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A tonary is a liturgical book in the Western Christian Church which lists by incipit various items of Gregorian chant according to the Gregorian mode (tonus) of their melodies within the eight-mode system. Tonaries often include Officeantiphons, the mode of which determines the recitation formula for the accompanying text (the psalm tone if the antiphon is sung with a psalm, or canticle tone if the antiphon is sung with a canticle), but a tonary may also or instead list responsories or Mass chants not associated with formulaic recitation. Although some tonaries are stand-alone works, they were frequently used as an appendix to other liturgical books such as antiphonaries, graduals, tropers, and prosers, and are often included in collections of musical treatises.
Tonaries were particularly important as part of the written transmission of plainchant, although they already changed the oral chant transmission of Frankish cantors entirely before musical notation was used systematically in fully notated chant books. Since the Carolingian reform the ordering according to the Octoechos assisted the memorization of chant. The exact order was related to the elements of the "tetrachord of the finales" (D--E--F--G) which were called "Protus, Deuterus, Tritus", and "Tetrardus". Each of them served as the finalis of two toni--the "authentic" (ascending into the higher octave) and the "plagal" one (descending into the lower fourth). The eight tones were ordered in these pairs: "Autentus protus, Plagi Proti, Autentus Deuterus" etc. Since Hucbald of Saint-Amand the eight tones were simply numbered according to this order: Tonus I-VIII. Aquitanian cantors usually used both names for each section.
The earliest tonaries, written during the 8th century, were very short and simple without any visible reference to psalmody. Tonaries of the 9th century already ordered a huge repertoire of psalmodic chant into sections of psalmtone endings, even if their melody was not indicated or indicated by later added neumes. Most of the tonaries which have survived until now can be dated back to the 11th and 12th centuries, while some were written during later centuries, especially in Germany.
The treatise form usually served as a bridge between the Octoechos theory and the daily practice of prayer: memorizing and performing the liturgy as chant and reciting the psalms. This can be studied at a 10th-century treatise called Commemoratio brevis de tonis et psalmis modulandis, which used the Dasia-signs of the Musica enchiriadis treatise (9th century) in order to transcribe the melodic endings or terminations of psalmody. 11th-century theorists like Guido of Arezzo (Regulae rhythmicae) or Hermann of Reichenau (Musica) refused the Dasia tone system, because it displayed tetraphonic tone system and not the systema teleion (corresponding to the white keys of the keyboard) which had all the pitches needed for the "melos of the echoi" (ex sonorum copulatione in "Musica enchiriadis", emmelis sonorum in the compilation "alia musica"). Nevertheless, the first example of the eighth chapter in Musica enchiriadis, called "Quomodo ex quatuor Sonorum vi omnes toni producantur", already used the fifth of the Protus (D--a) for an illustration, how alleluia melodies are developed by the use of the intonation formula for the "Autentus protus".
The different forms of a tonary
Tonaries can differ substantially in length and shape:
As a treatise they usually describe the octave, fifth and fourth species of each tone, but also their modal characteristics like microtonal shifts or the change to another melodic frame.
It can also be an abridged form or breviary, which just show the sacramentary (for mass chants) or antiphonary (for the office chant of the Vigils and the Hours) according to the liturgical year. The tonus of the antiphonal chant genres is indicated by later added rubrics as "ATe" for "Autentus Tetrardus" (see the Gradual-Sacramentaries of Corbie and Saint-Denis) or the Roman Ordinals I-VIII according to Hucbald's system, as we can find it in the early Troper-Sequentiary of St. Géraud in Aurillac (F-Pn lat. 1084) and the abridged Antiphonary of St. Martial (F-Pn lat. 1085).
The most common form was the shortest one which had no theoretical explanation. Since the late 9th century each section started with an intonation formula and the psalmody of the mode, its pitches represented by letters or later by diastematic neume notation. Subsections followed the different chant genres quoted as examples for the represented tone. Antiphonal refrains in psalm recitation (antiphons like introits and communiones), usually represented by its text incipit, were sorted according to various terminations used in psalmody, the so-called "differentiae".
