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http://www.nicovideo.jp/watch/sm9129998
Thanks to Anon from NICONICO Douga，who pointed out the song author's comment that notes Rangge Poppel is a hint to "Doppelganger" in English.
(d→Poppel Rangge←R, DoppelanggeR = Doppelganger)
Because of that, I have a clearer idea on the meaning of this song，Below are my personal opinion:
(Please quote me as the source if you are using the information below)
To the people who wanted to save time reading, you may scroll to the bottom of this topic, looking for the Summary Note.
Making a direct translate from 初音ミク Wiki
二人きり 椅子取りゲーム
喜劇のように 開催を
彼女は言う 彼女に言う
「私には要らないわ」
The musical chair game that belongs to the two of us
has begun like a comedy act
She said And I said to her
「I don't need it」
At the beginning of the song，it is said that a critically ill girl (Diva Miku) who is near death, one day she suddenly saw another self, who is known as dear Rangge Poppel (Doppelganger *Note1). They exist together, but for each of them, they don't think they need an extra existence of themselves. So the musical chair game starts, whoever wins the game survives and whoever lost will leave the world (*Note2).
猫の目に 黒い服
流れるは 滑稽な歌
まだ二人きり 椅子取りゲーム
そして どちらにも どちらにも
In the cat's eyes, The black dressed
is flowing out a funny song
And again, this is a musical chair game that belongs to the two of us
Thereafter, whoever it is whoever it is
The cat could mean a stray cat who is wandering near the hospital, the Black dressed may refer to the death god(*Note3). The both of them were struggling to deny this destiny/fate.
与えられたのは 羊皮紙の
契約書
I was given a parchment
contract
The parchment a.k.a the goatskin paper，is referring to the contract with the Satan or devil or God of Death. Here, it is also referring to the contract to conduct the surgery (I assume it is a high risk surgical operation).
アナタの声が 私の 声 と
ひとつになることを 嫌がった
隠してみても 隠せないんだ
君と私は同じだから
さあ このゲームを終えようか
それは 二人の歌
Your voice, and, my voice
has become one. This is annoying
I am trying to hide it away. But I can't
Because you and me, we are the same (person)
Come on, let us end this game together
Let's end it with our song
Between the two of them，only one is allowed to continue to exist，So they decided to end this "game", which means to accept the operation. The musical chairs game start with playing the music, when the music or the song ends, everyone must sit on the chairs and those who don't manage to get a chance lost （*Note4).
窓の外 廃線を
辿り行く ガゼルの群れ
蔦が巻く 階段に
うずくまる お下げの子
The abandoned railway outside of the window
A herd of Gazelle passed by
On the staircase with winding ivy
A girl with pony tails bent down and
This stanza is a description of the environment outside of the girl's ward, and possibly her spiritual world and experience with Doppelganger. Gazelle is an animal that is about to extinct. So it could be a metaphor that refers to the patients who could not live long.
彼女は言う 彼女に言う
「アナタとは居られないわ」
カラカラと 笑い出す
猫の目が 笛を吹く
本当は寂しいの 彼女は言う
She said And she said to her
「I cannot be with you」
Kekeke She chuckled
In the cat's eyes The sound of flute is heard
"Actually, I feel lonely" She said so
They understand that, one of them must disappear，and that is unavoidable.
The God of death is going to bring one of them along, whoever is going away, the one who is left in this world must have felt lonely.
この花束を 君に捧げよう
たおやかなまでに 赤い花
悲しげな顔 耳を塞いだ
触れると壊れてしまいそうで
ねぇ 君の声が聞きたいな
それは 二人の歌
Let me present you This bouquet of flower
A nearly perfect aesthetic red flowers
with sad expression I am covering my ears
If I touched you as if you will break down
Hey I wanna hear your voice
And that is our song
The operation began, it is when the life is at its most fragile moment, and people can die at any moment. The another self is encouraging her to live on.
世界で 一人だけ
美しい 君に言う
私を愛してよ
こんなにも こんなにも
私の声で あと少しだけ
君にこの歌を 歌おうか
何でもないわ 気にしないでね
私のことは もう
忘れてね
またいつの日か 会える時まで
その時はもっと 遊ぼうね
鳴り止んでいた この歌の中
椅子に座る君に幸せを
"In this world, there is only one person,
who is so beautiful" I said this to you
Fall in love with me
Just like this, just like this
I use my voice for a little longer
to sing this song for you
There is nothing really, Don't mind about it
Please forget everything about me
Until one day When we meet again
By then We will play a little longer
In this song which the voice has stopped
I give happiness to you who is sitting on the chair
So finally the girl died (possibly it's a failed surgery), which is indicated by "the voice has stopped", and Rangge Poppel, had become the one sitting on the chair.
世界で 一人だけ
美しい 君に言う
私を 愛してよ
こんなにも こんなにも
世界は 一つだけ
君が言う 「一つだけ」
「あなたとはいられない」
「さようなら」
"In this world, there is only one person,
who is so beautiful" I said this to you
Fall in love with me
Just like this, just like this
"In this world, there is only one"
You said so 「only one」
「I am unable to be with you」
「Goodbye」
「Goodbye」
In this world，there is only one "me"，so the two of "us" cannot be together forever，so they bid farewell to each other.
Rangge Poppel. my dear.
Thank you at short time.I hope that you're health.
I'm sorry.
I'm sorry.
The last message to Rangge from the girl:
Dear Rangge Poppel，Thank you for the short time companion. I wish that you are healthy. (*Note5)
I'm sorry.
And thank you.
I interpret this as：The letter is written in the heaven to Rangge，the girl thanked her for her encouragement and companion，and felt sorry that she left her alone in the world.(*Note6)
Note：
1，A Doppelganger is the ghostly double of a living person. In some traditions, a doppelgänger seen by a person's friends or relatives portends illness or danger, while seeing one's own doppelgänger is an omen of death (Wikipedia). In this song, the girl saw her own Doppelganger and that Doppelganger whose name is Rangge replaced her to continue living in the world of another dimension.
2, The musical chairs is a game played with the number of the chair is one fewer than the number of player. In this song, there is only 2 players and hence only one chair (so i use "musical chair" instead of the traditional "musical chairs" for the lyric translation)。The winner of the game is the one who manage to sit on the chair, and the survivor is the ghostly double of the sick girl, Rangge.
3,The cat is said to have the sixth sense and is able to see spiritual and ghostly things. So from the cat's eyes，she saw the reflection of the God of death who is clad in black dress.
4, This is a song by Vocaloid，Vocaloid=Vocal=Singing=Life。The "our voice", "music" and "song" in the lyrics is referring to singing and music as the lifeline of vocaloid.
5, Because of her illness, she wishes Rangge can remain healthy and not died of illness like her.
6,The girl (Diva Miku) died so she left a message to the still living Rangge. Actually there is another point of view：
Rangge the Doppelganger who likes/loves the girl so much that she substitutes Diva Miku to accept the death （which means the surgery is successful）. Noting that Miku the girl repeatedly said "I'm sorry I'm sorry, and thank you", which could also mean another way round.
Thanks for reading，all are welcome to leave comments and discuss about the PV and the song。
