“I feel like Wriggle's a bit slow-headed. I mean, it's a pity she has to face player characters here. She's at the rank where it might be better for her to go play with Cirno instead.”
– ZUN, on Wriggle's “Unseasonal Butterfly Storm” spell card

The Baquartet (バカルテット, Bakarutetto), or Bakartet, is a somewhat dated grouping of Touhou Project characters, consisting of early stage bosses with zero relevance at the time. Ever since the soft reboot in 2007, ZUN has intentionally avoided making these characters.

During the early Windows era of Touhou Project, the early stage bosses had zero relevance to the plot and no existing relationships, aside from an off-hand comment saying Wriggle and Cirno were the same rank in Touhou Eiyashou. Then in 2005, we'd see Touhou Kaiedzuka give birth to the “⑨” phenomenon and portray Mystia as bird-brained, then Rumia was portrayed as carefree for her Bunbunmaru Shinbun article.

Nobody has officially found when or where the idea originated, but I've managed to narrow it down to either 2005 or 2006 since the “⑨” phenomenon could not have existed before Touhou Kaeidzuka was released and the first known fan artwork of the group was uploaded to Danbooru on August 8, 2006,¹⁾ which is prior to Comiket 70. Any time after 2006 is tainted by the rise of Niconico and Pixiv.

While they started out as a fan creation, the group has formally appeared together in Chapters 3 and 4 of Oriental Sacred Place in 2009 where they help out with the events of that chapter. Shortly after, they also appear in Chapter 12 of Oriental Sacred Place in 2010 to enjoy the New Year's festival at the Hakurei Shrine where they seem to be chatting amongst each other with Tewi in the background.

After that, the group hasn't really appeared as much together, but some of them cameo at the festivals and social gatherings in latter Touhou Sangetsusei chapters. Then in 2013, the group would be spectators for ongoing matches at the “Hall of Dreams' Great Mausoleum” stage in Hopeless Masquerade. However, they're mostly just standing around in random groups.

• Rumia (ルーミア, Rūmia)
• Cirno (チルノ, Chiruno)
• Wriggle Nightbug (リグル・ナイトバグ, Riguru Naitobagu)
• Mystia Lorelei (ミスティア・ローレライ, Misutia Rōrerai)

• Daiyousei (大妖精, Daiyōsei) - As the midboss to Cirno, fans often group Daiyousei with Cirno and made her an honorary, unofficial member. However, she arguably isn't a character.
• Letty Whiterock (レティ・ホワイトロック, Reti Howaitorokku) - Cirno was her stage's midboss, so fans often depict her as a mother figure to her and the group by extension.

There have been plenty of attempts to add new members to the lineup, forming a “Kyuuintet” (⑨インテット, Kuintetto), but it usually ends up with Daiyousei filling in as the fifth member. It doesn't help that ever since the soft reboot in 2007, early stage bosses have more relevance than ever before, meaning that the chances of adding a new character are very unlikely. Some proposed candidates are listed below.

• Chen (橙, Chen) - She's a mischievous, early stage boss on her own. However, she isn't considered because she's typically grouped with the Yakumo family, so support has generally been low.
• Utsuho Reiuji (霊烏路空, Reiuji Utsuho) - Utsuho is a bit bird-brained. However, she's a powerful final stage boss and heavily associated with the Satori family and the Chireiden group.

• Referencing the Touhou Wiki, the English community would discover the group around June 2007.²⁾
  • The unofficial English name, “Team ⑨” or “Team Nineball”, surfaced around April 2009.³⁾
• They inspired the name, “Babaquartet” (ババルテット), the four-member iteration of Touhou Gotairou.
• It's popular to draw them as Keine's students, but note that Keine only teaches humans in canon.
• To tell you the truth, I'm not really a fan of this grouping, but I felt obligated to write something for it.

• List of Touhou Group Tags

• Baquartet on the Niconico Encyclopedia
• Baquartet on the Pixiv Encyclopedia