Discant

Discant, or descant (descant), (, meaning "singing apart") originated as a style of liturgical setting in the Middle Ages, associated with the development of the Notre Dame school of polyphony.
In origin, it is a style of organum that either includes a plainchant tenor part (usually on a melisma in the chant) or is used without a plainchant basis in conductus, in either case with a "note against note" upper voice, moving in contrary motion. It is not a musical form, but rather a technique. The term continued to be used down to modern times with changing senses, at first for polyphony in general, then to differentiate a subcategory of polyphony (either in contrast to organum, or for improvised as distinct from written polyphony). By extension it became the name of a part that is added above the tenor, and later as the name of the highest part in a polyphonic setting (the equivalent of "cantus", "superius", and "soprano"). Finally, it was adopted as the name of the highest register of instruments such as recorders, cornets, viols, and organ stops.
"English discant is three-voice parallelism in first-inversion triads." However, because it allowed only three, four, or at most five such chords in succession, emphasizing contrary motion as the basic condition, it "did not differ from the general European discant tradition of the time". Because English discant technique has commonly been associated with such a succession of first-inversion triads, it has inevitably become confused with "fauxbourdon", with which it has "no connection whatsoever". This misinterpretation was first brought forward in 1936 by Manfred F. Bukofzer, but has been proved invalid, first in 1937 by Thrasybulos Georgiades, and then by Sylvia Kenney and Ernest H. Sanders. A second hypothesis, that an unwritten tradition of this kind of parallel discant existed in England before 1500, "is supported neither by factual evidence nor by probability".
Characteristics.
This style was dominant in early 12th century Aquitanian polyphony, and can be identified by the following characteristics:
Examples of this can be found in some of Léonin’s late 12th-century settings. These settings are often punctuated with passages in discant style, where both the tenor and upper voice move in modal rhythms, often the tenor part in mode 5 (two long notes) and the upper part in mode 1 (a long then short note). Therefore it is easier to imagine how discant style would have sounded, and we can make a guess as to how to recreate the settings. It is suggested by scholars such as Grout, that Léonin used this non-melismatic style in order to mirror the grandeur of Notre Dame Cathedral itself. 
Current research suggests that the word 'discantus' was formed with the intention of providing a separate term for a newly developed type of polyphony. If true, then it is ironic that the newer term, "discantus", ended up being applied to the older note-against-note style, while the older word "organum" was transferred to the more innovative style of florid-against-sustained-note polyphony. This may have been partly because the 12th century was an era that believed in progress, so that the more familiar "organum" was kept for the style then considered to be the most up-to-date.
Discant in three or four voices.
The development of modal rhythms enabled the progression from two part discant style to three and four part discant style. This is because, only voices, confined to a set rhythm can be combined effectively to make a set phrase. This was mainly related to Pérotin, around 1200. The parts in these three and four past settings were not necessarily related to each other. Evidence suggests that the parts were either related to the tenor part, or composed independently. Either way, this formed the first ‘composition’, and provided a foundation for development, and a new style, "conductus" was developed from the three and four part discant ideas.