During the Carolingian reform the tonary played a key role in the organization and the transfer of Roman chant, which had to be sung by Frankish cantors according to Charlemagne's admonitio generalis after it was decreed in 789. The historical background was the Second Council of Nicaea in 787 during which Pope Adrian I accepted the Eastern Octoechos reform also for the Roman church. Fully notated neume manuscripts like the gradual and the antiphonary were written much later during the last decades of the 10th century, and the oral transmission of Gregorian chant is only testified by additions of neumes in sacramentaries. In the tonary the whole repertory of "Gregorian chant" was ordered according to its modal classification of the Octoechos.
Michel Huglo developed in his dissertation the hypothesis about an original tonary which preceded the Metz tonary and the tonary of St. Riquier. It was probably a coincidence, that Pope Adrian I supported the Eastern Octoechos reform, but it is also evident that Carolingian diplomates present at the synode did not get interest in the communication of the modes by intonations called enechemata for the first time. Nevertheless, it was the difference between Greek and Latin chant sources and especially the particular function of the tonary in chant transmission, which led Peter Jeffery to the conclusion, that the huge repertoire of Roman chant was classified according to the Octoechos a posteriori. While early manuscripts of Greek chant always used modal signatures (even before neume notation was used), the fully notated graduals and antiphonaries of the first generation (10th century), written by Frankish cantors, report a lot of details about accentuation and ornamentation, but the melodic structure was remembered orally by tropes. Sometimes a tonary was attached to these manuscripts, and the cantors could use it by looking for the incipit of an antiphon in question (e.g. an introit to communio), in order to find the right psalmody according to the mode and the melodic ending of the antiphon, which was sung as a refrain during the recitation of the psalm. A Greek psaltes would sing a completely different melody according to the echos indicated by the modal signature, while Frankish cantors had to remember the melody of a certain Roman chant, before they communicated their idea of its mode and its psalmody in a tonary--for all the cantors who will follow them. In this complex process of chant transmission, which followed Charlemagne's reform, the so-called "Gregorian chant" or Franco-Roman chant, as it was written down about 150 years after the reform, was born.
The tonary's function within chant transmission explains, why local schools of Latin chant can be studied by their tonary. Hence, the tonary was still substantial for every chant reform between the 10th and the 12th centuries, like the reform of the Cluniac Monastic Association (tonaries of Aquitania, Paris, and Fleury, but also in Northern Spain), the reform of a monastic orders like the one around Bernard of Clairvaux for the Cistercians (Tonale Sci Bernardi), a papal reform, like Abbot Desiderius realized at the Abbey Montecassino (Tonary of Montecassino), or the reform of some monasteries of a certain region, as Abbot William of Volpiano did for certain Abbeys in Burgundy and Normandy (William of Volpiano's Toner-Gradual and Antiphonary).
The Carolingian names or "Byzantine" intonations for the 8 tones
In Carolingian times each of the eight sections was opened by an intonation formula using the names like "Nonannoeane" for the authentic and "Noeagis" or "Noeais" for the plagal tones. In the living traditions of Orthodox chant, these formulas were called "enechemata" and they were used by a protopsaltes to communicate the basis tone for the ison-singers (a kind of bordun) as well as the first note of the chant for the other singers.
In his theoretical tonary "Musica disciplina", Aurelian of Réôme asked a Greek about the meaning of the intonation syllables used in Latin tonaries:
Caeterum nomina, quae ipsis inscribuntur tonis, ut est in primo tono Nonaneane, et in secundo Noeane, et caetera quaeque, moveri solet animus, quid in se contineant significationis? Etenim quemdam interrogavi graecum, in latina quid interpretarentur lingua? respondit, se nihil interpretari, sed esse apud eos laetantis adverbia: quantoque maior est vocis concentus, eo plures inscribuntur syllabae: ut in authento proto, qui principium est, sex inseruntur syllabae, videlicet hae Noeane Nonannoeane; in authentu deuteri: in authentu triti, quoniam minoris sunt metri, quinque tantummodo eis inscribuntur syllabae, ut est Noioeane. In plagis autem eorum consimilis est litteratura, scilicet Noeane, sive secundum quosdam Noeacis. Memoratus denique adiunxit graecus, huiusmodi, inquiens, nostra in lingua videntur habere consimilitudinem, qualem arantes sive angarias minantes exprimere solent, excepto quod haec laetantis tantummodo sit vox, nihilque aliud exprimentis, estque tonorum in se continens modulationem.
