A short musical form written especially for the piano is called a

That is called a prelude.

Sra

P.S. Here is a definition from an online dictionary:

a : a musical section or movement introducing the theme or chief subject (as of a fugue or suite) or serving as an introduction to an opera or oratorio b : an opening voluntary c : a separate concert piece usually for piano or orchestra and based entirely on a short motif

Sra

Sonata also fits your definition.

n. A composition for one or more solo instruments, one of which is usually a keyboard instrument, usually consisting of three or four independent movements varying in key, mood, and tempo.

Hmmm. Here in Texas, a jig also fits. It is music in three quarter time, for a lively dance, and it doesn't last long.

Another composition that would fit would be an "etude"

A short piece of music, designed to give a soloist performer practice in a particular area or skill

The short musical form written especially for the piano is called a "piano piece" or "piano solo." These compositions are typically created to be played by a single pianist and are specifically tailored to showcase the capabilities and expressiveness of the piano.

To find examples of piano pieces, you can explore various avenues:

1. Sheet Music: Visit your local music store or search online platforms that offer sheet music such as music publishing websites, online marketplaces, or digital music libraries. Look for specific terms like "piano piece," "piano solo," or the name of a specific composer or genre.

2. Classical Repertoire: Classical composers have written numerous piano pieces throughout history. Familiarize yourself with notable composers like Ludwig van Beethoven, Wolfgang Amadeus Mozart, Franz Schubert, Frederic Chopin, or Claude Debussy. Explore their works and look for compositions labeled as piano pieces.

3. Contemporary Repertoire: Many contemporary composers also write piano pieces. Research and listen to modern pianists or composers such as Ludovico Einaudi, Yiruma, Joe Hisaishi, or Nils Frahm. They often create compelling and evocative piano solos.

4. Streaming Platforms: Utilize music streaming platforms like Spotify, Apple Music, or YouTube Music. Search for playlists dedicated to piano pieces or solo piano music. These curated playlists can introduce you to a variety of compositions from different genres and eras.

Remember that terminology may vary, and different musical genres may refer to these compositions by slightly different names. By exploring these resources, you'll find a vast array of piano pieces to enjoy and perhaps even try playing yourself.