The construction of a musical user interface providing access to all pure harmonies is a very complex problem that defies a completely satisfying solution. The notion of the so-called isomorphic keyboard, invented by Bosanquet and advocated by many key figures in tuning theory since the 19th century, offers a good but not a perfect solution. In this paper, I propose an alternative approach based on the concept of a ‘just intonation (JI) plane.’ A JI plane is a true isomorphic image of higher-dimensional affine spaces modeling tones in extended just intonation. JI keyboards are defined as sets of keys located in a JI plane.