Octoechos

Oktōēchos (here transcribed "Octoechos"; Greek: Ὀκτώηχος, from ὀκτώ "eight" + ἦχος "sound, mode" called echos) is the name of the eight mode system used for the composition of religious chant in Syrian, Coptic, Byzantine, Armenian, Latin and Slavic churches since the middle ages. In a modified form the octoechos is still regarded as the fundament of the living tradition of monodic Orthodox chant today.

Oktōēchos is also the name for a Byzantine liturgical book, the Great Octoechos, composed in eight parts, consisting of analogous sets of hymns for each of the eight echoi. In fact each echos subordinates various melodic models or modes than just one (in Greek those might rather be called "meloi" than "echoi"), it was more important to group chants according to its mode and to divide the year into eight-week-cycles starting in numerical order from tone 1 (echos protos, ἦχος πρῶτος)[1] following Easter Week.[2] This liturgical octoechos concept was the invention of monastic hymnographers at Mar Saba in Palestine and in Constantinople, and a synod held 692 in Constantinople accepted their reform which also aimed to replace the homiletic poetry of the kontakion and other forms sung during the morning service (Orthros) of the cathedral rite. Hagia Sophia and other cathedrals of the Byzantine Empire did not abandon their habits, and the eight mode system came into use not earlier than in the mixed rite of Constantinople, after the patriarchate and the court had returned from their exile in Nikaia in 1261.

The reason that another eight mode system was established by Frankish reformers during the Carolingian reform, could be that Pope Adrian I also accepted on the synod in 787 the seventh-century Eastern reform for the Western church. The corresponding "chant book" is the tonary, a list of incipits of chants ordered according to the intonation formula of each church tone and its psalmody. Later also fully notated and theoretical tonaries had been written.

Contents

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The Hagiopolitan Octoechos and its Reception in the Carolingian Tonaries

Traditional singers today often memorize the history of Byzantine chant in three parts, identified with the names John of Damascus as the "beginning" (the inventor of the octoechos), John Kukuzelis as the "flower" (the inventor of the psaltic art and its soloistic style called "kalophonia"), and Chrysanthos of Madytos as the "great teacher" of the living tradition today (the translator of psaltic art into the modern neume notation).

Origins

The fact behind this simple imagination is, that the octoechos reform was already accepted some decades ago, before John and Cosmas became monks in Mar Saba, but the earliest sources which gives evidence of the octoechos used in Byzantine chant is a ninth-century treatise called "Hagiopolites" ("Holy Polis" after Jerusalem), which only survived in a complete form in a late copy dating back to the fourteenth century.[3] It is supposed that it was an introduction of a book called tropologion – a chant book used during 9th century which was soon replaced by the book octoechos. Despite that the first paragraph ascribes the treatise to John of Damascus, it was probably written about 100 years after his death and it went through several little redactions during the following centuries. There is no doubt that the octoechos reform itself has taken place already in 692, because certain passages of the Hagiopolites are paraphrasing certain canons of the synodal decree.[4] Eric Werner assumed that the eight mode system developed in Jerusalem since the late fifth century and that the reform by the hymnographers of Mar Saba were already a synthesis with the Hellenic names used for the tropes, applied to a model of Syrian origin already used in the Byzantine tradition of Jerusalem.[5] During the eighth century, long before Hellenic treatises were translated into Arabic and Persian dialects between the ninth and the tenth centuries, there was already a great interest among Arabian theorists like Abū Yūsuf al-Kindī, whose Arabic terms were obviously translated from the Greek.[6] He adored the universality of the Greek octoechos:

Sämtliche Stile aller Völker aber haben Teil an den acht byzantinischen Modi (hiya min al-alhān at-tamāniya ar-rūmīya), die wir erwähnt haben, denn es gibt nichts unter allem, was man hören kann, das nicht zu einem von ihnen gehörte, sei es die Stimme eines Menschen oder eines anderen Lebewesens, wie das Wiehern eines Pferdes oder das Schreien eines Esels oder das Krähen des Hahns. Alles, was an Formen des Schreis einem jeden Lebewesen/Tier eigen ist, ist danach bekannt, zu welchem Modus der acht es gehört, und es ist nicht möglich, daß es sich außerhalb eines von ihnen [bewegt].[7]

Every style of any tribe takes part of the Byzantine eight tones (hiya min al-alhān at-tamāniya ar-rūmīya) which I mentioned here. Everything which can be heart, be it the the human or be it the animal voice – like the neighing of a horse, the braying of a donkey, or the carking of a cock, can be classified according to one of the eight modes, and it is impossible to find anything outside of the eight mode system.

