The axis system is "concerned with harmonic and tonal substitution",[1] and posits a novel type of functional relationship between tones and chords.
Lendvai's analyses aim to show how chords and tones related by the intervals of a minor third and tritone can function as tonal substitutes for one another, and do so in many of Bartók's compositions.
By establishing the veracity of this novel set of relationships, Lendvai "attempts to 'explain' Bartók's chromaticism within a tonally functional model.
By way of analogy with common practice harmony, the three axes are categorised as tonic, subdominant, and dominant.
"[4] Essential to Lendvai'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).
"[5] The form of the first movement of Music for Strings, Percussion and Celesta provides an illustration of axis-based substitution, where the opening is based upon the pole of the principal branch of the tonic axis (A, A-C-E♭-F♯), the middle contrasts the opening and the end of the first movement by being based on E♭.
The pattern Tonic-Super Tonic-Subdominant relationship repeats itself counter clockwise around the circle of fifths.