Wu Dao-gong —
presentation at the conference on the first Chinese publication of the *Treatise on the Hexagram*, published in the national monthly periodical Music of the People, n° 11 of 1995.

On 11 April 1995, in the meeting room of the Central Conservatory of Music in Beijing, the conference was held on the first publication in Chinese of the

During the past five centuries, the Pentagram (five-line staff) music notation as a form of representative musical ideography has been widely used in Europe and throughout the world, contributing greatly to a universal musical culture. Though still in use today, Pentagram notation has created and presented certain difficulties, due to its historical evolution with its intrinsic limitations and attendant problems. There is consequently an increasing gap between the Pentagram notation, on the one hand, and the demands of advancing musical development, on the other. Sensitive musicians have been aware of this problem for some time and have drawn attention to this tendency, while at the same time hoping for and seeking a new breakthrough.

In the course of the last two centuries, there have been numerous proposals of linear music notation reform, from those of one line to those of sixteen lines, with more than 30 proposals being of six lines. All these proposals have, however, consistently disregarded a fundamental principle: that if one seeks to completely overcome the past, it is necessary to fully retrieve its heredity. Furthermore, the general tendency has been to focus the attention on a renewal of the form, while neglecting further research into the logic.

It is necessary to recognize that the academic community and the theoretical foundation of Western music are well consolidated, but precisely for this, it is necesssary also to admit that such a theory, in spite of a vivacious and vital appearance, acts in a very deep-rooted and conservative way. As a result, the attempt at reform must deal with many restrictions and limits, and overcome apparently unsurmountable obstacles. In fact, for about two hundred years, in spite of the hundreds of proposals of linear notation reform, a plausible solution for the reform of musical ideography has never been found.

In order to resolve this difficult historical problem and continue the search for an exact strategy, it is necessary to keep in mind the reality expounded above and the cause-and-effect relation between theoretical and practical research, in order to deal with possible difficulties. In fact, the practice is even more difficult than the theoretical research, since we are in the presence of a problem that is old, enormous, and difficult. Old, because the musical Pentagram is a usage that has lasted for five hundred years; enormous, for the fact that it is a notation widespread throughout the world; difficult, in the sense that it is necessary to review and re-elaborate the entire system of the score and the related applicative theory. Thus the appraisal and study of the theoretical formation of the musical Pentagram, practiced for five hundred years, and of the attempts to reform it in the course of two hundred years, constitute the basic preparations for the examination and research of a correct means of reform, keeping in mind the key points, in order to elaborate the most efficacious means and method.

Given the perceptions and considerations mentioned above, one can establish several premises for the theoretical conception of the notation reform plan:

1. The first premise of the theoretical conception consists in fully recognizing the theoretical and artistic success of the Pentagram notation, in order to then study and analyse the difficult problems and intrinsic limits of its system, with the purpose of identifying a correct direction for the reform.

The musical Pentagram, developed in the 15th century, is based upon the Tetragram notation, already in use for sacred songs. The musical Tetragram was invented by Guido d’Arezzo, a religious Italian musician of the 11th century, who made a synthesis of the European musical notations up until his time. The musical Pentagram was established after two centuries of development and gradual unification, thanks to the creative efforts of European musicians. At the end of the 16th century, the Pentagram notation, widespread as an ideogram in European musical practice, had freed itself from the religious setting and entered into the social life of the people. It had also become perfected on the theoretical plane with the introduction of semitones, ledger lines, bar lines, etc. It reached the peak of its evolution in the 18th century, with the first establishment of the applicative dimension and theoretical structure that would then be transmitted up to the present time. It was further developed in the Baroque period (1600-1750 ca.), thanks also to the historical opportunities, and its perfection was already universally recognized. After the 19th century, it was accepted by all Nations and became the only musical ideography adopted in all the world, and the common denominator of the development of musical culture. With its incomparable advantage and its artistic values, the musical Pentagram plays a decisive role in the general development of musical culture, and it in fact obtains the greatest affirmation in history. Therefore, only the full recognition of the success of the Pentagram notation allows one to examine and then resolve the difficult problems and intrinsic limits of its system, and to search for a new and correct means of reform.