My mind was usually moved by some of the names, which were inscribed for the tones, as "Nonan[no]eane" for the protus, and "Noeane" for the deuterus. Did they have any significance? So I asked a Greek, how these could be translated into Latin. He answered that they did not mean anything, but they were rather expressions of joy. And the greater the harmony of the voice, the more syllables were inscribed to the tone: as in the "authentus protus" which was the first, they used six syllables as "No[neno]eane" or "Nonannoeane"; for "authentus tritus", which was smaller in measure [not so much worth], five syllables as "Noioeane" were inscribed. In plagal tones the letters were similar to "Noeane", as "Noeacis" according to them. When I asked him, if there might be something similar in our language, the Greek added, that I should rather think of something expressed by charioteers or ploughing peasants, when their voice had nothing else than this joy. The same contained the modulation of the tones [during their intonation].
The practice of using abstract syllables for the intonation, as it was common for the use of enechemata among Byzantine psaltes, was obviously not familiar to Aurelian of Réôme. It was probably imported by a Byzantine legacy, when they introduced the Greek Octoechos by a series of procession antiphons used for the feast of Epiphany. Although the Latin names were not identical, there is some resemblance between the intonation formula of the echos plagios tetartos ? and the Latin name "Noeagis", used as a general name for all four plagal tones. But there are some more obvious cases as particular names like "Aianeoeane" (enechema of the Mesos Tetartos) or "Aannes" (enechema of the echos varys) which can be found in very few tonaries between Liège, Paris, Fleury, and Chartres. Two of these tonaries have treatises and use a lot of Greek terms taken from Ancient Greek theory.
The oldest tonaries, especially the Carolingian like those of St. Riquier, Metz, Reichenau and the earliest tonary in a troper of Limoges (F-Pn lat. 1240), only used the so-called "Byzantine" intonation formulas, as they were discussed by Aurelian of Réôme (Musica disciplina), Regino of Prüm (Tonarius), and Berno of Reichenau (Tonarium). But since the 10th century, also biblical verses were used. They were composed together in one antiphon with each verse changing the tone and referring to the number of the tonus according to the system of Hucbald (Tonus primus, secundus, terius etc.), similar to Guido of Arezzo's use of the solmization hymn "Ut queant laxis". They were several different antiphons as they can be found in the Hartker-Antiphonary or the treatise collection of Montecassino (Ms. Q318, p. 122-125), but no one became so popular than a compilation of verses taken from the New Testament which started with "Primum querite regnum dei". Usually each verse is finished by a long melisma or neuma which clearly show its potential to become a tool of improvisation and composition as well. The origin of these verses is unknown. In some tonaries, they replaced the Carolingian intonations as in the tonary by Berno of Reichenau, but more often they were written under them or alternated with them in the subsections like in a certain group which Michel Huglo (1971) called the "Toulouse tonaries" (F-Pn lat. 776, 1118, GB-Lbl Ms. Harley 4951), but also in the tonary of Montecassino. Concerning the earliest fully notated chant manuscripts, it seems that the practice of singing the intonation formulas was soon replaced by another practice, that a soloist intoned the beginning of an antiphon, responsorium, or alleluia, and after this "incipit" of the soloist the choir continued. These changes between precantor and choir were usually indicated by an asterisk or by the use of maiuscula at the beginning the chant text. The psalmody could be indicated by an incipit of the required psalm and the differentia notated over the syllables EVOVAE after the communio or introit antiphon.
