"Japanese Square Dance" was written specifically for episode 505 of The Muppet Show by music associate Derek Scott.
In the episode's closing number, the Muppet cast and The Tokyo Tai-Chi, Karate, and Chowder Society attempt a serene "Salute to Japan," but when Animal grows bored with the serene music and the set is invaded by cowboys, the number erupts into a boisterous musical square dance production combining the Eastern and Western themes.
As for host James Coburn, he realizes keeping the quiet theme is a hopeless task and then plays the square dance caller which includes having the ladies beat up the cowboys and destroy the set.