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The name of "Shitori Egumo" derives from a line in Japanese poetry "永訣の朝(Eiketsu no asa)", which means "The morning of last farewell".
It was written by famous Japanese poet Kenji Miyazawa(1896-1933).
The line including shitori egumo is this:
"…もう けふ おまへは わかれてしまふ
（Ora Orade Shitori egumo）*
ほんたうに けふ おまへは わかれてしまふ
ああ あの とざされた 病室の
くらい びゃうぶや かやの なかに
やさしく あをじろく 燃えてゐる
わたくしの けなげな いもうとよ…"
*note:This line is also Japsnese , but originally written in alphabet.
Kenji had little sister, but unfortunately she had been heavily sick and passed away so early.
This line is about last farewell between Kenji and his little sister in a cold winter morning.
Even when she was dying, She asked Kenji for only single cup of snow not to worry him.
And said, "Ora Orade Shitori Egumo" ,which means "I go alone." She didn't want Kenji trapped and depressed by her death.
All these attitudes show the deep affection and bond between Kenji and his little sister.
It is same between Iroha and Ui. Especially, "heavily sicked little sister only hopes their family's happiness, even when facing death" perfectly correspond to Ui.
Kenji Miyazawa is famous for not only poetry but also fairy tale. And one of his tale is "The night of milky way train " ,which doppel of Iroha "Giovanna" derives from.