Axis system

In music, the axis system is a system of analysis originating in the work of Ernő Lendvai, which he developed in his analysis of the music of Béla Bartók.

The axis system is "concerned with harmonic and tonal substitution", 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.

In classical and common-practice systems of harmony, certain chord substitutions are recognised and are commonly made use of by composers and arrangers: "certain chords have been able to act as substitutes for others; for example, the submediant chord ... can replace the tonic, most familiarly in an interrupted cadence." In his analyses of Bartók's music, Lendvai identifies a novel set of tonal substitutions; substitutions that relate chords and keys in a flat mediant relation to one another, and also those related by the tritone, a tonal relationship "normally regarded as the most remote pitch/chord/key area from the tonic." Lendvai argued that these relationships had a naturalistic basis (that is, were not merely an analytical or compositional contrivance), and argued that many of Bartók's compositions made essential use tonal substitutability he described. By establishing the veracity of this novel set of relationships, Lendvai "attempts to 'explain' Bartók's chromaticism within a tonally functional model."

In his analysis, Lendvai groups the twelve tones of the chromatic scale into three sets; each set of tones contains those notes that are found at intervals of a minor third and tritone from one another (equivalent to the notes that make up the three possible diminished seventh chords). Thus, there are four notes in each of the three sets, sets which Lendvai refers to as axes. By way of analogy with common practice harmony, the three axes are categorised as tonic, subdominant, and dominant.

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