The Gulbenkian is an extraordinary collection: it is all, without exception, incredibly beautiful. M. Calouste was not merely very rich, and immensely knowledgeable about what he collected (and he collected an extraordinary range of stuff -- his range was certainly broader than George Steiner's), but he also had impeccable taste: he did not buy a single second-rate item.
This piece of embroidery is one of the most extraordinary items in the Gulbenkian. As far as I know it may be unique -- there may literally not be another item like this in the world. (Although the Kantha embroidery is similar in style and can on occasion come close in technical attainment).
This perhaps explains the difficulty the museum has with attribution; it used to be marked as "Canton, China (?), early 19th century", reflecting perhaps its similarity to the yueh techniques (not mentioned in the English wikipedia entry on Chinese embroidery); and the Chineseness of the phoenixes; but I notice it has now been re-attributed to "Japanese, 19th century", presumably on its mindboggling obsession with technical virtuosity, the extraordinary color scheme -- gorgeous without being gaudy, and perhaps also on the geometrical arrangement, balanced rather than symmetrical.
I will try to find out what occasioned this re-attribution, but personally doubt it. While the Chinese have had a history of making embroidered wall-hangings, a tradition of free-standing embroidery, and a history of Imperial embroidering workshops, the Japanese had none of these. Further, no piece of Japanese embroidery which I have ever seen I looks remotely similar in technique, using, as it does very thin thread to produce smooth, flat images easily mistaken for print.
But I am prepared to be surprised.
The cloth is about 6 feet x 4 feet; uses several different embroidering techniques in several different thicknesses of silk; and seems by and large missed by most visitors.
Here are some close-ups of the work. Note that it is embroidered all over, the background having been embroidered in a subtle, barely perceptible pattern of spirals.
PS. The high cultural status of embroidery in China is reflected by the fact that the great Ming Dynasty scholar-painters Wen Zhengming, Dong Qichang and Shen Zhou had all been famous in their lifetimes as great embroiderers.