Substitutability
The essential idea behind the axis system is that the axes group together "substituable key areas", and categorises key areas within a particular axis in reference to the strength and appropriateness of their inter-substitutability. Counterpoles that form one branch of an axis are more closely related than the counterpoles of the other branch of that axis: inter-substitutability within a branch is a stronger relationship than between the two branches of an axis. However, each axis possesses a "two-fold affinity", one being the relationship between pole and counterpole, the other being the relationship between the principal branch with the secondary branch. The relation between pole and counterpole, "its closest replacement" is judged to be stronger much more sensitive than the relation between the other poles of an axis, and due to this Lendvaï states that "a pole is always interchangeable with its counterpole without any change in its function."
Essential to Lendvaï's conception of the axis system and the relationships it describes is the idea that "the particular axes should not be considered as chords of the diminished seventh, but as the functional relationships of four different tonalities, which may best be compared to the major-minor relations of classical music (e.g. C major and A minor, E♭ major and C minor)."
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