![]() 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. 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. 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. If 'C' is taken as tonic, then the categorisation proceeds as follows: Thus, the twelve tones of the chromatic scale are identified in a two-part system of categorisation: each tone is a member of a four note axis (tonic, dominant, and subdominant) each tone is part of a branch within that axis that is either the principal or secondary branch of that axis and each branch consists of a pole and counterpole. Continuing with the language of axes, the members of each branch are known as "pole and counterpole". Thus, each of the three axes contains two branches, and are further categorised as either the 'principal' or 'secondary' branch of axes in question. Tones related to each other by the interval of a tritone are said to be part of a pair or branch (e.g. By way of analogy with common practice harmony, the three axes are categorised as Thus, there are four notes in each of the three sets, sets which Lendvai refers to as axes. 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). By establishing the veracity of this novel set of relationships, Lendvai "attempts to 'explain' Bartók's chromaticism within a tonally functional model." Terms and definitions 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 of the tonal substitutability he described. ![]() 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. 5 Composition and analysis with the axis system.4 Analysis of Music for Strings, Percussion and Celesta.
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