Editing Rhythmic mode (section)

==Notation==
[[File:Pérotin - Viderunt omnes.jpg|thumb|Pérotin, ''Viderunt omnes'' (Gradual for Christmas Day), in the first rhythmic mode. MS Florence, Biblioteca Medicea-Laurenziana, Pluteo 29.1, fol. 1 recto.]]
Devised in the last half of the 12th century,{{sfn|Seay|1975|p=97}} the notation of rhythmic modes used stereotyped combinations of ligatures (joined noteheads) to indicate the patterns of long notes (longs) and short notes (breves), enabling a performer to recognize which of the six rhythmic modes was intended for a given passage.

Linked notes in groups of:{{sfn|Hughes|1954a|pp=323–4}}
:3, 2, 2, 2, etc. indicate the first mode,
:2, 2, 2, 2, … 3 the second mode, 
:1, 3, 3, 3, 3, etc. the third mode,
:3, 3, 3, … 1 the fourth mode,
:3, 3, 3, 3, etc. the fifth mode, 
:and 4, 3, 3, 3, etc. the sixth mode

The reading and performance of the music notated using the rhythmic modes was thus based on context. After recognizing which of the six modes applied to a passage of [[neume]]s, a singer would generally continue on in that same mode until the end of a phrase, or a [[cadence (music)|cadence]]. In modern editions of medieval music, ligatures are represented by horizontal brackets over the notes contained within it.

All the modes adhere to a ternary principle of metre, meaning that each mode would have a number of beat subdivisions divisible by the number 3. Some medieval writers explained this as veneration for the perfection of the Holy Trinity, but it appears that this was an explanation made after the event, rather than a cause.{{sfnm|Reese|1940|1p=274|Hughes|1954a|2pp=319–20}} Less speculatively, the flexibility of rhythm possible within the system allows for variety and avoids monotony. Notes could be broken down into shorter units (called ''fractio modi'' by [[Anonymous IV]]) or two rhythmic units of the same mode could be combined into one (''extensio modi'').{{sfn|Seay|1975|pp=98–9}} An alternative term used by Garlandia for both types of alteration was "reduction".{{r|Grove2001_RhythmicM}} These alterations may be accomplished in several ways: ''extensio modi'' by the insertion of single (unligated) long notes or a smaller-than-usual ligature; ''fractio modi'' by the insertion of a larger-than-usual ligature, or by special signs. These were of two types, the ''plica'' and the ''climacus''.{{r|Grove2001_NotationParaIII}}

The ''plica'' was adopted from the liquescent neumes (''cephalicus'') of chant notation, and receives its name (Latin for "fold") from its form which, when written as a separate note, had the shape of a U or an inverted U. In modal notation, however, the plica usually occurs as a vertical stroke added to the end of a ligature, making it a ''ligatura plicata''. The plica usually indicates an added breve on a weak beat.{{r|Grove2001_NotationParaIII}} The pitch indicated by the plica depends on the pitches of the note it is attached to and the note following it. If both notes are the same, then the plica tone is the upper or lower neighbor, depending on the direction of the stem. If the interval between the main notes is a third, then the plica tone fills it in as a passing tone. If the two main notes are a second apart, or at an interval of a fourth or larger, musical context must decide the pitch of the plica tone.{{sfn|Apel|1961|p=227}}

[[File:Climacus.gif|thumb|The ''climacus''.]] [[File:Clivis cumpunctis carrée.jpg|thumb|''climacus'' with ligature]]
The ''climacus'' is a rapid descending scale figure, written as a single note or a ligature followed by a series of two or more descending lozenges. Anonymous IV called these ''currentes'' (Latin "running"), probably in reference to the similar figures found in pre-modal Aquitanian and Parisian polyphony. [[Franco of Cologne]] called them ''coniunctura'' (Latin for "joined [note]"). When consisting of just three notes (''coniunctura ternaria'') it is rhythmically identical with the ordinary three-note ligature, but when containing more notes this figure may be rhythmically ambiguous and therefore difficult to interpret.{{r|Grove2001_NotationParaIII}} The difficulty was compounded in the later half of the 13th century, when the lozenge shape came also to be used for the [[semibreve]]. A general rule is that the last note is a longa, the second-last note is a breve, and all the preceding notes taken together occupy the space of a longa. However, the exact internal rhythm of these first notes of the group requires some interpretation according to context.{{sfn|Apel|1961|p=240}}

It was also possible to change from one mode to another without a break, which was called "admixture" by Anonymous IV, writing around 1280.{{r|Grove2001_RhythmicM}}

[[File:Alteratio.png|thumbnail|Tenor from Motet "Homo, luge!"/"Homo miserabilis"/"Brumans e mors" (13th century). Third rhythmic mode, syllabic notation.]]
Because a ligature cannot be used for more than one syllable of text, the notational patterns can only occur in [[melisma]]tic passages. Where syllables change frequently or where pitches are to be repeated, ligatures must be broken up into smaller ligatures or even single notes in so-called "syllabic notation", often creating difficulty for the singers, as was reported by Anonymous IV.{{sfn|Apel|1961|p=225}}{{r|Grove2001_RhythmicM}}

An '''ordo''' (plural ''ordines'') is a [[phrase (music)|phrase]] constructed from one or more statements of one modal pattern and ending in a rest. Ordines were described according to the number of repetitions and the position of the concluding rest. "Perfect" ordines ended with the first note of the pattern followed by a rest substituting for the second half of the pattern, and "imperfect" ordines ended in the last note of the pattern followed by a rest equal to the first part. Imperfect ordines are mostly theoretical and rare in practice, where perfect ordines predominate.{{sfn|Hoppin|1978|p=223}}

Other writers who covered the topic of rhythmic modes include Anonymous IV, who mentions the names of the composers Léonin and Pérotin as well as some of their major works, and [[Franco of Cologne]], writing around 1260, who recognized the limitations of the system and whose name became attached to the idea of representing the duration of a note by particular notational shapes, though in fact the idea had been known and used for some time before Franco.{{sfn|Hughes|1954b|pp=379–80}} Lambertus described nine modes, and Anonymus IV said that, in England, a whole series of irregular modes was in use.{{sfn|Reese|1940|p=288}}