Cantata No. 31 ("Heaven laughs, the earth rejoices") is a jubilant and lavishly scored work composed in Weimar, where it was first performed on April 21, 1715. Following his promotion to concertmaster at the Weimar court at the end of 1713, Bach was required to prepare and perform one cantata every month in the ducal chapel. BWV 31 is one of approximately 20 extant cantatas composed between 1714 and 1716 to fulfill these duties. One of only two extant cantatas by Bach composed for Easter Day (the other is BWV 4), it was also used the following year, and the composer is known to have revived it with minor alterations in Leipzig at least twice: in 1724, and again in 1731. Like almost all of Bach's Weimar cantatas composed after 1713, the text is by the Weimar court librarian Salomo Franck. The orchestral scoring includes parts for three trumpets, timpani, three oboes, oboe da caccia, strings, and continuo.

The cantata opens, as do many from this period, with an instrumental movement featuring a prominent trumpet motif; its dance-like character and festive mood introduce the following chorus. The long recitative for bass that follows announces Christ's resurrection ("Awaited day"). "Prince of life, strong warrior," the text of the following bass aria might lead one to expect further celebratory pomp, but instead Bach scores it with only a vigorously articulated continuo accompaniment. Two further pairs of recitative and short arias follow—the first for tenor, the second allotted to the soprano. The tenor aria is lively, as befits words that bring faith in the true believer's own resurrection. The soprano's recitative and aria become more reflective; the soloist's radiant expectation of life after death is sympathetically supported by an obbligato oboe, while the strings play the melody of Nicolaus Herman's "Wenn mein Stündlein vorhanden ist" (1575). The same hymn provides the material for the closing four-part chorale setting, which is augmented by obbligato trumpet and violin parts that ascend high above the choral texture.

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