Al-Kindī demonstrated the intervals on the keyboard of a simple four-stringed oud, starting seven steps in ascending and descending direction from the third string.

According to Eckhard Neubauer, there is another Persian system of seven advār ("cycles") outside the Arabian reception of the Byzantine octoechos, which was possibly a cultural transfer from Sanskrit treatises. Persian and Hellenic sources were the main reference for the transfer of knowledge in Arabian-Islamic science.

The Monastic Reform of Mar Saba and the 16 Echoi of the Constantinopolitan Cathedral Rite

According to the Hagiopolites the eight echoi were divided in four "kyrioi" (authentic) echoi and their four respective plagal (enriched, developed) echoi, which were all in the diatonic genus.

The eight diatonic echoi of the Hagiopolitan octoechos

Despite the late copies of the Greek Hagiopolites treatise, the earliest Latin description of the Greek system of eight echoi is an eleventh-century treatise compilation called "alia musica". "Echos" was translated by "sonus" by the anonymous compilator, who commented with a comparison of the Byzantine octoechos:[8]

Quorum videlicet troporum, sive etiam sonorum, primus graeca lingua dicitur Protus; secundus Deuterus; tertius Tritus; quartus Tetrardus: qui singuli a suis finalibus deorsum pentachordo, quod est diapente, differunt. Superius vero tetrachordum, quod est diatessaron, requirunt, ut unusquisque suam speciem diapason teneat, per quam evagando, sursum ac deorsum libere currat. Cui scilicet diapason plerumque exterius additur, qui emmelis, id est, aptus melo vocatur.

Sciendum quoque, quod Dorius maxime proto regitur, similiter Phrygius deutero, Lydius trito, mixolydius tetrardo. Quos sonos in quibusdam cantilenis suae plagae quodammodo tangendo libant, ut plaga proti tangat protum, deuteri deuterum, triti tritum, tetrardi tetrardum. Et id fas est experiri in gradalibus antiphonis.[9]

It is known about the tropes, as to say: the ἦχοι, that the Greek language call the First πρῶτος, the Second δεύτερος, the Third τρίτος, the Fourth τέταρτος. Their Finales were separated by a pentachord, that is: a falling fifth [between kyrios and plagios]. And above [the pentachord] they require a tetrachord, that is: a fourth, so that each of them has its species of diapason, in which it can move freely, rambling down and up. For the full octave another tone might be added, which is called ἐμμελῆς: “according to the melos”.

It has to be known that the “dorian” [octave species] is usually ruling in the πρῶτος, as the “phrygian” in the δεύτερος, the “lydian” in the τρίτος, or the “mixolydian” in the τέταρτος. Their πλάγιοι are derived by these ἦχοι in that way, that the formula touch them [going down a fifth]. So the πλάγιος τοῦ πρώτου touch the πρῶτος, the plagal Second [τοῦ δευτέρου] the δεύτερος, the plagal Third [βαρύς] the τρίτος, the plagal Fourth [πλάγιος τοῦ τετάρτου] the τέταρτος. And this should be proved by the melodies of the antiphonal graduals as a divine law.

This Latin description about the octoechos used by Greek singers (psaltes) is very precise, when it says that each kyrios and plagios pair used the same octave, divided into a fifth (pentachord) and a fourth (tetrachord): D-a-d in protos, E-b-e in devteros, F-c-f in tritos, and C-G-c in tetartos.[10] While the kyrioi had the finalis (final, and usually also base note) on the top, the plagioi had the finalis on bottom of the pentachord.

