Editing Gregorian chant (section)

===Modality===
{{Main|Mode (music)}}
Early plainchant, like much of Western music, is believed to have been distinguished by the use of the [[diatonic scale]]. Modal theory, which postdates the composition of the core chant repertory, arises from a synthesis of two very different traditions: the speculative tradition of numerical ratios and species inherited from ancient Greece and a second tradition rooted in the practical art of cantus. The earliest writings that deal with both theory and practice include the [[Musica enchiriadis|Enchiriadis]] group of treatises, which circulated in the late ninth century and possibly have their roots in an earlier, oral tradition. In contrast to the ancient Greek system of tetrachords (a collection of four continuous notes) that descend by two tones and a semitone, the Enchiriadis writings base their tone-system on a tetrachord that corresponds to the four finals of chant, D, E, F, and G. The disjunct tetrachords in the Enchiriadis system have been the subject of much speculation, because they do not correspond to the diatonic framework that became the standard Medieval scale (for example, there is a high F{{music|#}}, a note not recognized by later Medieval writers). A diatonic scale with a chromatically alterable b/b-flat was first described by [[Hucbald]], who adopted the tetrachord of the finals (D, E, F, G) and constructed the rest of the system following the model of the Greek Greater and Lesser Perfect Systems. These were the first steps in forging a theoretical tradition that corresponded to chant.

Around 1025, [[Guido d'Arezzo]] revolutionized Western music with the development of the ''gamut'', in which pitches in the singing range were organized into overlapping [[hexachord]]s. Hexachords could be built on C (the natural hexachord, C-D-E^F-G-A), F (the soft hexachord, using a B-flat, F-G-A^B{{music|b}}-C-D), or G (the hard hexachord, using a B-natural, G-A-B^C-D-E). The B-flat was an integral part of the system of hexachords rather than an [[accidental (music)|accidental]]. The use of notes outside of this collection was described as [[musica ficta]].

Gregorian chant was categorized into eight [[mode (music)|modes]], influenced by the eightfold division of [[Byzantine chant]]s called the ''[[oktoechos]]''.{{sfn|Wilson|1990|p=11}} Each mode is distinguished by its ''final'', ''dominant'', and ''ambitus''. The ''final'' is the ending note, which is usually an important note in the overall structure of the melody. The ''dominant'' is a secondary pitch that usually serves as a [[reciting tone]] in the melody. ''[[Ambitus (music)|Ambitus]]'' refers to the range of pitches used in the melody. Melodies whose final is in the middle of the ambitus, or which have only a limited ambitus, are categorized as ''plagal'', while melodies whose final is in the lower end of the ambitus and have a range of over five or six notes are categorized as ''authentic''. Although corresponding plagal and authentic modes have the same final, they have different dominants.{{sfn|Hoppin|1978a|pp=64–65}} The existent pseudo-Greek names of the modes, rarely used in medieval times, derive from a misunderstanding of the Ancient Greek modes; the prefix "[[wikt:hypo-|hypo-]]" (under, Gr.) indicates a plagal mode, where the melody moves below the final. In contemporary Latin manuscripts the modes are simply called Protus authentus /plagalis, Deuterus, Tritus and Tetrardus: the 1st mode, authentic or plagal, the 2nd mode etc. In the Roman Chantbooks the modes are indicated by Roman numerals.

:Modes 1 and 2 are the authentic and plagal modes ending on D, sometimes called [[Dorian mode|Dorian]] and [[Hypodorian mode|Hypodorian]].
:Modes 3 and 4 are the authentic and plagal modes ending on E, sometimes called [[Phrygian mode|Phrygian]] and [[Hypophrygian mode|Hypophrygian]].
:Modes 5 and 6 are the authentic and plagal modes ending on F, sometimes called [[Lydian mode|Lydian]] and [[Hypolydian mode|Hypolydian]].
:Modes 7 and 8 are the authentic and plagal modes ending on G, sometimes called [[Mixolydian mode|Mixolydian]] and [[Hypomixolydian mode|Hypomixolydian]].

Although the modes with melodies ending on A, B, and C are sometimes referred to as [[Aeolian mode|Aeolian]], [[Locrian mode|Locrian]], and [[Ionian mode|Ionian]], these are not considered distinct modes and are treated as [[Transposition (music)|transpositions]] of whichever mode uses the same set of hexachords. The actual pitch of the Gregorian chant is not fixed, so the piece can be sung in whichever range is most comfortable.

Certain classes of Gregorian chant have a separate musical formula for each mode, allowing one section of the chant to transition smoothly into the next section, such as the psalm verses that are sung between the repetition of antiphons, or the Gloria Patri. Thus we find models for the recitation of psalmverses, Alleluia and Gloria Patri for all eight modes.{{sfn|Hoppin|1978a|p=82}}

Not every Gregorian chant fits neatly into Guido's hexachords or into the system of eight modes. For example, there are chants – especially from German sources – whose [[neume]]s suggest a warbling of pitches between the notes E and F, outside the hexachord system, or in other words, employing a form of [[chromaticism]].{{sfn|Wilson|1990|p=22}} Early Gregorian chant, like Ambrosian and Old Roman chant, whose melodies are most closely related to Gregorian, did not use the modal system.{{sfn|Apel|1990|pp=166–178}}{{sfn|Hiley|1995|p=454}} The great need for a system of organizing chants lies in the need to link antiphons with standard tones, as in for example, the psalmody at the Office. Using Psalm Tone i with an antiphon in Mode 1 makes for a smooth transition between the end of the antiphon and the intonation of the tone, and the ending of the tone can then be chosen to provide a smooth transition back to the antiphon. As the modal system gained acceptance, Gregorian chants were edited to conform to the modes, especially during 12th-century [[Cistercian]] reforms. Finals were altered, melodic ranges reduced, melismata trimmed, B-flats eliminated, and repeated words removed.{{sfn|Hiley|1995|pp=608–610}} Despite these attempts to impose modal consistency, some chants – notably Communions – defy simple modal assignment. For example, in four medieval manuscripts, the Communion ''Circuibo'' was transcribed using a different mode in each.{{sfn|Apel|1990|pp=171–172}}