vertonen
to set to music
To provide a text, especially a poem or a libretto, with a musical composition.
Franz Schubert hat viele Gedichte von Goethe vertont.
Franz Schubert set many poems by Goethe to music.

to set to music
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to set to music
To provide a text, especially a poem or a libretto, with a musical composition.
Franz Schubert hat viele Gedichte von Goethe vertont.
Franz Schubert set many poems by Goethe to music.

'vertonen' (to set to music) is an inseparable verb derived from the noun 'der Ton' (tone/sound). The prefix 'ver-' here means something like 'to provide with something'. So you provide a text with tones, that is, with music.
Der junge Komponist möchte als Nächstes einen Roman vertonen.
The young composer would like to set a novel to music next.
What is set to music is typically a literary work. Common combinations are 'ein Gedicht vertonen' (to set a poem to music), 'einen Text vertonen' (to set a text to music), or 'ein Libretto vertonen' (to set a libretto to music).
Es ist eine große Herausforderung, ein so bekanntes Gedicht neu zu vertonen.
It is a great challenge to set such a well-known poem to music in a new way.
This verb is very often used in the passive in order to put the work at the center. The structure is then: [text] wurde von [composer] vertont ([text] was set to music by [composer]).
Dieses Gedicht wurde bereits von mehreren berühmten Komponisten vertont.
This poem has already been set to music by several famous composers.
to arrange
'arrangieren' and 'vertonen' can both appear in the area of music, but there they do not mean the same thing. 'arrangieren' is used when an existing piece of music is adapted for different instruments, voices, or a different form. 'vertonen' means that a text is given music, for example a poem or song lyrics. The words can be confused because both have to do with music and composition. A practical distinction is: music is 'arrangiert' (arranged), while a text is 'vertont' (set to music).

Paul hat ein Gedicht vertont, damit die Klasse es morgen singen kann.
Paul set a poem to music so that the class can sing it tomorrow.
Anna arrangiert das alte Lied für die Schulband neu.
Anna is rearranging the old song for the school band.