Their immediate successor, =Guido=, has been credited, unjustly, with being the inventor of nearly every improvement in the art up to his time. The old organum closed with his. The earliest writer who treats of the new organum is =John Cotton=, in the 11th century. He was the first to promulgate the rule that contrary motion is always to be preferred to similar or oblique. He says: “At least two singers are required in diaphony formed from different sounds. While one voice sings a melody, the other surrounds it with different tones, and at the end of the phrases the two voices unite at the unison or octave.” The fullest development of the new organum was attained in the works of =Guy de Chalis=, about the close of the 12th century. He gives examples in which we find intervals of the eleventh and twelfth, a demonstration of the existence of a system differing from the Gregorian, which does not exceed the octave. In the same epoch, =Denis Lewts=, of Liége, a Carthusian monk, gives rules to fix the use of accidental signs, a flat to lower B, a sharp to raise F. He speaks of these as if they had been in use for a long time, and indicated that the idea was to avoid the occurrence of the diminished fifth or the _augmented fourth_, known in harmony as the _tritone_. This process is called _Musica Ficta_, and formed a part of the instruction of singers. The examples cited by Lewts conform to this theory, and show that although in the songs, motets and other compositions of the period the sharps and flats are not found, it is because musicians knew the principles and made the application for themselves. Instruction in those days was chiefly oral, a method which placed a premium on a retentive memory. By the time that the 13th century was reached, musical forms and melodies were widely spread, and as we look back to the 9th century it is possible to note the gradual development. Harmony always existed, in a limited sense; but it did not take on a scientific development until the Middle Ages. It is to the musicians of this latter period, from the 13th to the 15th centuries, that we must give the honor of having taken the germ of a science of harmony and of having brought it forward to mature development. REFERENCE. Williams.—The Story of Notation. QUESTIONS. Explain the earliest system of notation used for the Church scales. What was the next improvement? State the defects. What was the system of Notation by Neumes? Did they indicate absolute or relative pitch? Give the successive steps making use of lines. What was the origin of our Clef signs? Who is credited with introducing signs to indicate Duration? Name the signs adopted. Compare them to the notes now in use. Explain Faburden; Diaphony; Organum; Discant; Measured Music. Who were the early writers on the subject of music? LESSON VII. MUSIC OUTSIDE THE CHURCH.