Meiji Tokyo Renka

On the night of a crimson full moon, high school girl Mei Ayazuki, lured by the magic of mysterious magician Charlie, enters into a box. When she awakens, she's in Tokyo during the Meiji Period. The lost and confused Mei is aided by Ougai Mori and Shunso Hishida, who take her in their carriage to the Rokumeikan, a lavish ballroom full of powerful high officials. where she meets historic figures such as Kyoka Izumi, Otojiro Kawakami, Yakumo Koizumi, and Goro Fujita. In this world, during the "Misty Hour" between sundown and sunup, "mononoke" appear. Those who can see them are called "Tamayori," and Mei herself possesses this power. As she navigates an unfamiliar life, romance begins to bloom between Mei and these men -- and the power of the tamayori will only strengthen their bonds. She may choose to never return to her original time.

Synopsis from Anime News Network