B. The "Complete staff" of the Hexagram

Illustration: After having formed the Hexagram "Great staff" of 13 lines by means of a symmetrical extension from "Middle-c" as a center line, according to the modalities of the binary system and of graduality, then by evolving and duplicating a uniform staff one level above the "Treble staff" and another uniform staff one level below the "Bass staff", including the "Great staff" of 13 lines, one forms the "Complete staff" of 27 lines of the Hexagram, which combined with the transitory natural ledger lines, constitutes a group of scales of 8 octaves. The formal logic and the mathematical logic of the four different levels of the "Complete staff" are unified and yet symmetrical, identical but also differentiated, as in figures 4, 5, 6, and 7:

Figure 4) Unified and symmetrical figure on the "Complete staff" of the Hexagram

Figure 5) Scale structure on the "Complete staff" of the Hexagram

Figure 6) New symmetrical composition on the "Complete staff" of the Hexagram

Figure 7) Scale system on the "Complete staff" of the Hexagram

Demonstration: Four 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 is now complete, the addition of ledger lines is reduced or avoided; the reading of the notes has been unified, the rules simplified. The structure of four levels grouped together in a single form, comprises all the ranges of executable tones of both the treble and bass register systems.

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