Editing Medieval music (section)

===Polyphony===
[[File:Pérotin - Viderunt omnes.jpg|thumb|right|170px|[[Pérotin]]'s ''Viderunt omnes'', {{circa|13th century}}.]]
Of equal importance to the overall history of western music theory were the textural changes that came with the advent of polyphony. This practice shaped western music into the harmonically dominated music that we know today.{{sfn|Hoppin|1978|p=187}} The first accounts of this textural development were found in two anonymous yet widely circulated treatises on music, the ''[[Musica enchiriadis|Musica]]'' and the ''[[Scolica enchiriadis]]''. These texts are dated to sometime within the last half of the ninth century.{{sfn|Christensen|2002|p=480}} The treatises describe a technique that seemed already to be well established in practice.{{sfn|Christensen|2002|p=480}} This early polyphony is based on three simple and three compound intervals. The first group comprises fourths, fifths, and octaves; while the second group has octave-plus-fourths, octave-plus-fifths, and double octaves.{{sfn|Christensen|2002|p=480}} This new practice is given the name ''[[organum]]'' by the author of the treatises.{{sfn|Christensen|2002|p=480}} ''Organum'' can further be classified depending on the time period in which it was written. The early ''organum'' as described in the ''enchiriadis'' can be termed "strict ''organum''"{{Sfn|Ultan|1977|p=52}} Strict ''organum'' can, in turn, be subdivided into two types: ''diapente'' (organum at the interval of a fifth) and ''diatesseron'' (organum at the interval of a fourth).{{sfn|Ultan|1977|p=52}} However, both of these kinds of strict ''organum'' had problems with the musical rules of the time. If either of them paralleled an original chant for too long (depending on the mode) a [[tritone]] would result.{{sfn|Ultan|1977|p=53}}

This problem was somewhat overcome with the use of a second type of ''organum''. This second style of ''organum'' was called "free ''organum''". Its distinguishing factor is that the parts did not have to move only in parallel motion, but could also move in oblique, or contrary motion. This made it much easier to avoid the dreaded tritone.{{sfn|Ultan|1977|p=55}} The final style of ''organum'' that developed was known as "[[melismatic]] ''organum''", which was a rather dramatic departure from the rest of the polyphonic music up to this point. This new style was not note against note, but was rather one sustained line accompanied by a florid melismatic line.{{sfn|Ultan|1977|p=58}} This final kind of ''organum'' was also incorporated by the most famous polyphonic composer of this time—[[Léonin]]. He united this style with measured [[discant]] passages, which used the rhythmic modes to create the pinnacle of ''organum'' composition.{{sfn|Ultan|1977|p=58}} This final stage of ''organum'' is sometimes referred to as [[Notre Dame school]] of polyphony, since that was where Léonin (and his student [[Pérotin]]) were stationed. Furthermore, this kind of polyphony influenced all subsequent styles, with the later polyphonic genera of motets starting as a trope of existing Notre Dame ''organums''.

Another important element of medieval music theory was the system by which pitches were arranged and understood. During the Middle Ages, this systematic arrangement of a series of whole steps and half steps, what we now call a [[Musical scale|scale]], was known as a [[Gregorian mode|mode]].{{Citation needed|date=May 2017}} The modal system worked like the scales of today, insomuch that it provided the rules and material for melodic writing.{{sfn|Seay|1965|p=32}} The eight church modes are: ''[[Dorian mode|Dorian]]'', ''[[Hypodorian]]'', ''[[Phrygian mode|Phrygian]]'', ''[[Hypophrygian mode|Hypophrygian]]'', ''[[Lydian mode|Lydian]]'', ''[[Hypolydian mode|Hypolydian]]'', ''[[Mixolydian]]'', and ''[[Hypomixolydian mode|Hypomixolydian]]''.{{sfn|Seay|1965|p=33}} Much of the information concerning these modes, as well as the practical application of them, was codified in the 11th century by the theorist [[Johannes Afflighemensis]]. In his work he describes three defining elements to each mode: the final (or ''finalis)'', the reciting tone (''tenor'' or ''confinalis''), and the range (or ''ambitus''). The ''finalis'' is the tone that serves as the focal point for the mode and, as the name suggests, is almost always used as the final tone. The reciting tone is the tone that serves as the primary focal point in the melody (particularly internally). It is generally also the tone most often repeated in the piece, and finally the range delimits the upper and lower tones for a given mode.{{sfn|Ultan|1977|p=25}} The eight modes can be further divided into four categories based on their final (''finalis'').

Medieval theorists called these pairs ''maneriae'' and labeled them according to the Greek ordinal numbers. Those modes that have d, e, f, and g as their final are put into the groups ''protus'', ''deuterus'', ''tritus'', and ''tetrardus'' respectively.{{sfn|Hoppin|1978|p=64}} These can then be divided further based on whether the mode is "authentic" or "plagal." These distinctions deal with the range of the mode in relation to the final. The authentic modes have a range that is about an octave (one tone above or below is allowed) and start on the final, whereas the plagal modes, while still covering about an octave, start a perfect fourth below the authentic.{{sfn|Christensen|2002|p=311}} Another interesting aspect of the modal system is the use of "[[Musica ficta]]" which allows pitches to be altered (changing B{{music|natural}} to B{{music|flat}} for example) in certain contexts regardless of the mode.{{sfn|Hoppin|1978|p=66}} These changes have several uses, but one that seems particularly common is to avoid melodic difficulties caused by the tritone.{{sfn|Seay|1965|p=34}}

These ecclesiastical modes, although they have Greek names, have little relationship to the modes as set out by Greek theorists. Rather, most of the terminology seems to be a misappropriation on the part of the medieval theorists{{sfn|Seay|1965|p=33}} Although the church modes have no relation to the ancient Greek modes, the overabundance of Greek terminology does point to an interesting possible origin in the liturgical melodies of the [[Byzantine music|Byzantine]] tradition. This system is called ''[[octoechos]]'' and is also divided into eight categories, called ''echoi''.{{sfn|Christensen|2002|p=310}} 
 
For specific medieval music theorists, see also: [[Isidore of Seville]], [[Aurelian of Réôme]], [[Odo of Cluny]], [[Guido of Arezzo]], [[Hermannus Contractus]], [[Johannes Cotto]] (Johannes Afflighemensis), [[Johannes de Muris]], [[Franco of Cologne]], [[Johannes de Garlandia (music theorist)|Johannes de Garlandia]] (Johannes Gallicus), [[Anonymous IV]], [[Marchetto da Padova]] (Marchettus of Padua), [[Jacob of Liège|Jacques of Liège]], [[Johannes de Grocheo]], [[Petrus de Cruce]] (Pierre de la Croix), and [[Philippe de Vitry]].