An organization must be logic and for this reason after several centuries the content of the modes is organized in scales, creating this way ambiguity with the modern classic music which is an arbitrary procedure as the Middle age and the Byzantine world ignore this principle and consider a mode to be a species of melody, a reservation of melodic types where there could be clauses corresponding to an immediate need. Four great medieval formulas exist on the starting points D, E, F or G. According to the development of ascending or descending sense, these modes are considered to be authentic or plagal which raises to eight the number of modes. Besides, every formula can be transposed two times in the medieval scale.

The space covered with every scheme is that of an octave, which can be considered to be better as a fourth joined to a fifth; that is really an octave in strict sense. The ancient treatises enunciate these forms by means of melodic clauses and not for successions of joint grades. The medieval melody appeals to this scheme in order to constitute his pieces but not at random. The fragments have value of beginning, linkage, completion, etc., as it happens in all the oriental music.

THE RHYTHM

The rhythm of any plainchant is imposed for itself when a manuscript is read in neumes and the recited melodies and the vocalizations of the oriental rites are remembered. Leaving out material differences (musical dialect, different emission that modifies the voice, language) the substance of the chants is the same in both cases. It turns out to be easy to see that properly the liturgical melody is free, whereas the poems, poetical human genius, are measured delicately. All the texts of the celebrant can be considered to be expressed freely, as well as the liturgical singings of the schola, even in the last term, a solfa so demanding is already outlined as that of Solesmes, needed for a complete study of the text. This solfa being founded on the indivisibility of the first time, does not bother to the performer in the same way that the beats do not bother to the pianist. In both cases as much in the audition as in the execution, it is important not to confuse skill and musical sense.

Inside the Solesmes system generally practiced in the abbeys and in much of the parishes when both of them have accepted in singing the liturgy there have been very rough discussions. Dom Pothier, authentic founder of the scriptorium and of the studies, was a fierce defender of the Latin accent as a pole to whose around the melody was organized, while his successor, Dom Mocquereau, was organizing this melody by herself and for herself. In opposition, the measuring theories tend to superpose to any situation a measurement to the melody. Many theories appear of which none has managed to impose yet.

1. Father Dauchebreau measures the neumas and divides them in long and brief. It is necessary to ask him what explanation gives this theory to the fact of which, according to the manuscripts, the melody remains, though the neumas used for translating it, change often.
   
2. G. Houdard was thinking that every neume must be considered solely as a one time. All his notes must be expressed in this time. Now then, there can be many notes in certain neumes of the 10th century and even later.
   
3. Dom Giannine organizes the melodies in long and brief, giving irregular measurements but that prolong the melody farther than of the incredible.
   
4. Peter Vagder constitutes a few metric feet with the neumas.
   
5. Monsignor Foucault re-constitutes differently a few metric feet.
   
6. E. Hammer steadies himself delicately in the prosody of the language and discards deservedly any possibility of measurement for the vocalizations.
   
7. For J. W. A. Voaler the neumes are long or brief by themselves.