The intonation formulas, called enechema (gr. ἐνήχημα), for the authentic modes or kyrioi echoi, usually descend within the pentachord and turn back to the finalis at the end, while the plagal modes or plagioi echoi just move to the upper third. The later dialogue treatises (gr. ἐροταπωκρισεῖς) refer to the Hagiopolitan diatonic eight modes, when they use the kyrioi intonations to find those of the plagioi:

Περὶ πλαγίων

Ἀπο τοῦ πλαγίου πρώτου ἤχου πάλιν καταβαίνεις τέσσαρας φωνάς, καὶ εὑρίσκεται πάλιν πλάγιος πρώτου· ὅυτως δὲ / ἄνανε ἄνες  νὲ ἄνες·

Ὁμοίως καὶ ὁ β’ ἤχος καταβαίνων φωνάς δ’, εὑρίσκεις τὸν πλάγιον αὐτοῦ, ἤγουν τὸν πλάγιον τοῦ δευτέρου. πλ Β οὕτως δέ.

Ὁμοίως πάλιν ὁ τρίτος καταβαίνεις φωνὰς τέσσαρας, καὶ εὑρίσκεται ὁ πλάγιος αὐτοῦ, ἤγουν ὁ βαρύς, οὕτως·

Ὁμοίως καὶ  πὸ τὸν τέταρτον καταβαίνων φωνὰς τέσσαρας, εὑρίσκεις τὸν πλάγιον αὐτοῦ, ὡς ἐστὶ ὁ πλ δ’ οὕτως·[11]

About the Plagioi

You descend 4 steps [φοναὶ] from the echos protos [kyrios protos/authentic protus] and you will find again the plagios protos, this way:

You do the same way in echos devteros. If you descend 4 steps to find its plagios, i.e. πλ β', thus:

Hence, you descend four steps from echos tritos 4 steps and you will find its plagios which is called "grave" [βαρύς], this way:

Also from echos tetartos you descend 4 steps [φοναὶ] and you will find its plagios, which is πλ δ', like this way:

Phthorai and Mesoi

The Hagiopolites as "earliest" theoretical treatise says, that two additional phthorai ("destroyers") were like proper modes which did not fit into the diatonic octoechos system, so the Hagiopolitan octoechos is in fact a system of 10 modes. Despite of a tendency that the two phthorai developed their proper melos and their models sung during the eight-week cycle, the original concept of phthora was a change useful for certain transitions. Changes between the echos tritos and the echos plagios tetartos were bridged by the enharmonic phthora nana, and changes between the echos protos and the echos plagios devteros by the chromatic phthora nenano. The theoretical concept of the Hagiopolites strongly suggested that nenano and nana as phthorai "destroy" some of the 7 diatonic degrees used within the octave of a certain echos, so that the chromatic and enharmonic genus was somehow subordinated and excluded from the diatonic octoechos. This raises the question whether music in the near eastern Middle Ages was entirely diatonic, before certain melodies were coloured by the other enharmonic and chromatic genoi.

The Hagiopolites also mentioned an alternative system of 16 echoi, with 4 phthorai and 4 mesoi beyond the kyrioi and plagioi of the Octoechos, and the author called this system the "echoi of the Asma":

Οἱ μὲν οὖν τέσσαρρεις πρῶτοι οὐκ ἐξ ἄλλων τινων ἀλλ’ἐξ αὐτῶν γινονται. οἱ δὲ τέσσαρεις δεύτεροι, ἤγουν οἱ πλάγιοι, ὁ μὲν πλάγιος πρῶτος ἐκ τῆς ὑπορροῆς τοῦ πρώτου γέγονε. καὶ  ἀπὸ τῆς ὑπορροῆς τοῦ πληρώματος τοῦ δευτέρου γέγονεν ὁ πλάγιος δευτέρου· ὡς ἐπὶ τὸ πλεῖστον δὲ καὶ τὰ πληρώματα τοῦ δευτέρου [εἰς τὸν πλάγιον δευτέρου] τελειοῖ. ὁ βαρὺς ὁμοίως καὶ ἀπὸ τοῦ τρίτοῦ· καὶ γὰρ εἰς τὸ ἆσμα ἡ ὑποβολὴ τοῦ βαρέως τρίτος ψάλλεται ἅμα τοῦ τέλους αὐτοῦ. καὶ ἀπὸ τοῦ τετάρτου γέγονεν ὁ πλάγιος τέταρτος. καὶ ἀπὸ τῶν τεσσάρων πλαγίων ἐγεννήθησαν τέσσαρεις μέσοι· καὶ ἀπ’αὐτῶν αἱ τέσσαρες φθοραί. καί ἀνεβιβάσθησαν ἦχοι ις’, οἵτινες ψάλλονται εἰς τὸ ἆσμα, οἱ δὲ δέκα ὡς προείπομεν εἰς τὸν Ἁγιοπολίτην.

