Work on their second studio album had already begun by July 2008, as they released their ninth major label single "Love the World".
Member Kashiyuka commented that she was delighted with the recording process as it featured material differing from their previous output, in particular the largely instrumental and plainly-spoken songs of "Take Off" and "Speed of Sound": "I could never have imagined [that] from Perfume before.
In an interview with Rockin'On Japan, Kashiyuka was happy at the idea that Nakata no longer felt compelled to create conventional idol music for Perfume and could now experiment with their sound, closer in vein to his work with Capsule.
[12][13] Its overlapping synth arpeggios are reminiscent of Yoshinori Sunahara's album The Sound of ’70s (1998), with other comparisons to Nakata's work for the Liar Game film.
[7] Perfume's Japanese spin on black music was compared to Yellow Magic Orchestra's 1980 cover of "Tighten Up", and Speed's 1999 single "Long Way Home".
Triangle's penultimate number is the disco-styled French house of "One Room Disco",[26] before reaching its conclusion with the ballad "Negai (Album Mix)".
[7] In June 2009, Perfume's official website revealed the album title as the symbol ⊿, accompanied by a simple graphic of an isosceles right triangle.
[27] Through the group's Tokyo FM radio show Perfume Locks, the members clarified that it is read as toraianguru (トライアングル) or "triangle" in English.
Music, Perfume explained that the title evolved from flying and vehicular-related ideas, until they settled on shapes, from which triangles were decided as Yasutaka Nakata thought it was fashionable.
[29] The album artwork for Triangle was photographed by Hiroshi Nomura, under the art direction of Kazuaki Seki with styling by Ken Uchizawa.
[30] Uchizawa dressed them in all white in the image of "a young girl changing into an grown woman", symbolizing Perfume's evolution and maturity.
As a part of the album's promotional campaign, both physical props were put on display in records stores around Shinjuku and Shibuya the weekend of its release.
Yuki Sugioka of Hotexpress opined, "Nakata's paradox is that the music is [not intended for karaoke], yet it still makes you want to hum along [...] With Perfume, he is presenting a future that is half a step ahead of the scene".
[33] Takaji Deshima of Bounce magazine called Triangle a "stunning result proving straight away that [Perfume] still has an edgy presence".
[citation needed] Perfume's "maturity" was a focal point in Musico's review of Triangle, who characterized the album as "fresh" and "moody".
[34] Kiyohiko Koike of Listen Japan commended its stylistic range that keeps Nakata's deep bass sound and Perfume's expressive singing.
Other reviewers echoed this atmospheric departure from Game, with Excite Music finding its predecessor's high energy to have cooled-down and become "dancier".
Despite finding production highlights elsewhere, they wrote: "For basic background music at a pop-heavy dance party, something like Triangle would be hard to beat.