G. The "Demonstrative staff" of the Hexagram
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
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.
: 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
: 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