The first embarkations in to organum are hidden in obscurity but most probably involve forms of parallel singing, possibly with a bourdon, not unlike practice in Eastern liturgies. Considering that the trained singers were imbibed in an oral tradition that was several centuries old, singing a small part of the chant repertory in straightforward heterophony of parallel harmony or other ways of 'singing by the ear' would come naturally. It is made clear in the Musica enchiriadis that octave doubling was acceptable, since such doubling was inevitable when men and boys sang together. The 9th-century treatise Scolica enchiriadis treats the subject in greater detail. For parallel singing, the original chant would be the upper voice, vox principalis; the vox organalis was at a parallel perfect interval below, usually a fourth. Thus the melody would be heard as the principal voice, the vox organalis as an accompaniment or harmonic reinforcement. This kind of organum is now usually called parallel organum, although terms such as sinfonia or diaphonia were used in early treatises.
The Musica enchiriadis documented a practice which obviously had been in use for some time, although it has not been possible to establish even an approximate dating for the commencement of the practice, which may go back hundreds of years. Both of the Enchiriadis treatises are primarily works on the concept of a mathematical derivation of the gamut and the modes based on theories of conjunct and disjunct tetrachords (series of four pitches involving fixed tone and semitone relationships within them). To some extent it is probable that the treatment given to organum was a treatment designed to explain it in the terms of the evolving theory of the gamut (not least by the observation that parallel fourths outline tetrachords), and was not a descriptive or prescriptive manual of practical organum. For that, we can turn to Ad Organum faciendum, (Anonymous, c 1100) which is just such a manual: how to make organum. In letter-notation two organa are given as examples: Alleluia V.Iustus ut palma and Kyrie trope Cunctipotens, in two voices, predominantly puncta contra punctam, "note against note". The Kyrie chant is the lower part, the new part finds a different harmony for every note of the chant and the same applies to the Alleluia. It is also worth noting that strict parallel organum does not generally occur in either of these early treatises as an end in itself. The treatises begin from a premise of parallelism and then move on to suggest better ways of making the organum, involving boundary tones, and the vast majority of musical examples in the treatises in fact use intervals of 2nds, 3rds, 4ths, 5ths, and 6ths (by inversion/octave doubling), to create a more artistic result. The aesthetic underpinning the use of these other intervals (usually to do with the concept of a "boundary tone" to preserve the modal integrity, or in order to avoid harmonic tritones or accidentals foreign to the mode) was explored in more detail by Guido d'Arezzo in his Micrologus of around AD 1020. Scholars have tended to describe this more varied organum as "free organum" (see below).
Scholarship has not yet established whether this early organum was chronologically derived from a more primitive strict parallelism, or from a kind of modally-constrained heterophony. The most pervasive examples of strict "parallel organum" in fact occur only in insular Germanic repertories of the 13th century onwards, and not in the very much earlier Enchiriadis treatises, the works of Guido, or in the various interpretations of the Winchester Troper (in which can be found passages which appear to be notated heterophony at the unison, although transcription problems confound absolute certainty in this).
The basic principle of florid organum is that there are anywhere from two to six notes in the organal voice sung over a single sustained note in the tenor. Saint Martial organum and Paris organum duplum follow from the same principle, but in a different form.
During the course of the twelfth century, the age of the Cathedrals, melismatic (or "florid") organum developed in Aquitania, and is linked to Saint Martial de Limoges. This form of organum is based on a plainchant melody that is sung in extended note-values in the lower voice, the length of which are determined by the length of the phrase in the organal part. The chant thus transforms into a succession of long held notes according to the original melody and comes to be called "tenor" from the Latin tenere meaning "to hold". The upper organal voice moves in extensive melisms on long protracted vowels. This newer style became known as "organum", "organum duplum", or "organum purum" and the older note-against-note style became known as discant (discant).
The Saint Martial organum is rhapsodic in character as rhythms are not yet organized according to the six rhythmic modes, for the introduction of which Leonin seems to deserve to be credited.
