After the renaming of the band to T-Square the imprint changed respectively (in all caps) and their typical logo became a capital letter "T" printed over a red square.

[17] In 1976, the Square started as a small jazz fusion group in Meiji University with a very basic line-up, made of bassist Yuhji Nakamura, guitarist Masahiro Andoh, pianist Jun Hakamazuka and drummer Shunichi Harada.

Meanwhile, in the Nihon University of the Arts, saxophonist Takeshi Itoh and Drummer Michael S. Kawai played in a few other college bands together.

When those disbanded, Kawai became fast friends with Andoh, replacing Harada on drums within the Square, and Takeshi Itoh made many guest appearances with the band, officially joining on saxophone and flutes, in 1977.

[20] With backing guitarist Yuhji Mikuriya, keyboardist Shiro Sagisu and percussionist Kiyohiko Senba joining in 1978, the band was signed to CBS/Sony and released their first studio album, Lucky Summer Lady.

[30] Their 1988 album, Yes, No was released in Japan only, with no Western reprint, and thus still referred to them as "the Square",[31] but they performed at the Roxy in Los Angeles on November 3 that same year as "T-Square".

[35] Their second album with Honda, Impressive, begins with the song "Faces", which, like "Truth", came to be closely associated with Fuji TV broadcasts of Formula 1, more specifically, with Ayrton Senna's victories.

[42] With Takahiro Miyazaki leaving his role as a sax player, Takeshi Itoh performed and recorded with Masahiro Andoh for the first time in a decade.

[43] Fence of Defense guitarist Kenji Kitajima, former Seikima-II bassist Shunsuke "Xenon" Ishikawa and session keyboardist Takehiro Kawabe joined them briefly in 2002.

[57] After the end of the Wonderful Days tour,[58] the group added even more former members to form T-Square Super Special Band and played on Yaon de Asobu for their 30th anniversary show.

[68] The group later released another cover album in 2012, Niji no Uta (虹曲), this time employing the help of special guest musicians, such as jazz pianist Yosuke Yamashita.

[70] They retained all members of the Super Band from 2008, including percussionist Kiyohiko Semba and excluding pianist Hirotaka Izumi.

The first one included their 1982–1985 lineup of Masahiro Andoh, Takeshi Itoh, Tohru Hasebe, Toyoyouki Tanaka, and Hirotaka Izumi with Keizoh Kawano playing backing synth;[87] the second one included their 1987–1990 lineup of Masahiro Andoh, Takeshi Itoh, Hiroyuki Noritake, Mitsuru Sutoh, and Hirotaka Izumi with Keizoh Kawano playing backing synth.

This particular concert included a special guest appearance by the Nishiarai Junior High School Brass Band Club, who performed "Takarajima".

[92] T-Square had planned to record their next album Horizon in Los Angeles, but on February 6, 2019, their keyboardist Keizoh Kawano was hospitalized due to an intracerebral hemorrhage which paralyzed the left side of his body.

[96] With both Shirai and Kawano providing synthesizer parts, the band recorded and released AI Factory to a two-month delay as a result of the COVID-19 pandemic.

[99][100] On February 1, 2021, Masahiro Andoh announced that he would leave T-Square after releasing their upcoming album (not yet named at the time) and completing their 2021 tour, wishing to continue activities as a solo guitarist.

[114] This album marked the first time in close to 25 years that Masato Honda and Keiji Matsumoto recorded Studio Parts with T-Square.

[124][125] The T-Square Alpha X Lineup performed on a Blue Note Tokyo special event titled Jazz Fusion Summit 2023 on July 17.

[157] In order to differentiate from the current/ongoing group known as "T-Square" (who are officially just Itoh and Bandoh as of 2022), Since September 2000 (beginning, specifically, with the live album Moment – Memorial Live at Chicken George[note 9]), the band has occasionally held throwback concerts, going under their old name of "the Square" (with the word Reunion added in 2017), with their classic lineups from the 80s and 90s, performing almost-exclusively their songs from that era.

Thus, the name "T-Square Family" refers to any random lineup of those who were formerly officially in the band, or were at the very least supporting members, and are appearing for one-off concerts.

[215] Later in 2000, Hiroyuki Noritake and Keiji Matsumoto, along with bassist Tomohito Aoki and guitarist Jun Kajiwara, would become the backing band of former T-Square saxophonist, Masato Honda.

[216] The backing band was put on hold in 2005, then fully deactivated in early mid-2006 to make way for Voice of Elements, which also featured T-Square alumni Hiroyuki Noritake, Mitsuru Sutoh and Keiji Matsumoto.

[123] This group was a fusion supergroup led by 3 guitarists: T-Square's Masahiro Andoh, Casiopea's Issei Noro and Rocket Jam's Hirokuni Korekata.

[225] Hirokuni Korekata also created a new band named Rocket Jam with bassist Shingo Tanaka and drummer Satoshi Bandoh in 2013.

[226] Although "Casiopea vs. the Square" was performed as a one-off event in 2003 (the DVD[227] and the CD[228] have different audio sources, suggesting that there may have been 2 shows[45]), this extension of 2 different jazz fusion bands goes back to 1989.

[note 10] Both groups still have somewhat of an alliance, seeing as Casiopea's 1993 – 1997 drummer, Noriaki Kumagai and former T-Square bassist, Mitsuru Sutoh are both in TRIX.

[199] A group that features pianist Hirotaka Izumi (who would die in 2021), drummer Akira Jimbo and guitarist Yuji Toriyama, along with other studio musicians.

[235] After the dissolution of Trio the Square, Mitsuru Sutoh and Keiji Matsumoto would later become backing musicians for Japanese a cappella pop group, 'The Gospellers'.

Drummer Hiroyuki Noritake, keyboardist Keizoh Kawano, and bassist Ko Shimizu (from Naniwa Express) would record as supporting members for Japanese fusion/rock guitarist Kumi Adachi in 2007–2008.