This music is the Nocturne No.5 in B-flat major by the Irish pianist and composer John Field. As the name suggests, a Nocturne was thought of as a piece of music to be played in the evening, and musically it consists of a melody and accompaniment, with the melody being restated with embellishments and elaborations. John Field first popularised the Nocturne for piano, and it was he who inspired Chopin to compose his own more famous Nocturnes. Below you can play the mp3 or midi files and see the sheet music before downloading. Alternatively to download the sheet music, mp3 file and midi file, use the links in the left-hand menu. On mfiles you can also find an arrangement of this Nocturne for Violin and Piano by the German violinist and composer Friedrich Hermann (1828-1907).
Here is a video of Field's Nocturne no.5 in B-flat for piano:
The audio controls below allow you to play the mp3 version of Field's Nocturne no.5 in B-flat for piano or you can download the MP3 file. You can also download the midi version of Field's Nocturne no.5 in B-flat for piano.
The image below is the first page of the sheet music, and here you can download the full sheet music for Field's Nocturne no.5 in B-flat for piano in PDF format.