縁の下の舞
((e)n no shita no mai; “dance below the veranda”)
Definition:
Working hard to support someone from out of sight; doing a thankless task. By extension, someone in an unacknowledged position who is nonetheless of use and help. A power behind the throne. An unsung hero.
Breakdown:
This is a noun phrase. The dominant noun is 舞 (mai), “dance.” This noun is connected by the associative particle の (no) to the noun 下 (shita), “below,” which in turn is connected by の to 縁 (en), which can mean many things, but in this case refers to the raised walkway that runs around the outside of each building in a traditional Japanese estate-home.

The most relevant part is (b). You can see that there’s ample space below – the floor is a good meter off the ground.
Notes:
This is one of two possible ゑ entries for the Kyoto iroha karuta set. (The other is 縁と月日.) An apparently more common, but less evocative, saying of the same meaning is 縁の下の力持ち ((e)n no shita no chikaramochi) – literally “a powerful person below the veranda.”
This phrase apparently originates with a particular dance, in the style of the old Imperial court, held at the Shitennou Temple in Osaka in honor of the spirit of Prince Shōtoku on the anniversary of his death, the 22nd day of the second month of the old lunar calendar. The dancers did not actually ascend up to any stage, and so the dance was held at ground level – where it would be difficult for those inside the building to see. It used to be believed that the spirits of deceased emperors needed to be kept appeased lest they inflict their wrath on the nation, so from this dance was born the image of someone doing vital work despite being out of sight.
Example sentence:
「あの金権政治家、本人は何の腕もないからきっと、彼の成功を支えるために多くの人が縁の下の舞を必死に舞ってるに違いない。可哀そうに」 「ある意味でね。でも、自業自得とも言えるかも」
(“Ano kinkenseijika, honnin wa nan no ude mo nai kara kitto, kare no seikou wo sasaeru tame ni ooku no hito ga en no shita no mai wo hisshi ni matteru ni chigainai. Kawaisou ni.” “Aru imi de ne. Demo, jigoujitoku to mo ieru kamo.”)
[“That plutocrat has absolutely no skills whatsoever. A lot of people must be working thanklessly behind the scenes for ‘his’ successes. I feel sorry for them.” “In a way, yeah. But you can probably say they’re getting what they asked for.”]
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