While the Oslo building is the result of a collaboration between public and private entities, the new Copenhagen Opera, an overnight sail away, is the result of a single vision. Maersk McKinney Møller, Denmark’s wealthiest man, provided the $442 million needed to build this house, which opened in 2005. It’s highly unusual in this part of the world for such a project to be funded entirely from a private gift.

Danish opera fans had long hungered for a proper theater. The Royal Danish Theatre (known locally as the Old Stage), an intimate space that was periodically modernized, had presented opera, ballet, and plays since the 1870s. The backstage areas were too small for elaborate, compelling opera productions, but the theater was, and is, perfect for ballet, in which Denmark has always rivaled Russia and France for preeminence.

From architect Henning Larsen, Møller requested—and got—a design-oriented opera house that showcases rich materials and national brands: Georg Jensen silverware, Royal Copenhagen porcelain, Erik Bagger glassware, Sorenson furniture. The building itself is sleek and elegant, more gratifying than challenging to the eye. A flat roof projects over a public square like the wing of an airplane. After Oslo, I had to remind myself that not every opera house roof is meant to be climbed on.

The materials include German limestone, Chinese granite, maple wood, glass, and a ceiling adorned with 105,000 leaves of 24-karat gold. Three huge, globeshaped chandeliers designed by the Danish-Icelandic artist Olafur Eliasson dominate the arching public space. They change color from gold to pink to blue depending on the outside light.

The auditorium is as dark as the lobby is bright, creating a sense of removal from daily life and an immersion in the special realm of opera. The stage is modern, spacious, and functional, and unlike other Nordic opera houses, all the scenery shops are in a separate building that serves the three major theaters of Copenhagen. As in Oslo, the coat check is an open area where people leave their possessions, with seemingly no concern for their safety.

Reaching Helsinki, with its blend of Russian-type onion domes, Art Nouveau, and edgy contemporary design, made me realize that Finland is at once related to its big neighbors and fiercely distinct from them. The nation was contested for centuries by Sweden and Russia, but even when it was controlled by foreigners, its people never yielded their traditions or their language, which they sang as a way of preserving it. Opera was staged in Finland as early as 1873, usually in Italian until the first Finnish-language opera, Oskar Merikanto’s Pohjan Neiti (Maiden of the North), premiered in 1898. At that time Helsinki had a Swedish theater and a Russian theater (the Alexander Theater, built in 1878). Though small (456 seats) and not suited to big productions, the Alexander served as the home of the Finnish National Opera until 1993, when the Nordic country’s first modern opera house opened.

This, the 1,350-seat Finnish National Opera, sits on the edge of a lake like a tall white boat covered in glass. It has a huge backstage area for making costumes and scenery. With typical Nordic frugality, the company recycles its materials and scenery from one opera to the next. The entire building is attractive, airy, and functional.

Where the Finnish character comes to the fore is in the coat check, right at the main entrance and no doubt the biggest I’ve ever seen. During the long, snowy winters, when Finns arrive at the opera house, they remove their heavy coats and take chic two-tone black plastic bags to store their boots. Then they hand the coats and boots to the attendants, who stand guard. After the performance, hundreds of people huddle in this room to bundle up, put their boots back on, and venture into the night.

I arrived in Stockholm with mixed feelings. The cruise was coming to an end, but at least I had plans to stay for a couple of days at the brand-new Hotel Stureplan, with design elements taken from the 18th to 21st centuries. And Sweden does have the longest opera tradition in Scandinavia. Queen Louisa Ulrika (1720–82) created the court theater at Drottningholm Palace, on the grounds of the Swedish monarchy’s summer palace, an hour-long boat ride from the city center. Opened in 1766, it’s one of the world’s oldest opera houses still in use. Ulrika’s son, King Gustav III (1746–92), pioneered opera in Swedish and created the Royal Swedish Opera in Stockholm. Verdi depicted the King’s assassination at a masked ball in Un Ballo in Maschera.