Difficulty​ is a key principle of the Picturesque. In a landscape garden, the eye must never be allowed to take in the whole view at once. The visitor passes through successive scenes by way of transitions that are often carefully complicated. Stepping stones across a stream are slightly uneven, the gap in a hedge is too narrow to pass through without a small push, the scale shifts from expansive to miniature and so the mind is kept alert. Theories that developed along these lines in Europe in the later 18th century had been developing in Japan since the seventh century into the ‘strolling gardens’ of the Edo period. The same principles apply in traditional Japanese architecture; the shoji screens can be moved to alter interior space, and house and garden are connected across verandahs or through windows which may frame precise views. Not all Japanese gardens are meant to be entered; some are intended only to be viewed from a particular room, often from a seated or kneeling position.

This habit of seeing only what you are meant to see and from the right angle is useful in modern Japan, where a population of 123 million is concentrated around the edges of the four mountainous main islands. Tokyo, the largest city in the world, has almost forty million inhabitants. The Hama-rikyū Gardens in the Chūō ward, once the private grounds of a shogun’s villa, are now a popular public park. You can rest your eyes on the deep pools, the seawater moat that surrounds the garden, changing level with the tides, and the narrow bridges that lead to a tea house on an island. Look up and you see an unbroken ring of bland high-rise office blocks looming over the trees. Look back and there is a Buddhist monk in black robes, his socks bright white on his wooden pattens, standing on the verandah of the tea house, the perfect photograph, which you duly take. Most Japanese seem to have become adept at editing their overcrowded landscape. At onsens (hot springs) on the edge of towns, they sit in the sulphurous waters with their backs to the cement factory next door.

This is not the kind of difficulty that theorists of the Picturesque had in mind. The idea is to focus closely on what you do see, not on what you want to block out. But difficulty is increasingly difficult to achieve. Air travel, apps and star ratings drive expectations of ever easier access to top quality Instagrammable experiences. It has been a growing problem in Japan since the last century. By the mid-1970s, the 17th-century moss garden at the Saihō-ji Zen temple in Kyoto had already been trodden to the brink of destruction. It has survived to become a world heritage site by reintroducing the element of difficulty. To visit the garden it is essential to book but not possible to book for a same-day visit. At the nearest bus stop a polite notice explains that if you don’t have a ticket you won’t be able to buy one for today. When your day comes, you arrive to a courteous but silent welcome in the main hall of the monastery where rows of low tables are arranged. Signs indicate that phones, photographs and talking are prohibited. Before you go any further you are given paper on which you must copy out a sutra, tracing the characters with a thick felt-tip pen. You are advised to take five deep breaths before you start and it requires concentration, especially for those unfamiliar with the hiragana characters. The room soon becomes still. It’s a bit like giving colouring books to a class of overexcited six-year-olds, and just as effective. By the time the copying is complete, the room is all but silent, and the silence continues as the visitors are allowed into the garden. There are no more instructions, but instinctively nobody speaks above a murmur. You concentrate on the garden, which is exquisite and, being moss covered, rewards detailed attention to successive small areas of light and shade, contrasts of scale and the sounds of water and birdsong.

The Miho Museum, a project first conceived in the 1980s, takes a still more drastic approach to difficulty. Set high in the densely forested mountains of the Shiga prefecture to the east of Kyoto, it is easy and cheap to book, about £7 for a ticket. It is getting there that requires commitment. The train from Kyoto to Ishiyama takes fifteen minutes, and then there is a bus. It is slightly unnerving that when the engine of the bus starts the staff of the ticket office come out to bow and wave it off, as if this were the beginning of an epic and possibly hazardous journey. The road twists up into the mountains, dropping off locals here and there, and every so often seems to have reached open country only for another bend to reveal a motorway flyover sawing through the landscape, or a railway still under construction, until the idea of escaping infrastructure seems impossible.

Eventually the forest on either side is unbroken except for the narrow road by which the bus arrives at the Miho reception centre, a low white building sparsely but elegantly furnished, offering seats, water and, in the event of rain, sturdy green umbrellas. From there, if you can, you must walk, though a small electric buggy sometimes glides by. There is only one direction in which to go, into the broad mouth of a tunnel driven into the mountain. The tunnel is 120 metres long and lined with stainless steel plates. It bends in proper Picturesque fashion to prevent any direct view through from one end to the other, but at the same time the fan-shaped wall lights cast what appears to be a single beam of light, which always points ahead, drawing the walker onwards. This effect is created by the precise angling of each of the 850 steel plates in the tunnel lining. At the far end, it opens out through a spider’s web of suspension cables onto a bridge over a deep, forested ravine. The bridge is paved with porous fine-grained ceramic, which allows rain through to the trees beneath. Ahead is the museum, a glass and metal reimagining of a Japanese temple set above flights of wide steps, a quiet, even modest climax to the drama of the approach. Most of the museum, including all the galleries, is buried in the hillside. In the broad entrance hall the first exhibit is the landscape, a vast window framing a view of mountains.

