The Tonnetz

https://commons.wikimedia.org/wiki/File:Neo-Riemannian_Tonnetz.svg

In 1739, Leonhard Euler devised a “tone net” to represent graphically the traditional harmonic relationships in European classical music. In the version above, the dark blue triangle at the center is an A minor triad; the red triangle to its right is the relative major, C; and the red triangle below it is the parallel major, A. Every such pattern is mirrored in all the other keys. The tones are numbered from 0 (A♭) to 11 (G). Major triads are red, and minor are blue. The thinnest lines denote minor thirds, thicker are major thirds, and the thickest horizontal lines are fifths. See this page for further relationships.

The heart of the figure, shown in somewhat darker colors in the diagram, is a parallelogram composed of 24 triangles. The top edge of this parallelogram can be joined to the bottom, which lists the same notes in their enharmonic equivalents, and if the resulting cylinder is twisted slightly then its ends can be joined in the same way, forming a torus.

| Art · Science & Math

New Leaves

https://commons.wikimedia.org/wiki/File:John_Constable_-_Wivenhoe_Park,_Essex,_1816.jpg

Constable said that the superiority of the green he uses for his meadows derives from the fact that it is composed of a multitude of different greens. What causes the lack of intensity and of life in verdure as it is painted by the common run of landscapists is that they ordinarily do it with a uniform tint. What he said about the green of the meadows can be applied to all the other tones.

— Eugène Delacroix, Journal

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Noted

https://commons.wikimedia.org/wiki/File:Straight_tusked_elephant_Eemian_landscape.jpg
Image: Wikimedia Commons

J.M. Roberts’ 1987 Hutchinson History of the World contains this arresting sentence:

At one site in Spain the mind of what one scholar called a ‘primitive Archimedes’ has been seen at work three hundred thousand years ago, directing the removal and use of the tusks of slaughtered elephants as levers to shift the carcasses for cutting up.

The scholar seems to be archaeologist François Bordes, who had written in his 1968 book The Old Stone Age that the Acheuleans of Torralba-Ambrona had killed elephants half engulfed in mud, “and that a primitive Archimedes had the idea of using their tusks as levers for shifting their enormous bulk and making it easier to cut them up.”

From what I can understand, the evidence for butchery at these sites is now thought to be ambiguous, but it’s a striking image nonetheless.

Completely unrelated, but similarly notable: In Days With Bernard Shaw, his 1948 memoir of his friendship with George Bernard Shaw, Stephen Winsten remembers Shaw remarking, “Leonardo da Vinci ruled his notebooks in columns headed fox, wolf, bear and monkey and made notes of human faces by ticking them off in these columns.” I can’t confirm this either, but it seems worth recording.

| Art · History · Science & Math

Perspective

https://www.flickr.com/photos/timtom/6420755669
Image: Flickr

These yellow rings are not superimposed on an existing photograph — they’re actually painted on the landscape. Swiss artist Felice Varini created Three Ellipses for Three Locks in 2014 by painting segments on roads, walls, and nearly 100 buildings in the historic center of Hasselt, Belgium. The effect was visible only to a viewer in one particular vantage point.

Here’s another project by the same artist.

04/12/2026 CORRECTION: The installation pictured above was created in 2007 by Varini at Cardiff Bay Barrage in South Wales. He created a second installation with the same title seven years later in Hasselt. My mistake. (Thanks, Christian.)

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Infinite Digest

https://samizdat.co/digest/notes/

To mark the 30th anniversary of Infinite Jest, David Foster Wallace’s sprawling 1996 novel, Brooklyn-based data visualization artist and design professor Christian Swinehart is creating a graphical companion to the book.

Infinite Digest is a series of interactive visualizations of the novel’s plotlines, characters, and self-referential structure. The first two installments, exploring the book’s timeline and its many footnotes, are currently live, and more will appear over the next few months.

(Thanks, Christian.)

| Art · Literature

Hue and Cry

The story goes that one day when Cézanne was picknicking in the country with some friends and a collector, the latter suddenly realized that he had dropped his overcoat somewhere on the way. Cézanne raked the landscape with his gaze, then exclaimed: ‘I’ll swear that black over there doesn’t belong to nature!’ Sure enough, it was the overcoat.

— André Malraux, The Voices of Silence, 1978

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“The Worst of All Puns”

https://blog.le-miklos.eu/wp-content/HabeMortemPraeOcculis.jpg

At Nuremburg a wolf’s tooth was shown to travellers … on which an Abbé is represented lying dead in a meadow, with three lilies growing out of his posteriors. This is not only the worst pun that ever was carved upon a wolf’s tooth, but the worst that ever was or will be made. The Abbé is designed to express the Latin word Habe. He is lying dead in a meadow, … mort en pré; this is for mortem præ; and the three lilies in his posteriors are to be read oculis, … au cu lis. Thus, according to the annexed explanation, the whole pun, rebus, or hieroglyphic, is Habe mortem præ oculis.

— Robert Southey, Omniana, 1812

In other words, the French phrase Abbé mort en pré au cul lys (“Abbot died in a meadow with lilies in his rump”) sounds like the Latin phrase Habe mortem præ oculis (“Keep death before your eyes”). This joke appears to be referenced in Hieronymus Bosch’s 1504 triptych The Garden of Earthly Delights:

https://commons.wikimedia.org/wiki/File:The_Garden_of_earthly_delights.jpg

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