The koto piece "Kogō no kyoku" ("The Song of Kogō") and the Noh play Kogō (translation and more by Michael Watson available here) are both based on the same well-known episode in the Heike monogatari.

To summarize, Emperor Takakura's beloved Kogō has fled to Saga fearing the wrath of Taira no Kiyomori (to whose daughter Taira no Tokuko Emperor Takakura was already married). The Emperor sends Nakakuni to find Kogō based on a single lead: she's staying in a place with a "single-hinged folding door", kata-orido. Fortunately, Nakakuni hears her playing her koto and singing of her love for the Emperor as he passes by that door, and after taking out his flute to play along a little, successfully completes his mission. The image of Nakakuni and Kogō separated by the kata-orido was a very popular one (try looking in museum catalogs for "Nakakuni"), but more interesting to me is the fate of the word kata-orido.

Paul S. Atkins points out in Revealed identity: the Noh plays of Komparu Zenchiku that kata-orido is one of the "few distinctive phrases [in the Noh play] that can be directly identified as coming from Heike". The koto piece has slightly more Heike material (for example, it opens with the extended Heike quotation "'Ojika naku kono yamazato' to eiji ken, Saga no atari no aki no koro....," i.e. "Saga in autumn, of which the poet sang, 'This mountain village where the stags call'..."), but the word kata-orido retains a particular importance in the lyrics — it comes at a major climax right before the instrumental break diegetically representing Kogō's playing.

The fact is that by the Edo period at the latest the word kata-orido had become sufficient to evoke the whole scene. Consider this senryū from Haikai mutamagawa:

垣間見の　尻ハ出て居　片折戸
The peeper's / butt is sticking out/ kata-orido

In Edo Satirical Verse Anthologies, R.H. Blyth translates this:

Out of the wicket/ Protrude the buttocks/ Of the peeping chap

... but this will not do. The joke here is the sudden reveal that the ridiculous peeping Tom of the first two lines (all right, ku) is actually the noble Nakakuni — that we have been tricked into seeing the Kogō episode as a case of sordid voyeurism. All accomplished with a single word that, etymologically/morphologically speaking, doesn't even hint at the weight it carries.