The unmeasured Fantasias by Johann Gottfried Müthel appear as part of a collection of pedagogical exercises to foster improvisation. The information he gives in the notation of his fantasias can be elucidated with a historiographical interpretation of musical rhetoric. Müthel developed musical figures and contrasting textures in accordance with contemporary rhetorical principles of inventio, dispositio and elaboratio. An analysis of Müthel’s G-minor Fantasia provides a link between musical rhetoric and performance, as seen through its improvisatory gestures. Issues of performance practice that arise in the G-minor Fantasia are the execution of ornaments, rhythmic alterations, registration, and articulation. This paper explores primary sources contemporary to Müthel to make sense of these issues. The unmeasured Fantasias are written for a keyboard with pedal. At the time that they were written, the pedal fortepiano and pedal clavichord were seen by musicians such as Carl Phillip Emanual Bach to be the superior instruments for performing improvisations. While the notation and texture of the Fantasias suggests that Müthel intended them for organ, a consideration of the possibilities provided by the fortepiano suggests that it may be more suited to conveying aspects of the galant aesthetic.