Cross-references between tonaries during the reforms between the 10th and the 13th centuries
Nevertheless, the tonary was not replaced by these manuscripts. While the first generation of notated manuscripts became less and less readable until the end of the 10th century, the production of tonaries as useful appendix highly increased, especially in Aquitania, the Loire valley (Île-de-France) and Burgundy. Probably the oral tradition of the melody was no longer properly working since the early 11th century, or there was still a need in a lot of regions to teach certain cantors an unknown tradition, or the tradition itself had to change under certain innovations of cantors who were in charge of an institutional reform. Studies of the reforms of various regions in Spain, Germany, Italy, and France have found evidence for all these cases whatever was the centre of each reform which had taken place between the late 10th and the 12th centuries. The monk Hartvic added some Dasia signs for certain differentiae as a kind of rubric or comment on the margin (Tonary of St. Emmeram, Regensburg). He knew them from the treatises Musica and Scholica enchiriadis which he copied in this manuscript, and thus he discovered a new way of using them: as an additional explanation or second pitch notation interpreting the adiastematic neumes.
"Plagi Protus" intonation in the Tonary of the Auch region (Aquitaine, end 10th century): F-Pn lat. 1118, fol. 105v
The Cluniac reforms and the counter-reforms
During the late 10th and the 11th century, the early use of a second alphabetical pitch notation was soon replaced by a new diastematic form of neume notation, which indicated the pitch by the vertical position of the neumes, while their groups indicated by ligatures were still visible. Aquitanian and English cantors in Winchester were the first who developed a diastematic form, which could be written in such an analytical way.
William of Volpiano and the Norman line
William of Volpiano elaborated the concept of an additional letter notation and created a new form of tonary which became an important part of his monastic reforms, he did the first reform for Cluny, after he became abbot of St. Benignus of Dijon in Burgundy. Since 1001 he changed to the Abbey of Fécamp, after he was asked by the Norman Duke Richard II to guide secular and monastic reforms in the Duchy of Normandy.
The fully notated tonary which he wrote for St. Benignus (F-MOf H159), is following the order of other tonaries, which were created under the influence of the Cluniac Monastic Association. These tonaries usually had sections dedicated to the antiphonary and the gradual, within the gradual and the antiphonary there were subsections like the antiphons which were sung as refrains during psalm recitation (introits and communions), responsories (the introduction of epistle readings), but also other genres of the proper mass chant as alleluia verses (the introduction of gospels), and offertories (a soloistic processional antiphon for the procession of the gifts). Several Aquitanian troper-sequentiaries had a libellum structure which sorted the genres in separate books like alleluia verses (as the first part of sequentiaries and tractus collections), offertorials, and tropers. But William of Volpiano subdivided these books into eight parts according to the octoechos system like the tonary, or the troparia in the Byzantine book Octoechos, and within these sections the chant was ordered according to the cycle of the liturgical year starting with advent. He used the neumes of Cluny, the central French forms, without changing them, but he added an own system of alphabetic notation in a second row, which defined the pitches of the melody precisely according to the Boethian diagramm. Like any other chant manuscript around 1000, the book was not written for a use during a ceremony, it was a "book of memory" for cantors who alone had the competence of reading and writing neumes, and the responsibility to organize the chant sung during the liturgical year. During his reforms, several Abbeys followed his example and his system was used by the teachers of the local grammar schools which included the daily practice of singing the liturgy.
William's reform and its monastic foundations of Fécamp and the construction of the Abbey on the island of Mont Saint-Michel were not the first, and there were a lot of later abbots who founded monasteries not only in Normandy, but also in the conquered territories of Northern, and Southern Italy, including Arabian Sicily, after the Norman Kingdom was established in the conquered Island. His fully notated tonaries were only copied in Brittany and Normandy, the Norman-Sicilian manuscripts rather imitated the libellum structure of the Aquitanian troper-sequentiaries, and only a few of them (E-Mn288, F-Pn lat. 10508) have survived with a tonary using central French neume notation, in its style very close to the chant books of Cluny. The «Bibliothèque interuniversitaire de Médecin» still conserves the only manuscript with alphabetic notation which can be dated back to William's time. Thanks to the creative and innovative achievements of William as a cantor, reformer and architect, the local monasteries which he reformed, did not simply adapt to customs of the Cluniac reform, he contributed to the history of Norman chant his own local school which was as well inspired by elements of the local Norman tradition as by innovations of the Cluniac reform.