This peculiar combination of grandeur and humility, simplicity achieved by infinitely laborious attention to detail, reflects the age of Miho’s architect and its patron. The museum was a late work by the Chinese American I.M. Pei, creator of the glass pyramid entrance at the Louvre, for Mihoko Koyama, after whom it was named. Pei was 70 and Koyama 77 when they first met and by the time the museum opened in 1997 they were both in their eighties. Each in their way was a perfectionist and neither had anything to prove. Koyama, who died in 2003, had been inspired by the religious philosopher Mokichi Okada (known to his followers as ‘Meishu-sama’) to found a Shinto sect, the Shinji Shūmeikai, for whom she had acquired the 1.7-hectare site. Her first building was a sanctuary for the sect, designed by Minoru Yamasaki, architect of the World Trade Center. After Yamasaki’s death in 1986, she approached Pei to build a free-standing bell tower. Pei, at a stage in his career where he had made it known he would only undertake small, individual commissions, accepted. As Koyama spoke no English the two communicated in part through Chinese. They both admired classical Chinese poetry, and from the fifth-century legend of a mysterious peach blossom valley, the origin of the Western notion of Shangri-La, they began to conceive the idea of a treasure house hidden among mountains. Koyama and her daughter, Hiroko, who took on much of the practical management as her mother’s health declined, proved ideal clients. They were rich and almost comically biddable. When Pei didn’t care for the site they had chosen, they chose another. When he decided to place the entrance on the far side of a valley that they didn’t own and asked to tunnel through it, they agreed.

By now Pei’s idea of a small retirement project was presumably long since abandoned. The museum was intended to house the Koyamas’ fine but small collection of historic Japanese tea-ceremony vessels. Pei suggested to them that it would be more significant if the collection was expanded to include art from Europe and Asia. His clients obediently embarked on a seven-year buying spree that caused an international sensation. Advised by the collector and dealer Noriyoshi Horiuchi, they acquired works of major importance, including an Assyrian bas-relief from the palace of Ashurnasirpal II, which sold at Christie’s for £7.7 million. Pei designed a gallery specifically to house it, and another for the ‘Sanguszko’ carpet, a Persian design from the late 16th or early 17th century, whose animal motif medallions were the inspiration for a dozen or so other examples. This the Koyamas acquired in São Paulo, directly from Prince Sanguszko. There was an element of the sorcerer’s apprentice about their career through the art markets. Pei later admitted that when he made the original suggestion he had no idea what the budget might be. Now he found himself having to add one extra gallery after another to accommodate the arrivals, disrupting his original plan for the layout. This, as he later reflected, was one of the advantages of building underground: there was no need to rework any elevations. In the finished museum, one wing contains the original Japanese collection; the other is devoted to the Egyptian, Chinese, Greco-Roman and Persian galleries. Part of the collection was exhibited at the Metropolitan Museum in New York and the LA County Museum in 1996, ensuring that the Miho was world famous by the time it opened the following year.

A visit, however, has none of the razzmatazz of the Met or the Louvre. There are no queues or crowds. From the museum’s entrance hall, the original sanctuary and the bell tower, which chimes each day at noon, are visible but not visitable. The galleries are quiet and uncrowded, the captions mercifully brief. There is an audio guide, in Japanese, Chinese or English, which is helpful but to the point. A silent keeper carries a notice requesting no photography.

Despite Pei’s fame the museum has been ignored in the British architectural press; such coverage as exists is mostly in German and French and is relatively slight. Some critics have complained that Pei’s gallery spaces are bland, but it would be fairer to say they are tactful. Since Frank Lloyd Wright designed the spiral Guggenheim there have been few star architects self-effacing enough to create a museum that allows the contents to upstage the drama of the building. Daniel Libeskind’s Jewish Museum in Berlin and Tadao Ando’s sculptural concrete box at Naoshima are, typically, their own principal exhibits. Pei, in old age at least, was willing to bow to the art. The spaces are carefully scaled, lit sometimes from corner windows which give views of the mountains, or from concealed lighting above, where conservation considerations require it. Like the moss temple garden, the atmosphere is conducive to quietness. Visitors go slowly. In most other ways, it is like any modern museum, with a gift shop, extensive bookshop and spacious café that serves produce grown on site. Not the least of Pei and the Koyamas’ difficulties was getting permission to build in this protected area of natural beauty. The buildings occupy only a small portion of the land the Shinji Shūmeikai owns, the rest is devoted to organic farming and land management.

At Eskenazi, one of the London dealers from whom they bought Chinese bronzes, the Koyamas are remembered as friendly, elegant, but remote. Mihoko, by then frail, wore the traditional kimono; her daughter was ‘very smart’ in Western trouser suits. ‘They never talked about money – that was all left to Horiuchi.’ Such reticence is very Japanese, but, in the Western media, coverage of the museum has been marked by baffled scepticism bordering on hostility. ‘Who are these people? Where do they get their money?’ the Washington Post demanded to know when the museum opened. ‘And why have the Shumei collected this material and opened a museum?’ Nobody knows what the Miho cost to build, though one suggestion, of a quarter of a billion dollars (excluding the cost of the collection), seems plausible.

The Post also claimed that, since the sarin gas attack on the Tokyo underground network, which occurred two years before the museum’s opening, the phrase ‘Japanese religious cult’ had ‘taken on a sinister edge’. The Shinji Shūmeikai, which regards its leader, now Hiroko Koyama, as a divine being, has been the subject of some lurid speculation. There are rumours that members of the sect were pressured for large donations to pay for the museum. Perhaps they were, but it presumably helped that Mihoko Koyama was heiress to the immense Toyobo textiles fortune. Founded in 1882 and still in business, Toyobo was by the 1930s the largest cotton-spinning company in the world. The West with its predominantly monotheistic theologies finds it hard to see a ‘sect’ as anything other than a cult, a potential Jonestown, but Japan has hundreds of sects. In Shinto many things and people, including ancestors, natural springs and the emperor, are regarded as divine, and attitudes to religious practice are fluid. Since Shinto has no concept of an afterlife, it is not uncommon for the Japanese to have a Shinto wedding and a Buddhist funeral. If there is anything sinister about the Shinji Shūmeikai, which has premises in London and up-to-date accounts filed with the Charity Commission, it has not come to light in the last half-century. Its followers may just be doing what it says on their website, working for what Meishu-sama described as ‘the achievement of peaceful harmony through a combination of natural and artistic beauty’.