reserved for older artists?
Ackroyd, himself a noted teacher, offers a curt response: "Students are artists. To eliminate young artists would be disastrous."
We're both struck by a large powerful drawing in Gallery V of the rush-hour crowds on Liverpool Street Station, done in conte and crayon by Jeanette Barnes.
A magnificent John Hoyland abstract called Tree Music dominates Gallery VI. In Gallery VII Ackroyd singles out Poolside Mid-Afternoon by Steven Rendall. "It's painted in colours that look like skin that's had too much sun. And the acidic chemical green of the swimming pool gives it a sense of desolation. The whole thins is Benidorm as Hell."
Finally I ask the million dollar question - has the Academy a future?
Ackroyd is indignant: "It's essential that the Academy continues. Nowhere else is an art establishment run in this way, by artists, and it's a great way to do it. The Academy will always change slowly because its strength is that once somebody is elected they stay.
"Each year we probably elect two or three new Academicians, which means 25 or 30 Academicians over ten years, which is a third of the membership.
"We already have some terrifically talented Academicians - world figures - in architecture especially. Ultimately, this institution depends on the membership."
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