The course of the evolution of human civilization, and of the development of knowledge, is ongoing and uninterrupted, and this is a truth to be kept in mind for every kind of study or invention. The reform, then, cannot be isolated, without any precedents or successors, and it cannot demand originality by interrupting the historical continuity. It has the task of inheriting the past and of predicting the future, and it must allow the development of musical ideography to navigate towards a broader horizon and an even freer application. It must also consent the further evolution of a music notation suitable for the needs of our times, both on the theoretical and on the technical plane, which can provide new possibilities for a contemporary and scientific use of musical ideography.

2. The second premise of the theoretical conception is that of the in-depth search for the reform proposals of the last two hundred years, in order to analyse and identify the causes and effects of the successes and failures, with the purpose of accessing a new and feasible direction.

From a historical and academic point of view, the beginning of the Pentagram notation reform dates back to the end of the 18th century. During the last two centuries (precisely from 1789 to 1990), there have been hundreds of proposals concerning the linear notation in the West, from those of one line to those of sixteen lines (there has not yet been found one of fifteen lines), of which 41 are of five lines, and 32 are of six lines. From a formal point of view, these proposals are horizontal and vertical compositions of lines, and the staves can be made up of single, double, even quadruple lines; continuous, interrupted, rippled; horizontal and vertical parallels that can be equidistant and non- equidistant. As far as regards the notes, they are even more imaginative: the dot, the little oval, the little triangle, the little square, the long or short stripe, graphic designs, literary symbols, etc. Also the keys of the lines are of various forms, though it’s not the case to list here all the examples. There are still other reform proposals outside of linear notation. The examination and study of these proposals not only offer us suggestions, but they point out the problems of the Pentagram musical system from many points of view, and provide us also with ideas, projects, advice, and expectations concerning various ways and means of reform. Each proposal has its own peculiarity, and opens to us new exploratory horizons, along with suggestions of new directions to undertake. However, once all the proposals have been examined and studied, one passes to the cause-and-effect analysis of the successes and failures, in order to identify the pathway of reform, without falling back into the preceding errors.

In analyzing the general picture, one encounters three striking points: the general inclination of all the proposals listed here is that of having paid attention to, and in some way resolved, certain particular problems, but without furnishing a general transition and without having a continuity with the heredity of the past; the first cause of failure is to be attributed to the fact that these proposals aim at an innovative formal reform, while neglecting the research and the application of logic; although full of imagination and innovation, these proposals unfortunately do not have the completeness and complementarity of general knowledge, and this lesson must be kept in mind.

3. In the course of the evolution of human civilization, each thing contributes to the well-being of the other. Thus, in this work, one must look for interactive ties and relations between the art, philosophy, and science, and also find the complementary points and cultural incentives between East and West that favor civilization and common progress, in order to identify an efficient means and a workable method of reform. This is the third premise of the theoretical conception of reform.

The truth, as is natural and simple, helps us to grasp the nucleus of the development and the movement of things. The progress of contemporary civilization has confirmed an indisputable reality, from the academic point of view, stating that the more advanced the theory, the more concise is the concept; and from the technical point of view, that the more evolved the science, the more simple is the manoeuver. Art, especially music, is also a highly technical discipline. Thus the contemporary reform of music notation must follow the requirements and rules described above. The new notation must conform with the evolutive regularity of the theoretical development as an academic product and as a system, and it must have a synthetic structure and a rigorous logic, both of a formal and of a mathematic kind. All the conclusions must be based upon deductions, and all the deductions must be in conformity with logic. The foundation of the new system must satisfy the demands of the information- technology era, and it must be the result of the rational unfolding by means of the scientific essence and of the deductive philosophical method. The new system must not only resolve the present problems and intrinsic limits of the Pentagram system, but it must also eliminate everything that proves to be complicated, unreal, superfluous, and inadeguate. In short, it must adhere to a concise concept and to a simple application. Only in this way can one speak of a music notation reform that satisfies the needs of today, a reform that is worthy of being a mission of our time.

