The tea ceremony is done of course on tatami, but have you seen it on the table? It's called Ryurei (立礼). I always wondered why it was created. I kind of knew that it was for non-Japanese who were not used to sit on tatami, but today I got my act together and did some research.
And.., it really was for foreigners! In 1872 or Meiji 5, Kyoto Prefecture held the first exposition in Japan. The governor of Kyoto requested Gengen-sai, the 11th headmaster of Ura-senke, to create a new style so that their foreign guests could enjoy the most sophisticated Japanese culture comfortably. It had been created a year before, and presented to the public during this exposition.
Right after opening the country, in 1867, Saga and Kagoshima prefectures participated in Expo Paris. They learnt how important to show the world new technologies and also to learn Western culture. Since 1872, Kyoto exposition was held almost every year until 1928. Nishi-Honganji temple, Ken'ninji-temple and Chion'in temple are the venues for the first time.
Gengen-sai performed with Ryurei at the first exposition, but his second time, in 1876, he did it on tatami, just as it should be, and he passed away the year next.
It's only written in Japanese, but Professor Shoji Kamiya's paper is really interesting.