Etude might be the word you are going for. It is the French word for study. But Chopin put the old notion of 'etude' to rest when he wrote his. His etudes are groundbreaking. They are studies to be sure, but it is not at all unusual to hear them in concert settings. He wrote his etudes as pieces of music, interesting on their own independent of their technical aspects, which are formidable. His friend Franz Liszt was inspired by them, and created some of the most fantastic 'etudes' ever written, the Transcendental Etudes.
Maybe the word you are really going for, then, is exercise, as in Hanon or Pishna.
classical music yes others no
Improvisation
Badis, from Morocco(from an intermediate guitarist point of view)The scientific study of music is a "90/100" an absolute systeme of how music works, it involves how scales and chords function to give certain harmonies, each scale contain sven modes, each mode has its flavour, each mode is mixed with close modes to create a harmonized melody ,it also involves wriring music and perfect pitch..
improve that qestion
Imitative Counterpoint
It's called an etude - i.e. A musical composition written solely to improve technique.
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