Medieval Music - Richard H. Hoppin
Antiquity and the Middle Ages - Edited By James McKinnon
The relevant authors that write about Organum of the Notre Dame School, Anonymous IV, Ioh. de Garlandia, the St. Emmeram Anonymous and Franco of Cologne to name a few, are not always as clear as could be desired, nevertheless, a lot of information can be distilled from the comparative research of their writings. Organum purum is one of three styles of organum, which is used in section where the chant is syllabic thus where the tenor can not be modal. As soon as the chant uses ligatures, the tenor becomes modal and it will have become discant, which is the second form. The third form is copula (Lat. coming together) which in the words of Ioh. de Garlandia 'is between organum and discant' and according to Waite a bridge section between modal and non-modal sections. It seems that for most instances we can take Garlandia literally where he says 'between' organum and discant. In organa dupla the copula is very similar to a short, cadential organum purum section but in organa tripla or conducti it is seen that irregular notation is used. Either the last notes of ligatures are affixed with a plica which divides the notes in smaller values, or a series of disjunct rests is used in jolting succession in both parts, creating what is also called hocket. These features also can be frequently found in two-part discantus on special cadences or a preparation of a cadence, where they are also referred to as 'copulae'. De Garlandia states simply: 'a copula is where are any number of lines are found' referring to the plicae or rest-signs. Thus organum duplum can be schematized as follows:
Perotin "is the best composer of Discantus", according to Anonymous IV, an English student, writing ca.1275, who has provided at least a few morsels of factual information on Paris Organum and its composers. Perotin further developed discantus in three part Organum (Organum Triplum) where both organal voices are in discantus. Note that organum purum is not possible in three-part organa, the two upper voices need to both be organized according to the rhythmic modes. Perotin even went as far as composing two four-part organa (quadrupla), Viderunt omnes and Sederunt principes which were performed in Notre Dame in 1098 on New Year's Day and in 1099 on the feast of St. Stephen (a decree of Odon de Sully, Bishop of Paris, exists which stipulates the performance of 'organa tripla vel quadrupla') Apart from organa, Perotin extended the form of the Aquitanian Versus which was henceforth called conductus. Any conductus is a new composition on new texts and is always composed in the rhythmic modes. Perotin set several texts by Philippe le Chancelier, while some texts refer to contemporary events. Two-part conductus form the larger part, though conductus exist for one to four voices. Two, three and four part conductus are composed throughout in discantus style. As in organa tripla, handling three voices (or four) precludes the kind of rhythmic freedom found in dupla. In conductus the distinction is made between 'cum littera' and ' sine litera', texted sections and melismatic sections. The texted parts can sometimes go beyond the modal measure and then fall back in to regular mode in the melismatic discantus section, which is called cauda. Again according to Anonymous IV, Perotin wrote a number of replacement clausulae from organa dupla by Leonin. As the tenor in Leonin's organa dupla in discant sections proceeds always in the 5th mode (all longs in a rhythmic group ordine), Perotin, who was a generation removed from Leonin, saw fit to improve them by introducing different modes for the tenor and new melodic lines for the dupla, increasing the rhythmic organization and diversity of the section. However, in the largest compilation of Notre Dame repertoir (F) no less than 462 clausulae exist, many recurrences of the same clausulae in variant settings, according to Waite 'written in a variety of styles and with varying competence' A further innovation was the motellus, in which the upper part of a discant section is supplied with a new text, so that when the lower voice utters a single syllable, the upper part will pronounce several. This would have been the first instance of two different texts being sung in harmony. In turn, the motellus gave birth to the motet which is a poly-textual piece in discant, which obviously sparked a lot a creativity as it soon became a prolific form of composition.
The Organa that were created in Paris were disseminated throughout Europe. The three main sources are W1, St. Andrews, Wolfenbuttel 677,olim Helmstadt 628; the large and illuminated copy made in Florence, owned by Piero de Medici, the Pluteo 29.1 of the Bibliotheca Mediceo-Laurenziana (F), which is by far the most extensive copy of the repertory. Finally W2, Wolfenbuttel 1206, olim Helmstadt 1099, which was compiled the latest (and contains the greatest amount of motets).
There are arguments that support a relative freedom of rhythm in Organa dupla but others refute this, saying that the interpretation of the music should always be according to modal or Franconian principles. Two researchers, Apel and Waite, insisted upon a rigorously modal interpretation. Though Waite in his dissertation, notably in chapter 4: The notation of organum duplum' acknowledged that in in organum duplum and monophonic conducts are relative freedom may have been taken, he transcribed a selection of the Magnus Liber Organi of Leonin into strict modal rhythm. Apel argued that the rhythms in the piece, due to the rules of consonance is clearly non-modal. To this day, as behoofs scientists, debates on interpretation proceed as usual. However, Waite published 54 years ago and his point of vieuw has been superseded by ongoing research. "..but his (Waite) vieuw that the entire corpus (of the Magnus Liber Organi) should be transcribed according to the rhythmic modes is no longer accepted" (Peter Jeffery in the Notation Course Medieval Music 1100-1450 (music205), Princeton)
In the range of forms of compositions found in the later two manuscripts that contain the Notre Dame-repertory (F and W2) one class of distinction can be made: that which is (strictly) modal and that which is not. Organum duplum in its organum purum sections of syllabic setting, the cum littera sections in two-part conductus, copulae in general and monophonic conductus would be that part of the repertory which is not strictly modal. In monophonic song, be it chant or a conductus simplex by Perotin, there is no need to vary from the classical standards for declamation that were a rooted tradition at the time, going back to St. Augustine, De Musica. It has been firmly established by extensive research in chant traditions (Gregorian Semiology) that there is a fluency and varyancy in the rhythm of declamatory speech that should also govern chant performance. These principles extend to the not strictly modal sections or compositions, as a contrasting quality with musica mensurabilis.
As Parisian Organum is based on Gregorian chant, it is categorized under Ars Antiqua which is called thusly in contrast to the Ars Nova which embarked on new forms that were in every sense original and no longer based on Gregorian chant and as such consisted a breach with the musical practice of the ancients.