Now we shall examine the academic structural elements and theoretical applicative connotations of the

The Hexagram (six-line staff) music notation is an innovation inspired by the foregoing considerations and developed in response to the problems indicated in the premise. With respect to the Pentagram notation, it represents the total preservation of its heredity and at the same time its complete evolution. It derives from the logic of the theoretical development of notation, while preserving the traditional knowledge and customary rules for its application. At the same time it eliminates the Pentagram’s present difficulties and limitations, while unifying and normalizing to the utmost its forms and rules. It thereby allows the musical ideography to unfold with great precision and versatility, while at the same time achieving perfect simplicity and functionality. The innovation of the Hexagram notation could thus facilitate today’s most advanced theoretical and technical-musical demands, bringing new vigor to musical development.

Hexagram notation is based upon three essential elements: the theoretical and artistic achievements of Pentagram notation; the rational nucleus of the formal logic and of the mathematical logic; the system of philosophical thought and the deductive modality of the

The formative modalities of the new system are the following: 1) Each set of three horizontal parallel lines forms a half staff — precisely, based on the traditional Pentagram, with the three lower lines of the “Treble staff” and the three upper lines of the “Bass staff” — every combined with the transitory natural ledger line, constitutes a mutable scale group, i.e. precisely an octave, a series of twelve tones or a series of twenty-four tones; each set of six horizontal parallel lines, made up of the combination of these two adjacent and opposite groups of mutable scales, forms a staff that, by means of the principle of reciprocal complement, becomes an autonomous expressive musical mode. 2) Each staff is a symmetrical combination of the 2:1 ratio both formally and mathematically; each staff can be evolved and duplicated logically according to the modalities of the binary system and of the graduality, so as to produce the “Complete staff” and the “Inferential staff”. The “Complete staff”, that is to say, a combination of the staves of 4 different levels with the clefs of the seven applicative programs made up of 27 lines and 8 octaves, comprises all the ranges of executable tones; the “Inferential staff”, i.e. a series of variable combinations structured according to the principle of equivocality, can instead express specific categories of frequency and of the imaginary, beyond a practicable use. They can be concrete and abstract, realistic or fantastic, all at the same time. The application of this system, which has just one unified rule and one logical formula, 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.

In the Hexagram notation, the “Middle-c” is the centre of the staff structure and of the scale system. The staves and scales are formed by expansion from “Middle-c”; the “Middle-c” is the centre of unification for every combination of the staves and scales. They are at the same time complete and divided, similar and different. The rules are invariable and can be applied to different ranges.

The formal structure and theoretical basis of Hexagram notation, and especially its formal and mathematical logic, can also form the theoretical framework for the “Demonstrative staff” in the field of contemporary and avant-garde music, offering practicable and standardized rules for its application and future development.

The formation principle of the Hexagram system is a result of rational combination: from the applicative theory of notation, to the principles and deductive modality of the alternation of the Yin and Yang, and of the symbol and number changes, contained in the philosophy of the

The total system is composed of 20 illustrations of the notation and two theoretical frameworks of special application, along with the indications for using the generalization of the “Notation of the tonic Do/La solfège”. It is an ordinary structure of the key application, which is explained in a general way, with its multipurpose functionality and its adaptable versatility. Its applicative system of generalization can surpass and substitute the Simple notation of the Chevé System (see page 27*). This is a system of complete functional notation that facilitates the professional improvement and amateur divulgation, while being also an exact and efficient expressive system for a modernization of musical ideography that integrates form, mathematics, and philosophy.

From the viewpoint of the theoretical content, the Hexagram notation has inherited entirely the artistic and theoretical conquests of the Pentagram notation, while at the same time developing its theory and form in a revolutionary way and eliminating the current problems and persistent limits of the Pentagram system. It has unified and simplified the system for the writing and reading of the notes; diminished or avoided the use of complex ledger lines; fixed the “Middle staff”. It has corrrected the notation of inversion and of transposition, resolving the contradictions and erroneous impressions in the relation between the vertical and horizontal elements in the general score, and between reading and listening. It has established the practicable norm of use for the notation of the “abstractist” and expressionistic forms of contemporary music. It has furnished the means of efficient use for the computerization of notation, opening a vast perspective for a scientific use and a modernization of musical technique. It has the function and significance of inheriting the good qualities of the past and of anticipating the future with avant-garde inspiration.

When one comes to a halt in self-satisfaction and laziness, one does not realize that from that moment on there is the beginning of regression and degeneration. The hope of humanity lies in proceeding constantly with the search for evolution. The appearance of the Hexagram notation aspires to be a valid contribution to the universal development of musical culture in the world.

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