2D and 3D proximity maps for major and minor keys and chords

Abstract

Minor and major keys/chords are arranged along the joint subdominant-dominant axis. For this purpose, the relative minor for a major tonic (e.g. Am regarding C major) is put between the tonic and its subdominant (F), being interpreted as the ‘semi-subdominant’. Correspondingly, the relative major for a minor key (C for Am) is called its ‘semi-dominant’. Thereby, two axes of fifths for major and minor keys are merged into one. To reflect the proximity of other types of key/chord relations (parallel major-minor keys, major dominants in minor keys and minor subdominants in major keys), this axis is closed by analogy with the circle of fifths and twisted, as if wrapping a torus. The torus unfolded results in a key/chord proximity map. Due to using the subdominant-dominant axis, it is free from inconsistencies inherent in some known maps.