The 4 Echoi which come first are generated from themselves, not from others. As to the four which come next, i.e. the Plagal ones, Plagios Prōtos is derived from Prōtos, and Plagios Deuteros from Deuteros – normally Deuteros melodies end in Plagios Deuteros. Similarly, Barys from Tritos – “for in the Asma Hypobole of Barys is sung as Tritos together with its ending“. From the 4 Plagioi originate the 4 Mesoi, and from these the 4 Phthorai. This makes up the 16 Echoi which are sung in the Asma – as already mentioned, there are sung only 10 in the Hagiopolites.[12]

This clearly suggests a distinction of the monastic octoechos reform and an older "sung rite" (ἀκολουθία ᾀσματική) which was the name of the Constantinopolitan cathedral rite with its own chant books asmatikon ("book of the choir"), psaltikon ("book of the soloist called 'monophonaris'"), and kontakarion (the name of the psaltikon, if it included the huge collection of kontakia, sung during the morning service). Unfortunately no treatise about the Constantinopolitan sixteen echoi survived, so that there is only this short paragraph of the Hagiopolites which says, that the singers of Hagia Sophia and other cathedrals of the empire followed in their chant books an own modal system, which was distinct from the octoechos.

The Latin Reception of the Greek Octoechos since the Carolingian Reform

The invention of a proper Latin version of the eight mode system was mainly studied from two perspectives:

The Synthesis in Latin Music Theory

Latin theorists who knew the Hellenic tropes only by Boethius' 6th-century translation of Ptolemy (De institutione musica), did the synthesis of the Ancient Greek music theory with the Octoechos as a system of eight church tones, identified with the tropes. The synthesis has not been done earlier than during the Carolingian reform (usually dated according to Charlemagne's admonitio generalis which was decreed in 789), before music theory as science was strictly separated from chant transmission and the cantor as a profession dedicated to church music.

According to the Latin synthesis the plagal and authentic tones of protus, deuterus, tritus, and tetrardus did not use the same ambitus as in the Hagiopolitan Octoechos, but the same finalis, so that the finalis of the kyrios, the fifth degree of the mode, was no longer finalis, but "repercussa": the recitation tone used in a simple form of psalmody which was another invention by the Carolingian reformers. The ambitus of the authentic tones was made up the same way as used in the Greek Octoechos, while the plagal tones used a lower ambitus: not the tetrachord above the pentachord, but below it. Hence, the hypodorian octave referred the "tonus secundus" and was constructed A—D—a, and the dorian as "tonus primus" D—a—d, both tones used D as finalis of protus, the hypophrygian octave was B—E—b and was the ambitus of the "tonus quartus", and the phrygian octave E—b—e was related to the "tonus tertius" and its finalis E belonged to the deuterus, the hypolydian octave C—F—c was connected with the "tonus sixtus", the lydian octave F—c—f with the "tonus quintus" and both shared the finalis F called "tritus", the last was the seventh octave G—d—g called "mixolydian" which referred to the "tonus septimus" and its finalis G.

The terms tropus (transposition octave) and modus (the octave genre defined by the position of the tonus, the whole tone with the proportion of 9:8, and the semitonium, the half tone with the proportion of 256:243) were taken from Boethius' translation.[13] But the Antique names of the seven modi were applied to the eight church tones called toni. The first attempt to connect Ancient Greek music theory known by Boethius' translation and the theory of plainchant can be found in the treatise De harmonica institutione by Hucbald of Amand, written by the end of the 9th century, and the author adressed his treatise explicitly to cantors and not to mathematics[14], whereas the reduction of 4 "finales" which made up the tetrachord D—E—F—G, was already done in Carolingian times in the treatises Musica and Scolica enchiriadis. Musica enchiriadis is also the only Latin treatise which testifies the presence of tetraphonic tone system, represented by 4 Dasia-signs and therefore called "Dasia system", and even the practical use of transposition (metabolē kata tonon) in plainchant, called "absonia". Its name probably derived from "sonus", the Latin term for ἦχος, but in the context of this treatise the use of absonia is reservated to describe a primitive form of polyphony or heterophony rather than it served as a precise description of transposition in monodic chant, as it was used in certain genres of Byzantine chant.