The Aquitanian tonaries and the Winchester Troper
The Aquitanian innovation can be traced back to a very prominent cantor within the Cluniac reforms: Adémar de Chabannes was educated by his uncle Roger de Chabannes at the Saint-Martial Abbey of Limoges and this school redacted the first chant manuscripts by additional modal signatures and a remarkable production of tonaries, which Michel Huglo called the "Saint-Martial group" or the monastic tonaries of Aquitaine. Adémar was the next generation after William of Volpiano and he was one of the first notators who used the diastematic form of Aquitanian neume notation, which had already been developed during the late 10th century.
Another tonary corpus of the same region was Huglo's "Toulouse groupe" around the Gradual of the Saint-Étienne cathedral in Toulouse (GB-Lbl Ms. Harley 4951, F-Pn lat. 1118, and 776). All of these books of the local secular cathedral rite have a tonary libellum. The oldest one is the Troper Sequentiary of the Auch region (F-Pn lat. 1118) which was probably written in Limoges by the end of the 10th century. The intonation of the "plagi protus" (on folio 105 verso) is rather exposing the melos used in Old Roman chant of this tone (ranging between C and G), but the sequentiary (folio 114 recto) is opened by an "improvised" alleluia of the same tone simply made by a similar intonation which is also using the plagal fourth A-D under the final note D according to the Carolingian concept of the plagal mode. On folio 131 verso there is another alleluia made of the same intonation, but here the same intonation is rather artificially cut into segments for the words of the sequence «Almifona». Here, the improvised melodic structure developed by a repetitive use of the intonation formula had turned into a sophisticated composition which dealt with the syllables of poetry.
A central line, usually on F or G, was added and helped to recognize their horizontal organization, during the 12th century a second line was added until they were replaced by a pentagramm in square notation by the second half of the 12th century.
Thanks to Aquitanian cantors the network of the Cluniac Monastic Association was not only a problematic accumulation of political power during the crusades among aristocratic churchmen, which caused rebellions in several Benedictine monasteries and the foundation of new anti-Cluniac reform orders, they also cultivated new forms of chant performance which dealt with poetry, and polyphony like discantus and organum. They were used in all possible combinations which turned improvisation into composition, and composition into improvisation. The imitation of these forms in Spain, and Italy were caused by papal reforms which tried to organize the church provinces in newly conquered territories or territories which conserved older rites, because reforms could hardly be established for a long time.
The diastematic notation of Aquitanian cantors and their most innovative use in tropes and punctum contra punctum polyphony which can be also found in the Chartres cathedral, the Abbey Saint-Maur-des-Fossés near Paris, and Fleury Abbey, also influenced the Winchester troper (see its tonary), the earliest and hugest collection of early organum or discantus. Since 1100, the florid organum reproduced the original function of the earlier intonation formula as it can be found in the tonaries. An initial ornament called principium ante principium ("beginning before the beginning") in the Notre Dame school allowed the solistic organum singer to indicate the basis degree of the cantus by an individual intonation in the higher octave, while the finale octave of each section was prepared by an paenultima ornament, which had developed by the "meeting" (occursus) of chant and organum voice.
