Here’s one way to end a composition: Johann Jakob Froberger’s Suite II in C major, Lamento sopra la dolorosa perdita della Real Msta di Ferdinando IV, Re de Romani, ends with a picture of the clouds of heaven welcoming the soul of Ferdinand IV as it climbs up a scale of three octaves.

It was written to lament the death of the King of the Romans in 1654. Elsewhere Froberger had marked the fatal fall of lutenist Charles Fleury down a flight of stairs with a descending scale of two octaves. Perhaps he was just very literal-minded.

(From Wilfrid Hodges, “The Geometry of Music,” in John Fauvel et al., Music and Mathematics, 2006.)

Conservators at the National Galleries of Scotland have discovered “what is almost certainly a previously unknown self-portrait by Vincent van Gogh.”

The image emerged in an x-ray of the artist’s 1885 painting Head of a Peasant Woman, taken in preparation for an upcoming exhibition. To save money, van Gogh sometimes used both sides of a canvas; in this case the reverse image had been hidden by layers of glue and cardboard that were applied before an exhibition in the early 20th century. It’s not yet clear whether these layers can be removed without harming Head of a Peasant Woman.

This isn’t the first time a “lost” image has been discovered in a van Gogh painting. In 2008, x-rays revealed the portrait of a woman behind the artist’s 1887 painting Patch of Grass — apparently he had painted over an image he’d completed two years earlier.

This is a miniature, a tiny replica of an English dining room of the late 18th century. Between 1932 and 1940, American artist Narcissa Niblack Thorne made about 100 such diminutive rooms, often enlisting architects, designers, and craftsmen whose talents became available during the Depression.

Of the miniatures still in existence, most are on display at the Art Institute of Chicago, where they serve as documents of the decorating styles of periods past. Generally designed on a scale of one inch per foot, many of them include authentic materials: bowls of real silver, chandeliers of real crystal, even original paintings and sculpture contributed by admired artists.

In 2010, the institute began to decorate them for the holidays each year, after researchers discovered Thorne’s affection for Christmas. But “Some of the rooms will never have a holiday theme,” the museum’s Lindsey Mican Morgan told the Chicago Tribune. “That is because many of them depict a room from a time when holidays were simply not celebrated as they are now.”

The second act of Alban Berg’s 1937 opera Lulu includes a three-minute sequence that’s a musical palindrome — after the first 90 seconds, there’s an ascending piano arpeggio, a pause … and then the music unfolds in reverse, a perfect mirror image back to the start.

This music accompanies a silent film that is itself a palindrome in some ways — for example, three people arrest Lulu and put her in prison, and then three liberate her. And Lulu’s husbands in Act I are played by the same singers as her clients in Act III.

Here are two 16th-century German portraits of seated ladies wearing hats, shown in three-quarter view. The one on the left was painted by Hans Holbein, the one on the right by the lesser-known Hans Krell. A panel of 12 specialists agreed that the Holbein painting had more artistic merit, and subjects who said they were familiar with art agreed with them. But individuals with no art expertise often chose the “wrong” painting, the Krell. This would suggest that people’s judgment in art is shaped by their expertise.

But Holbein is also much more famous than Krell, and this factor is likely to influence judgments too. How important is it? That’s not clear.

“Only if we can show that art experts across cultures agree on the comparative aesthetic merit of works they have never seen before and never heard of can we conclude there is consensus independent of cultural learning,” notes Boston College psychologist Ellen Winner. “This kind of study has not been done.”

(Ellen Winner, How Art Works, 2018.)

American painter William Rimmer produced this enigmatic image in 1872. A man runs through a palace. Is he fleeing or pursuing? What is the ghostly figure in the parallel corridor beyond him? And whose shadow is entering from the right?

No one knows. “As the title confirms, the painting turns a general situation into an ambivalent one,” writes Victor I. Stoichita in A Short History of the Shadow (1997). “There have been numerous attempts to specify its contents, but these have only resulted in the principle being misunderstood, for everything leads us to believe that it was Rimmer’s intention to create a story that functioned through its enigmatic form.”