|
Music theorists have often used graphs, tilings, and geometrical spaces to represent the relationship between chords. We can describe these spaces as ''chord spaces'' or ''chordal spaces'', though the terms are relatively recent in origin. == History of chordal space == One of the earliest graphical models of chord-relationships was devised by Johann David Heinichen in 1728; he proposed placing the major and minor chords in a circular arrangement of twenty-four chords arranged according to the circle of fifths; reading clockwise, ... F, d, C, a, G, ... (Capital letters represent major chords and small letters represent minor.) 1737, David Kellner proposed an alternate arrangement, with the 12 major chords and 12 minor chords placed on concentric circles. Each chord was vertically aligned with its relative major or minor. F. G. Vial and Gottfried Weber suggested a grid graph or square lattice model of chordal space; Weber's graph, centered on C major, is: This was first proposed by Vial (1767) and later used by Gottfried Weber, Hugo Riemann, and Arnold Schoenberg. Its advantage over Heinichen's and Kellner's models is that it represents a much richer set of chordal relationships. On the graph, every triad is related to its upper and lower neighbors by fifth-transposition; its left and right neighbors are its parallel and relative triads. In addition, every major triad is diagonally adjacent to the minor triad whose root is a major third above, and which shares two of its three notes (this is the diagonal above and to the left); every minor triad is diagonally adjacent to the major triad whose root is a third below, and which shares two of its three notes (this is the diagonal below and to the right). A variety of other common-tone and voice leading relationships can be found among neighboring triads on the graph. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「chordal space」の詳細全文を読む スポンサード リンク
|