There are several forms of short written compositions. Two of the most common are essays and short stories.
A short written composition is an essay
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You might be thinking of the word essay (a short written composition.)
William Crotch has written: 'Elements of musical composition' -- subject(s): Composition (Music), Music, Composition
George Thaddeus Jones has written: 'Music composition' -- subject(s): Composition (Music), Composition (Musique)
A written composition is usually referred to as an essay, article, or piece of writing. It can also be called a composition or text, depending on the context and format.
Ben Clements has written: 'Photographic composition' -- subject(s): Composition (Photography)
"Literature" is one word that means "books and written composition."
A Schubert composition is a piece of music that was written by Schubert.
Elke Reufels has written: 'The role of short-term environmental cycles in determining zooplankton composition and abundance within a shallow, enlosed tidal basin and in waters immediately offshore'
A composition is a short essay. Composition also refers to how you structure your writing using the correct grammar rules and rhetoric.
A business letter.