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I. The new order of Hexagram notation and rules applied in the full score


1) With the Hexagram, each part relative to vocal or instrumental music can be inserted in a staff, in precise accord with the corresponding clef.

2) With the Hexagram, any clef of any part relative to vocal or instrumental music can be modified at will.

3) Thanks to the modality of alternation of the clef, one reduces the use of many ledger lines.

4) Thanks to the method of changing of the clef, the modifications of the alto clef are eliminated.

5) In the notation inverted, the parts remain in their original position, without inversion (see APPENDIX 1).

6) In the transposed notation, the parts — music for some wind instruments — must be written in the score in the original keys (with tones at real pitches). Thus, in the score, all the tones are notated in their original position, the reading is unified, and the rule is standardized (see APPENDIX 1).

Conclusion: The rules outlined above, solve the intrinsic difficulties of Pentagram notation, and in particular allow one to overcome the contradictions and erroneous impressions produced by the relations between vertical and horizontal elements in the score, as between listening and reading. Thus the reciprocal unification of formal and mathematical logic is achieved. The score is greatly normalized and standardized, is thus easier and simple to use, making possible greater efficiency and precision.

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