Because the first principle of the elaboration is the filling in of the tonal space by passing notes, an essential goal of the analysis is to show linear connections between notes which, filling a single triad at a given level, remain closely related to each other but which, at subsequent levels, may become separated by many measures or many pages as new triads are embedded in the first one.
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In older literature, the term " linear connection " is occasionally used for an Ehresmann connection or Cartan connection on an arbitrary fiber bundle, to emphasise that these connections are " linear in the horizontal direction " ( i . e ., the horizontal bundle is a " vector " subbundle of the tangent bundle of the fiber bundle ), even if they are not " linear in the vertical ( fiber ) direction ".
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