Fantasia

The Fantasia, by Mr. [Pio] Cianchettini, is upon [Gioachino] Rossini's air "Tu che accendi," so often made the theme of piano forte lessons. […] Mr. Cianchettini's imagination is very vivid and full, and we know of nothing more florid or requiring lighter and more delicate touching than this Fantasia.

Source: wiktionary

Miss [Eleanor Margaret] Geary is a brilliant pianiste, who make light of the modern difficulties set down for the instrument: her performance of [Theodor] Döhler's Anna Bolena fantasia was achieved without apparent effort, and won considerable applause; […] Miss E[lizabeth] Geary is a vocalist, possessing a sweet and flexible voice, […] this young lady also played a fantasia on the concertina very adroitly.

Source: wiktionary

The little Italian party, before alluded to, had collected around the piano. The white and plump fingers of the gay and black-eyed daughter of the Roman marchioness were tripping lightly up and down the octaves of the instrument, and her little tastefully arranged head was merrily dancing from side to side, keeping time to the half-improvised phantasia, which trickled like a wayward stream from her hands.

Source: wiktionary

She [Josepha Barbara Auernhammer] published subsequently many works of her own, (in all 63,) which, as well as her play, especially the extempore phantasias, were distinguished by much delicate feeling and a vivid imagination.

Source: wiktionary