One cannot write a treatise on harmony, without discussing the Rule of the Octave (*), because, in the last century (18th), in certain schools, this so-called rule was considered a sort of harmonic law, and even nowadays many musicians seem to attach great importance to it.
The Rule of the Octave (aka the Harmonic Scale) is the name given to two conventional and invariable harmonic formulas. The Bass of one of these formulas contains a major ascending and descending scale. In the other, the minor ascending and descending scale. Each note, of each of these two scales, contains a chord which is undeniably affected by its scale.
(*) This name does not, in fact, make sense.
Here are these two formulas:
These two formulas were considered the rule of harmonic sequences, with a bass which represents either the entire scale or part of it. Now, although this way of linking chords, in this case, is unquestionably good, its obvious there’s many other ways of quantifying the two scales. Furthermore, nothing justifies the exclusive use of these two unique formulas, and especially with the inexplicable name of rule of the octave given to them.
Old Music Theory 