select language

home | book | download | contacts

A. The "Great staff" of 13 lines of the Hexagram

Illustration: Starting from "Middle-c" as a center line, then by means of each set of three horizontal parallel lines that constitutes a half staff of an octave and by means of the symmetric unfolding of the 2:1 ratio, adding one parallel line both above to the Pentagram in the "Treble staff" and below to that in the "Bass staff", comprising the "Great staff" of 11 lines, one forms the "Great staff" of 13 lines of the Hexagram, which combined with the transitory natural ledger lines, constitutes a group of scales of 4 octaves. The formal logic and the mathematical logic of the two different levels of the "Great staff" are unified and yet symmetrical, identical but also differentiated, as in figures 1, 2, and 3:


Figure 1) Unified and symmetrical figure on the "Great staff" of 13 lines of the Hexagram





Figure 2) Scale structure on the "Great staff" of 13 lines of the Hexagram





Figure 3) Scale system on the "Great staff" of 13 lines of the Hexagram




Demonstration: Two different sets of six lines read like a single uniform set of six lines; a single uniform set of six lines reads like two different sets of three lines — precisely as, on the Pentagram the combination of the three lower lines of the "Treble staff" with the three upper lines of the "Bass staff".

Conclusion: The range of notation has been extended, the addition of ledger lines has been reduced; the reading of the notes has been unified, the rules simplified. The structure of two levels grouped together in a single form, comprises the tone ranges of normal performance.