Tonaries of the reform orders
During this long period Cluny's power and influence on less and less successful crusades which were well reflected in certain chant genres like conductus and motet, caused a decline and an increasing resistance among the monastic communities of the Cluniac Association between Paris, Burgundy, Île-de-France, and Aquitaine. New monastic orders were founded in order to establish anti-Cluniac counter-reforms. The most important was certainly created among Cistercians by a reform group around St. Bernard of Clairvaux. The innovations and corrections of Roman-Frankish chant during the Cluniac reforms were disregarded as a corruption of the Roman tradition, but the new books ordered from the scriptoria of Laon and Metz did not satisfy the expectations of the reformers. Instead rules based on Guido of Arezzo's Micrologus were codified to support the Cistercian cantors, while they were cleaning the corrupted tradition of plainchant. Despite certain ambitions concerning the performance practice of polyphonic organum, the first generation of reformers around Bernard did not allow these Cluniac practices. Nevertheless, they were established soon, as Bernard became one of the most important and powerful churchman involved in crusade policies which clearly corresponded to the refused aristocratic ambitions within the Cluniac Association. During Bernard's liturgical reform the tonary still served as an important tool and its modal patterns formed the basis of the corrections made by Cistercian cantors.
The tonaries in Italy
The local liturgical traditions in large parts of Italy remained stable, because there was simply no written transmission which could interfere with any reform until the end of the 10th century. A lot of local neumes used by Beneventan and Old Roman notators already started in a diastematic form, and the local scribes used the same opportunity to codify their own tradition, and in a second step of a reform which could not earlier be realized until a political conquest allowed the domination of a certain region, they had to deal with a codified chant repertory which was supposed to be "Roman". The transfer was done by written transmission, and this explains certain cross-references which can be studied in detail by the notated chant repertory, but more easily by the copies and the local neumes used in tonaries.
From this point of view, several tonaries, already transmitted by earlier French sources, can be found in later copies in Italian manuscripts, often written in French scriptoria and their neume notation. Nevertheless, a lot of Italian cantors were authors of tonaries which played a key role during Carolingian, Cluniac, and anti-Cluniac reforms in France and Lake Constance. As example, William of Volpiano from Piedmont, Guido of Arezzo, whose treatises were used during the Cistercian and Beneventan reform, while there is no source which testify the use of tonaries among Roman cantors. The famous Dialogus, falsely ascribed to Odo of Cluny, the second Abbot of Cluny Abbey, was compiled in the province of Milan, while only "Formulas quas vobis", a tonary used in Montecassino and Southern Italy, was written by another Odo, Abbot of Arezzo.
^The modal patterns, memorized by a short formula, and the deductive classification of chant played an active part in the process of oral transmission, so Anna Maria Busse Berger dedicated a whole chapter of her book (2005, pp. 47-84) to the tonary, in which she described the relationship between music and the medieval art of memory.
^E.g. a tonary added to Aurelian's theoretical one in a manuscript of the Abbey Saint-Amand (F-VAL148)--an important centre of the Carolingian Renaissance, has some intonation formulas in later added Paleofrankish neumes.
^An early copy of the Commemoratio brevis in a music theory collection written about 1000 (D-BAsVar.1). A list of the sources can be found here: "Commemoratio brevis". Retrieved 2012.
^Both systems were used by Byzantine psaltes and among them the former was never expected to contain all the degrees of the mode, as they were used "in the melos of the echoi".
^The practice of differentiae, terminations which were also called "divisio, diffinitio", or "formula", corresponded to the melodic beginning of the antiphons and was developed during the later 9th century. Hence, the different terminations of psalmody became a subsection of each section dedicated to the antiphons of the mass or the nocturn. There are tonaries which exemplified the whole psalmody with the small doxology ("Gloria patri") written out with neumes or letters (see the Dasia-signs used in D-BAsVar.1), but there was also the abridged form to notate just the termination over the vowels EVOVAE of the last six syllables: "seculorum. Amen." Often the eight sections for the eight tones were repeated for other chant genres without psalmody or different chant books as gradual and antiphonary (Responsories, Alleluia, Offertories etc.).
^In a long essay dedicated to the Latin treatises and the knowledge that Latin cantors had about music theory, Michel Huglo (2000) referred to an episode of a Byzantine legacy in Aachen, who celebrated troparia (processional antiphons) for the feast of Epiphany. Oliver Strunk (1960) had already published about this visit, but through Walter Berschin's essays about the Carolingian visits of Byzantine legacies Michel Huglo became convinced that this exchange could already have happened before his self-nomination as an Emperor of both Roman Empires.
