J. The Tonic Do/La solfeggio (relative solfeggio) notation and the applicative modality of the generalization on the Hexagram

Illustration:

1) On the basis of the Hexagram "Complete staff" scale system, as in figure 7, the notation and disposition of the scale of eight octaves and of the staff of seven levels follow the tonic Do/La solfeggio, which is formally composed so that it can be applied gradually. Every staff (clef) comprises the scale of two octaves and one degree of the voice range. The formal logic and the mathematical logic of the seven staves of different levels are unified and yet symmetrical, identical but also differentiated, as in figures 21, 22, and 23:

Figure 21) The unified and symmetrical module of every staff in the Notation of the tonic Do/La solfeggio on the Hexagram

Figure 22) The solfeggio structure and the scale system of every staff in the Notation of the tonic Do/la solfeggio on the Hexagram

Figure 23) The method of reading notes and the form of transcription in the Notation of the tonic Do/La solfeggio on the Hexagram

   The Hexagram is a structure of six parallel lines and five spaces, with the third space in the centre, while both above and below it are three lines and three spaces (comprising the first upper and lower ledger spaces). The third space of the centre and the first upper and lower ledger lines, are all tonic Do of the major mode both in solfeggio and notation, constituting a unified and symmetrical system of a scale of two octaves (see point C. in figure 23 above).
   Below the central Do, the solfeggio and notation of the three spaces are gradually Re, Fa, La; whereas above the central Do, the solfeggio and notation of the three lines are gradually Re, Fa, La (see point L. in figure 23 above).
   Below the central Do, the solfeggio and notation of the three lines are gradually Mi, Sol, Si; whereas above the central Do, the solfeggio and notation of the three spaces are gradually Mi, Sol, Si (see point R. in figure 23 above).
   The notes and the signs of rhythms in Hexagram notation are completely identical to those in Pentagram notation. They follow the same theoretical principle of the Simple notation (Notation of the Chevé System* — notation of the scale with Arabic ciphers (numerals), popularly used in China and Japan), and they originate from the traditional basis of musical theory.

2) The principle of this Notation function is applied in a fixed, though versatile way, with the variable key-signature and with the tonal pitch in modulation. The key-signature is made up of the tonic of the solfeggio (Do/La), the parallel sign (//), and the alphabetic key-note (C. D. E. F. G. A. B. / c. d. e. f. g. a. b.) written on the right side of the clef, showing the parallel and equalizing relationship between the tonic of the solfeggio and the tonic of the applicative key. The key-signature thus shows only the key that has really to be applied and the tonal pitch of modulation, without modifying the position and the modality of the original notation from the tonic Do/La solfeggio, as seen in figure 24:

Figure 24) The figure and the applicative system of the key-signature of every staff in the Notation of the tonic Do/La solfeggio on the Hexagram

The key-signature system of the 12 major:

The key-signature system of the 12 minor:

3) The applicative canon of the Tonic Do/La solfeggio notation on the Hexagram:

- The position and notation are placed by means of the tonic Do/La solfeggio in major and in minor diatonic modes.

- A determinant key and the intonation of the pitch by means the tonic Do/La of the solfeggio in major and minor diatonic modes, make it possible to find both the actual key and pitch to be applied.

- Music of particular tonalities can also be defined in key and be prepared according to the tonic (key-note) of the modes, for example, the five-tone Chinese modes.

- Atonal music has neither modes nor tonic to define, but is to be notated directly with 12-tone or 24-tone equal-temperament system.

4) The applicative modality of the Tonic Do/La solfeggio notation on the Hexagram:

The Human Voice

The Musical Instruments

All instrumental music that applies the Tonic Do/La solfeggio notation on the Hexagram can determine the staves according to the real pitch and tone range of instrumental execution, and can also modulate the clef (staff) provisionally, according to the needs of application, as advised in Appendix (1).

Demonstration: The Hexagram staff of seven different levels requires only one method of reading the notes, in a unified and symmetrical form of notation; a single method of reading the notes in a unified and symmetrical form of notation, can be applied to the staff (clef) of the seven different tone ranges and to the 24 key signatures of different tonal pitches (12 major and 12 minor).

Conclusion: The concise and easy method of reading the notes, and the simple and effective way of transcribing the Tonic Do/La solfeggio notation, not only can highlight the tonality and strengthen musical perceptiveness, but can also allow unrestricted modulation of key at pleasure; these methods are not only in effective accordance with professional application, but also surpass and substitute the range of functions of the Simple notation, thus providing both an efficient applicative modality for the popularization of singing activities, and a divulgative method of musical education in primary and secondary schools.

Hexagram notation represents a complete recuperation of the heritage of Pentagram notation as well as its natural evolution, with the Hexagram "Great staff" of 13 lines comprising the Pentagram "Great staff" of 11 lines. To learn the Hexagram means to understand and master perfectly the Pentagram. The practice of the Tonic Do/La solfeggio notation will stimulate the development of application of the professional system of Hexagram notation, and will afterwards facilitate its application on the computer.

* Notation of the Chevé System: Galin-Paris-Chevé System (Méthode élémentaire de la musique vocale). Émile Joseph Maurice Chevé (1804-1864), French musical theorist and pedagogue, intended to perfect and to popularize the method of numerical music notation (sight-singing system) conceived by Pierre Galin (1786-1821) and Aimé Paris (1798-1866). Then known as meloplasto and now also as the Chevé System, its fundamental characteristic is the use of numbers (Arabic ciphers) instead of the notes. The ciphers from 1 to 7 represent the tones of the scale (all referred to the tonic…). Chevé was a polemical supporter of his own theories and he tried in vain to provoke public discussion and comparison between his students and those of the traditional method, especially in the Conservatoire. In 1677, a Franciscan monk in Paris, C. Willems Souhaitty, had been the first to suggest using the ciphers from 1 to 7 instead of the notes of the scale, with the addition of points to locate their position on the staff. Later, in 1742, at the Academy of Sciences in Paris, Jean Jacques Rousseau (1712-1778), the Swiss-French philosopher, writer, and composer, expounded his own report on a new system of music notation based on the substitution of notes with ciphers (Projet concernant des nouveaux signes pour la musique). This method and system were imported to Japan, and later to China, during the twentieth century. The lack of their divulgation, unfortunately, has deprived Europe nowadays of a valid and simple system of popular music education in the ordinary schools.

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