In earlier work on voice leading, theorists have explored particular regions of musical space -- for example, the three-note chromatic chords dividing the octave most nearly evenly. This strategy works well in some cases, but it is not fully generalizable, since uneven chords are spread throughout musical space. In my talk, I describe an alternative approach that, as it were, derives musical space from chords themselves. This approach reveals a new world of analogies relating almost all possible chords in almost all possible scales. Using these structures it is possible to transfer musical techniques among arbitrary harmonic domains. I illustrate with The Thousand Faces of Form, an orchestral piece with live visual accompaniments reflecting the geometrical structure of its harmonies.