From the lexical underground, “rapport”

Symmetries in textiles, architecture and music.

Spider Monkeys by Vincent Desjardins is smarter than most tessellations.

Spider Monkeys by Vincent Desjardins is smarter than most tessellations. Image: Spoonflower.com.

Textile designers in Paris, Barcelona, and perhaps London use rapport, mostly verbally, for a decorative motif that can be repeated infinitely in two directions without leaving overlaps or gaps – hence “rapport infini”/”infinite rapport.” It is distinct from the Catalan report, Spanish reporte, English “transfer,” which in lithography is a master used to stamp a drawing onto slave stones and thus enable multiple runs. One of the first exercises given to commercial textiles students is to spot and analyse rapports on fabrics and elsewhere, but my impression is that the word is generally absent from (historical) dictionaries in any language. Larousse, however, defines rapport as the “dimensions in width and height of a decorative pattern to be repeated on a worked or printed fabric,” because this is basically about rectangular or square blocks of the type being used at 07:15 in this BBC documentary by a maker of colour-separated hand-printed tablecloths in the Isfahan bazaar:

This type of rapport shouldn’t be confused either with the “ſeveral peices of rapport-work after the Moſaic manner, upon a bottom of Tiſſue in a Feild Or” observed by Persia-traveller Jean Chardin (1643-1713) at the tomb of Shaykh Safi al-Din Ardabili in what it is now Iranian Azerbaijan. That is marquetry: “The Baſis that ſupports the Tomb, is ſurrounded with a Lift in the Middle of two Frizes, upon which are written in Golden Characters of Rapport-work the 62. Chapter of the Alcoran.”

Instead, I guess the use in translational symmetry of rapport comes from the word’s function in French to mean “relation,” where the relation here is the arithmetical ratio between the depth and breadth of the printing block. I think this etymology would make sense to the Chinese authors, one of whom has since Anglicised his name to Julian Wang, of “Enlightenment and Application of Infinite Rapport Structure in Architectural Design.” It introduces “infinite rapport structure” and “tilling graphics” (periodic tiling) to written English and asks, “When appreciating and praising the graphics, architects will naturally try to find the mystery and ask themselves: whether the craftsmen created the tilling graphics by accident?” Regarding the Institut du Monde Arabe/Arab World Institute in Paris, it hints at the use of tofu in Chinese architecture – “The architect did not select the simple way that using beancurd sheets to control light” – avoidance of which enabled Jean Nouvel to create the symmetries within symmetries in the diaphragmatic adaptive shutters on his splendid façade:

The chapter on symmetry in Aberdeen maths prof. David J. Benson’s brilliant Music: A Mathematical Offering begins with a terrible palindromic limerick, showing that what’s sauce for the eye isn’t always sauce for the ear:

First, let me explain that I’m cursed;
I’m a poet whose time gets reversed.
Reversed gets time
Whose poet a I’m;
Cursed I’m that explain me let, first.

Change ringing’s quite enough for organ-grinder and monkeys:

An explanation:

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