ng 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 or _punct_ being the name
for the written note. There being now two distinct melodies,
both had to be _noted_ instead of leaving it to the singers
to add their parts extemporaneously, according to the rules of
the organum, as they had done previously. Already earlier than
this (in 1100), owing to the tendency to discard consecutive
fourths and fifths, the intermovement of the voices, from
being parallel and oblique, became _contrary_, thus avoiding
the parallel succession of intervals. The name "organum" was
dropped and the new system became known as tenor and descant,
the tenor being the principal or foundation melody, and the
descant or descants (for there could be as many as there
were parts or voices to the music) taking the place of the
organum. The difference between _discantus_ and _diaphony_
was that the latter consisted of several parts or voices,
which, however, were more or less exact reproductions, at
different pitch, of the principal or given melody, while the
former was composed of entirely different melodic and rhythmic
material. This gave rise to the science of counterpoint, which,
as I have said, consists of the trick of making a number
of voices sing different melodies at the same time without
violating certain given rules. The given melody or "principal"
soon acquired the name of _cantus firmus_, and the other parts
were each called _contrapunctus_,[11] as before they had been
called tenor and descant. These names were first used by Gerson,
Chancellor of Notre Dame, Paris, about 1400.

In the meantime (about 1300-1375), the occasional use of thirds
and sixths in the diaphonies previously explain