Duple time did not come into general use until the beginning of the fourteenth century.  About the same time, the organum (as it was called) or system of harmonization of Hucbald was discarded, and Johannes de Muris and Philippe de Vitry championed the consonant quality of the third and sixth, both major and minor.  The fifth was retained as a consonant, but the fourth was passed over in silence by the French school of writers, or classed with the dissonants.  Successive fifths were prohibited as being too harshly dissonant, but successive fourths were necessarily permitted, as it would be an impossibility to do without them.  Nevertheless, the fourth was still considered a dissonance, and was permitted only between the upper parts of the music.  Thus the harsh consecutive passages in fifths and fourths of the organum of Hucbald disappeared in favour of the softer progressions of thirds and sixths.

In order to make clear how the new science of counterpoint came into existence, I must again revert to Hucbald.[09]

Before his time, all “recognized” music was a more or less melodious succession of tones, generally of the same length, one syllable being sometimes used for many notes.  He discovered that a melody might be sung by several singers, each commencing at a different pitch instead of all singing the same notes at the same time.  He also laid down rules as to how this was to be done to produce the best effect.  We remember why he chose the fourth, fifth, and octave in preference to the third and sixth.  He called his system an “organum” or “diaphony,” and to sing according to his rules was called to “organize” or “organate.”  We must remember that at that time fourths and fifths were not always indicated in the written music; only the melody, which was called the principal or subject.  By studying the rules prescribed for the organum, the singers could add the proper intervals to the melody.  We must keep in mind, however, that later fourths were preferred to fifths (being considered less harsh), and that the musical scale of the period compelled the different voices to vary slightly, that is to say, two voices could not sing exactly the same melody at the interval of a fourth without the use of sharps or flats; therefore one voice continued on the same note until the awkward place was passed, and then proceeded in fourths again with the other voice as before: 

    [G:  {e’ a’} {d’ g’} {d’ f+’} {d’ e’}]

On account of the augmented fourth that would occur by a strict adherence to the melodic structure of the subject, the following would have been impossible:  [G:  {e’ a’} {d’ g’} ({c’ f+’})] Thus we find the first instance of the use of thirds, and also of oblique motion as opposed to the earlier inevitable parallel motion of the voices.  This necessary freedom in singing the organum or diaphony led to the attempt to sing two different melodies, one against the other—­“note against note,” or “point counter point,"[10] point