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G. The "Demonstrative staff" of the Hexagram

Illustration:

l) The half staff, combined with the transitory natural ledger line constitutes a mutable scale. A whole staff, combined with the transitory natural ledger lines constitutes two adjacent and opposite groups of scales. Each of the staves, when combined with the transitory natural ledger lines constitutes a different level of register. All the registers, reciprocally combined with the transitory natural ledger lines create a system of gradual scales. They are at the same time similar to and different from each other.

2) There exists a symmetrical dividing-point of the 2:1 ratio, which is a formal and mathematical subdivision between any two half staves and between any two whole staves. This dividing-point exists also between two mutable scales and between any two of these groups. Connecting and transforming the scales are a symmetrical axis and a junction on the tone of "Do" (the note of "C"). All of it is abstract and concrete at the same time.

3) Each clef indicates the pitch and the register of the staves. The structure and form of every staff is a unification of opposites, forming a clearly marked entity.

4) A single invariable rule is applied to every kind of music. A simple identical form is applied to every different register. They are complex and yet simple.

5) Modifications of the regular tempered tones combined with irregular fluctuations of the lines, on the one hand, and modifications of the regular notes combined with irregular rhythmic signs, on the other, constitute the means and the rules for the expression of music. They are at the same time modern and traditional.

6) Applying the rules described here, on the basis of the data, norms, and fixed proportions, one can write the "sound spectrum" of lines, dots, and signs, indicating the fixed pitches and the registers. Thus it is possible to achieve vast objectives, whose function and meaning include not only the category of music notation but also that of research into the "sound spectrum". These objectives are both artistic and scientific.

Demonstration: The modality of the demonstrative notation is based upon the formal and mathematical logic of the Hexagram notation. The method of the demonstrative notation is formed of notes, lines, and signs. The structure of the demonstrative notation is built upon the "Complete staff" and the "Inferential staff", thus giving rise to the "Demonstrative staff".

Conclusion: In the Hexagram notation the theoretical basis of the "Demonstrative staff" in the field of contemporary and avant-garde music is founded on abstract concepts and concrete methods. Both its theoretical rules and its practical application have been verified.