The definitive text of the Treatise on the Hexagram is an enlarged and updated version of the first edition published in 1990, and is the result of re-examination and research over a period of twelve years. It is a practicable system independent of any tendency and particular school, can either fulfil the evolutional demands of contemporary and avant-garde music, or satisfy the need for the divulgation, promotion, and development of classical and traditional music. It is an elaboration whose goal is universal contact and the shared advancement of musical culture in humanity's third millennium.

Hexagram notation is the outcome of the rational evolution and comprehensive development of Pentagram notation. It is a system with applications of multiple functionality and adaptable versatility, composed of twenty illustrations of notation and two theoretical frameworks of special application, together with instructions for the generalization of the "Tonic Do/La solfeggio notation". Being a system made up of the unity of opposites, its application has just one single rule and one logical formula, which can be unfolded from the microcosm to the macrocosm, from the interior towards the exterior, always beginning again in an endless cycle, capable of infinite variations without detaching from its principle.

Hexagram notation has fully inherited the theoretical and artistic achievements of Pentagram notation, of which it thoroughly respects the traditional knowledge and preserves the applicatory uses. Its practical aspects are: to derive the logic of the music theoretical development; to unify and simplify the system of writing and reading of the notes; to expande and complete the range of notation; to reduce or eliminate the use of ledger lines; to determine the "Middle-c clef" (the "Alto clef" and "Tenor clef"); to correct the notation of inversion and of modification; to resolve and allow the overcoming of the contradictions and erroneous impressions concerning the relation between vertical and horizontal elements of the score, as also between reading and listening, to achieve a reciprocal unification based upon formal and mathematical logic; to simplify the page of the score, moreover the notation proves to be greatly rationalized and standardized, more practical to use, and of greater efficacy and precision. Hexagram notation, given the direct and efficient means and method, lends itself also to an use of generalization and computerization. The creation of the notation of registers beyond practicable use, and the particular categories of imaginative frequency, open a vast prospect for scientific use and a modernization of musical technique. Hexagram notation possesses the function and meaning of the heredity of the past together with the inspiration of the future and also of the avant-garde.

Some reflections and considerations elicited by the Hexagram notation:

A. The history of the evolution of human civilization and the course of development of human knowledge do not allow for any arbitrary human interruption. Thus if one seeks to completely overcome the past, it is necessary to fully retrieve its heredity. In academic research one cannot invent anything new, extraordinary, or unique that is without precedents that premise its future, much less can one invent something from nothing or elaborate conclusions that are without foundation. Hexagram notation rigorously respects these principles.

B. The truth is simple and natural. The search for truth requires an honest and straightforward attitude, even at the risk of not obtaining any precise and perfect result, it is preferable to present oneself as hypo rather than hyper, simple rather than complicated. Otherwise too much is too much and one strays further from the truth. Hexagram notation always refers back to the above reasoning.

C. "Each thing concurs in the good of every other". All things interact among themselves and influence each other. Cognitive developments are even more communicative among themselves. The integration and reciprocal complement between Western and Eastern cultures, can find new inspiration and stimulation in the search for a common civilization and a collective progress. Hexagram notation is the result of the integration and reciprocal complement of these two different cultures.

D. All existing things come about as a unity of opposites, this is the law of nature, from which nothing, from the atom to the cosmos, is excluded. Things are interdependent upon each other, but they also change. Hexagram notation presents itself as a complete formality, from the microcosm to the macrocosm, from the interior towards the exterior, from its integrity to the parts of a structure composed of the unity of opposites. This structure proves to be a unit divided in two, but also a group of two.

E. Music is an art, but also a science and a philosophy, for which music is a resonance of physical, mathematical, and philosophical theories; it is a tuning of time and space, as also of the body and soul. Music must therefore be sentimental and rational, or it will lack vitality. Hexagram notation is a completely rationalized applicative system.

F. The evolution of modern civilization has demonstrated the following rules: the more advanced the theory, the more concise the concept; the more developed the science, the simpler the operation. Hexagram notation corresponds to these requisites.

G. Evolution/degeneration and metabolism are inevitable laws of nature. The evolution of human society is like a ship going upstream, it goes backward if it doesn't go forward. When people languish in selfsatisfaction and laziness, then regression and degeneration begin without their realizing it, whereas the hope of humanity lies in proceeding constantly with the search towards evolution. The appearance of Hexagram notation aspires to be a valid contribution to the universal development of the world's musical culture.

The author hopes to elicit from all friends of the international musical community, to whom this treatise is addressed, the critical discussion, practical application, and the creative contributions regarding the music notation of the Hexagram system.