^The impact of the Cluniac Monastic Association on these reforms was often considered, neglected, and re-considered by various musicologists. Background was a discussion among historians around a book of Dominique Iogna-Prat, which was originally published in French in 1998 (see the English translation by Graham Robert Edwards: Iogna-Prat, Dominique (2002). Order & exclusion: Cluny and Christendom face heresy, Judaism, and Islam 1000-1150. Conjunctions of religion & power in the medieval past. Ithaca, N.Y.: Cornell UP. ISBN978-0-8014-3708-3.). The answer of the musicologist's question concerning the centre of the Aquitanian school laid simply there. Rather lately (2006) Bryan Gillingham tried a general study of the role that Cluny played in the written chant transmission between the 11th and the 13th century. Already in 1985Jacques Chailley studied an allegorical sculpture in the sanctuary of Cluny Abbey which is an important monument of the Cluniac approach to the tonary and its eight-mode system, according to him the sanctuary with the sculpture was inaugurated by Pope Urban II.
^The Taifa kingdom Toledo, an important domaine of the Mozarabic rite, was conquered by the Castilian King Alfonso VI in 1085. After he gave his daughters in marriage to Aquitanian und Burgundian aristocrats, the Council of Burgos had already decreed the introduction of the Roman rite in 1080. Hence, reforms can be studied by the distribution of Aquitanian manuscripts in Spain. See also the study of chant manuscripts by Manuel Ferreira (2007).
^It is not easy to prove this or another practice for medieval chant, neither for Greek nor for Latin singers, but concerning performance practice this is quite a controversial topic which is solved in different ways. It is possible that the Orthodox practice today helps the singers to sing subtle intonation changes, which are no longer practiced in Western music, while maqam singers usually sing without ison. It is as well possible to perform florid organa in a monodic way without the cantus in the tenor as a second voice.
^Aurelianus Reomensis: "Musica disciplina" (Gerbert 1784, p. 42).
^It was a coincidence that Carolingian cantors used more syllables for the Autentus protus, like the enechema of the echos protos as it was used by Greek psaltes (see Octoechos).
^For example in the 11th-century treatise compilation "alia musica" (Chailley 1965, "AIANEOEANE": p.141; "AANNES": p.160), and some tonaries are of particular interest as Hartvic's copy of the Chartres tonary and the second tonary of the Troper-Sequentiary of Reichenau, which uses "ANANEAGIES" for the "Autenticus Protus" and "AIANEAGIES" for the "Autenticus Deuterus". Unlike the Guidonian concept of "b fa", the plagios tritos which was called echos varys ("grave mode") by Greek psaltes, did not avoid the tritone to the basis and finalis F. The pure fourth was only used by the enharmonic phthora nana. According to Oliver Gerlach (2012) the very sophisticated intonation of the diatonic Mesos Tetartos, known by the name ? among Greek psaltes, was imitated by Latin cantors for certain phrygian compositions of the Gregorian repertory, among them the Communio Confessio et pulchritudo. Michel Huglo (NGrove) classified these tonaries as "transitional group" which he dated already to the 10th century.
^The Cluniac reforms can be verified in tonaries written in Cluny and Fleury Abbey, certain Abbeys around Paris as Saint-Maur-des-Fossés, Saint-Denis, but also in Burgundy and Aquitaine. The creativity of Aquitanian cantors played a key role concerning the Cluniac needs for an extravagant liturgy. Hence, it is hardly surprising that they were more productive concerning tonaries than any other local school in Europe.
^See Huglo's study of this particular tonary (1956). Including the enharmonic diesis which were represented by signs as "?" for E diesis, "?" for b diesis, and the last sign written from the right to the left for a diesis (see the figure in the main article). The Boethian diagramm was already used since centuries, with exception of the symbols of the tetraphonic Dasia system which were used in certain treatises since the Musica and Scolica enchiriadis (Phillips 2000).