Hucbald used an own Greek letter system which referred to the double octave system (systēma teleion) and called the four elements D, E, F, G, known as "finales", according to the Greek system "lichanos hypaton" (Digamma [like "F"] = D), "hypate meson" (Σ = E), "parhypate meson" (Ρ = F), and "lichanos meson" (Μ = G).[15]

The earliest Music Manuscript of the Carolingian Reform: the Tonary

The earliest chant theory which had a key role in memorizing chant, was the tonary.

According to Michel Huglo, there was a prototype tonary which initiated the Carolingian reform.[16] But in a later study he mentioned an even earlier tonary which was brought as a present to the Palatine Chapel in Aachen by a Byzantine legacy which celebrated procession antiphons for Epiphany in a Latin translation.[17] The tonary does not only allow to study the difference between local schools according to its modal classification, its redaction of modal patterns, and its own way of using Carolingian psalmody. They also showed a fundamental difference between the written transmission of Latin and Greek chant traditions, as it had developed between the 10th and 12th centuries. The main concern of Latin cantors and their tonaries was a precise and unambiguous classification of whatever melody type according the local perception of the Octoechos system. Greek psaltes were not interested at all in this question. They knew the models of each modes by certain simple chant genres as the troparion and the heirmoi (the melodic models used to create poetry in the meter of the heirmologic odes), but other genres like sticheron and kontakion could change the echos within their melos, so their main interest was the relationship between the echoi to compose elegant and discrete changes between them.

The eight sections of the Latin tonary are usually ordered "Tonus primus Autentus Protus", "Tonus secundus Plagi Proti", "Tonus tertius Autentus deuterus" etc. Each section is opened by an intonation formula using the names like "Noannoeane" for the authentic and and "Noeagis" for the plagal tones. In his theoretical tonary "Musica disciplina" Aurelian of Réôme asked a Greek about the meaning of the syllables, and reported that they had no meaning, they were rather an expression of joy as used by peasants to communicate with their working animals like horses.[18]

Since the 11th century tonaries also include the mnemic verses as used by Guido of Arezzo in his treatise Micrologus: "Primum querite regnum dei", "Secundum autem simile est huic" etc.

The question of general (interval-structures of the scales)

Some 19th century and early 20th century musicologists claimed that Arab music as well as Western medieval chant and Byzantine music were essentially diatonic and went so far as to challenge the capability of humans to distinguish and to sing microtonal inflections with any accuracy. However outmoded this view may seem now (see microtone), it is closely reminiscent of arguments amongst music theorists that started as early as late classical antiquity. Major Hellenistic theorists such as Ptolemy and others stated that the enharmonic genus was extinct since early classical times, while the chromatic genus was only rarely mastered, and on its way to extinction. Also, early Arab theorists such Ibn al Munajjim [19][20] and Ishak al Mawsili base their systems on the diatonic pythagorean scale. The struggle to accommodate microtonal inflections and non-diatonic scales in the modal system is an ongoing topic in near-eastern theory. The mathematical, theoretical and notational tools developed are often confusing and not easy to grasp. Thus on the whole one may say that the subject of non-diatonic scales and microtonal inflections is as difficult to formalize theoretically and to master in practice as it is attractive.

