This project is known only from two letters from Tchaikovsky to his distant relative Viktor Olkhovsky. In the first, dating from July 1854, the composer enquires when Olkhovsky will be coming to Saint Petersburg with the libretto: "Bring everything you have with you, my dear fellow, and as much as you care to write" . The second letter is undated, although it appears to have been written within a couple of months after the first. "Today I had the pleasure of reading your text for the opera 'Hyperbola', Tchaikovsky wrote, "which completely corresponds to my requirements, except that there are one too many arias and recitatives, and too few duets, trios, etc. However, in spite of this you still have my heartfelt thanks!" .
The original letters have disappeared, but one of the letters included a musical sketch by Tchaikovsky, accompanying the words «Борода ль моя бородушка» (the setting for which cannot be established from the libretto) . It is not known whether any other music was composed, and there are no references to this project in other documents.
Olkhovsky's manuscript libretto shows that the 'lyrical opera in one act' is set in the fictional town of Dopotopin (which translates roughly as 'Antedeluvia'), with a cast of six characters: Erully (a citizen of Dopotopin), Hyperbola (his daughter), His Highness Volovy (husband of Hyperbola), Prince Gostal (son of Volovy), Sapphire (a young peasant), Teorima (friend of Hyperbola), Kazulin (associate of Prince Gostal). The humorous nature of the opera is evident from the first stage direction: "The theatre represents the location".