^Gazeau, Véronique (2002). Guillaume de Volpiano en Normandie: état des questions. Tabularia « Études ». 2. Caen: CRAHM. pp. 35-46. Olivier Diard's study (2000) of a late copy of his tonary and antiphonary for the Abbey of Fécamp (Rouen, Bibliothèque municipale, Ms. 254, olim A.190) emphasized that William of Volpiano had not only introduced customs of Saint Bénigne and own compositions -- as it was common among Cluniac reformers -- in Normandy, but he also integrated and reinforced Norman customs by his school.
^About the Sicilian origin of the tonary in the Troper-Proser of the Saint-Évroult Abbey, see Shin Nishimagi (2008).
^In his monographical study (2006) James Grier regard two manuscripts (F-Pn lat. 909 and 1121) as documents of Adémar's work as a cantor and notator. Both of them have a tonary which offer insights to the modal framework of Adémar's school according to the local concept of the octoechos.
^See folio 131 verso of the Troper Sequentiary. Jørgen Raasted (1988) and Oliver Gerlach (2011, pp. 22-24) emphasized this creative or poetic function in their description of Western and Eastern intonation formulas.
^Already the Musica and Scolica enchiriadis (9th century) used rows defined by Dasian signs, and placed the syllables of the chant text according to the pitches sung with them. The odd tone system was a repetition of four tetrachord elements represented by four signs which were obviously taken from the Hagiopolitan Octoechos and Greek tetraphonic tone system: protus, deuterus, tritus, and tetrardus. These four Dasian signs and their derivations were used in a lot of tonaries. The innovation of the 10th century was the design of neumes which were so detailed, that they kept plenty of information concerning ornaments and accents. Rebecca Maloy (2009) even assumed that the use of transposition (mentioned as "absonia" in Scolica enchiriadis) might be found behind the diastematic Aquitanian neume notation--an assumption which clearly illustrates the weak side of Adémar's notation in comparison with the letter notation invented by William of Volpiano, which came never in use outside Normandy. Until this time very complex modal structures and microtonal shifts could be notated, as Maloy demonstrated by the most complex example of written transmission: the notation of the soloistic chant genre offertory. But Western notation did never develop modal signatures and the melodic structure was directly deduced by the diastematic notation. A second radical simplification became necessary, and so solmization was invented by Guido of Arezzo. On the background of his innovation, the later square notation was rather a reduction of the neume ligatures to a pure pitch notation, their performance was changed radically by an oral tradition of singing ornaments, of performing ligatures in a rhythmic way, and of more or less primitive models of polyphony which was no longer visible in the chant books of the 13th century.
^A list of the sources can be found in Christian Meyer's essay (2003) who also described the characteristics of Cistercian tonaries and the various redactions of Bernard of Clairvaux's preface.
^Part of a 15th-century chant treatise about improvised polyphony was once attributed to Limoges, later it was identified as an appendix to Abbot Guido's Regulae about habits of the Cistercian rite (Sweeney 1992). The edition of Ms. 2284 Bibliothèque Sainte Geneviève (Coussemaker, Sweeney) has been revised recently by an edition (Meyer 2009) based on four other sources. According to Christian Meyer there was no explicit rule in the treatise which excluded polyphonic performances of plainchant from the Cistercian rite, despite the fact, that reform orders had been founded with monks, who had left their former monastic communities, after a Cluniac abbot had taken over and changed the local rite with new practices including polyphonic performance ("cum organo").
^According to Christian Meyer (2003) the tonary in the Milanese Antiphonary of the Abbey St. Mary of Morimondo is one of the most complete sources which is very close to those used in the Cistercian foundations in Austria, Germany, and Poland.
^The term "repertorio neo-gregoriano" is taken from Luisa Nardini who also studied the Montecassino tonary and its role in the transmission of the Mass repertory (Nardini 2003).
Carolingian tonaries and gradual-sacramentaries (8th-9th century)
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