Cantabile
Singing, with a soft attack.
What it means
Cantabile means “singing” and asks that an instrumental part be performed as if it were sung. What is meant is a bundle of several qualities: connected lines, a soft attack, dynamics that follow the course of the melody, and a breath that articulates the phrase even where no breath would be needed.
The marking concerns the manner of performance, not the tempo, and usually stands as an addition to a tempo word. Nevertheless it has consequences for the tempo: a movement that is meant to sing tolerates no haste.
It differs from legato, which denotes the connection of the notes, in that it covers more than articulation. It differs from affettuoso and amoroso, which name a feeling, in that it means a way of producing tone.
In the notation
The word is written in italics above the staff, usually after the tempo word, and applies until a new marking. In piano music it can stand above a single voice and then indicates which line is to emerge as the melody — an important hint in multi-voiced textures.
Musical use
The designation belongs to instrumental music since the eighteenth century, in which singing was regarded as the model of beautiful playing. It heads slow movements, middle sections, and themes with a pronounced melody. In the piano literature of the nineteenth century, singing playing becomes the ideal, to which the construction and pedal technique of the instrument are accommodating.
The ideal of singing shaped instrumental music from the eighteenth century onward. Pianists try to produce a legato-like, sustaining tone on a percussion instrument. Strings and winds form long bows and even breaths for this purpose.
Performance practice
Think the melody with breath: articulate it as a singer would phrase it, and plan the breaks. Shape the dynamics according to the course of the melody — usually swelling upward, yielding downward. Keep the accompaniment clearly softer so that the line carries. And work on the transitions between the notes; singing arises there, not in the notes themselves.