The song was first uploaded on August 12, 2009; and is Yuuyu-P's second original Rin work. It's also one of his most notable songs with over 1,000,000 views to date; other notables include "Shinkai Shoujo" or "Clover Club" both sung by Hatsune Miku.
"Tengaku" was featured in various compilations, some include: On August 2009 it's featured in the compilation "DEBUTANTE IV", on December 2011, the compilation "Vocalo Vision", and also Exit Tunes' compilations such as "STARDOM 3" and "Vocalogemini". It's also one of the tracks for the games "Project Diva f" and "Project Diva Future Tone" along with the module "Kagamine Rin Ougetsu" designed by Melou.
On Yuuyu-P's previous Rin original work; "Gokurakuchou -bird of paradise-", the song have similar points to Tengaku and it may or may not connected to each other (for it's produced by the same group; with Yuuyu-P as the composer, and tamajam as illustrator).