The Papadic Octoechos and the Koukouzelian Wheel

The Papadike and the Mixed Rite of Constantinople during the Palaiologan Period

The Octoechos as a Wheel and the Trochos System

Ioannis Plousiadinos and the Triphonic System

The Octoechos in the Didactic Chant of Mega Ison

The Fanariots of the Ottoman Empire and their integrative Concept of "Exoteric Music"

The system of echoi is far more diverse and developed than a cursory look at the basics of the theory suggests. In practice, the system of echoi is complex and its details are encoded in the notation and in the nomenclature of derived echoi or of echoi variants. An interesting attempt at capturing the full extent of the modal system with a quasi-systematic nomenclature was published by Simon Karas in his multi volume work on the theory and practice of Greek music. Other valuable sources of information are treatises comparing the echoi with their corresponding Ottoman (Turkish) makamlar (see makam). Such are the works by Kiltzanidis (published in the late 19th century) and Kyrillos Marmarinos (his own original manuscript dated AD 1747, stored in the archives of the Historical and Ethnological Society of Greece, Athens).

The Octoechos and its Melos according to the New Method

The eight Echoi and their Meloi

The Byzantine echoi are currently used in the monodic hymns of the Orthodox Churches in Bulgaria, Greece, Romania, and Russia. Their melodic patterns were created by four generations of teachers at the "New Music School of the Patriarchate" (Constantinople/Istanbul), which redefined the Ottoman tradition of Byzantine chant between 1750 and 1830 and transcribed it into the notation of the New Method since 1814. Whereas in Gregorian chant a mode referred to the classification of chant according to the local tonaries and their psalmody, the Byzantine echoi were rather defined by an oral tradition how to do the thesis of the melos, which included melodic patterns like the base degree (ison), open or closed melodic endings or cadences (cadential degrees of the mode), and certain accentuation patterns. The melodic patterns were further distinguished according to different chant genres, which traditionally belong to certain types of chant books, often connected with various local traditions. The detailed transcription of the thesis of the melos and its various methods into the medium of the New Method redefined the genres according to parameters like tempo, rhythm, and the melodic treatment of text (between syllabic and highly melismatic). Often the strict rhythmic form of the melos was criticized as an innovation and an alternative slower style was created for the heirmologic and sticheraric melos.

The eight Byzantine Tones are:

Hymns are typically divided into four chant genres and their melodic patterns used for each echos:

This classification is reflected in the structure of a hymn's melody. Hymns of the same tone belonging to different genres are structured musically in different ways. This holds true for hymns belonging to every tone (with the possible exception of the third tone) but for some tones, e.g., the fourth tone and the grave tone, it is apparent. There is a popular misconception that the division into genres is based on the complexity of the melody versus the text. According to this misconception heirmologic hymns have one note per syllable, sticheraric two or more notes per syllable and papadic many notes per syllable. However one can encounter hymns of the three genres with exactly the same notes per syllable ratio. For example "syntomoi polyeleoi" or "doxologiai", "syntoma stichera" and "katavasiai" have all typically two notes per syllable, the first two being papadic hymns (based on troparia which were originally sung as refrains within psalmodic recitation), the third sticheraric and the fourth heirmologic. That being said, typically the heirmologic hymns are faster than the sticheraric and the sticheraric faster than the papadic.

There are typically two main notes that define each of the Byzantine Tones. The base note or ison is the final note on which the hymn ends. The ison is typically droned against the melody. Any other notes different than the ison that occur more often than others during the course of a hymn are called dominant notes and also help define the Tone. The plagal (oblique) tones mentioned above employ the same scales as their counterparts, however their base notes (ison) are a fifth below that of their counterparts.[22]

Genos and Phthora

Byzantine music does not distinguish between major and minor scales, and in fact the majority of Byzantine tones, as they are practically performed in Mediterranean churches, cannot be played on a conventionally tuned piano. Byzantine music theory and its reference to Ancient Greek music theorists and their distinction between the diatonic, chromatic and enharmonic genus (gr. γένος) widely employ microtones, with intervals either narrower or wider than the Western-style diatonic interval (both equally tempered and just). In the early Hagiopolitan octoechos (7th-12th century) the diatonic echoi were destroyed by two phthorai nenano and nana, which were like two additional modes with their own melos, but subordinated to certain diatonic echoi. In the period of psaltic art (13th-17th century), changes between the diatonic, the chromatic, and the enharmonic genos became so popular in certain chant genres, that certain echoi of the papadikan Octoechos were coloured by the phthorai – not only the traditional Hagiopolitan phthorai, but also additional phthorai which introduced transition models taken from maqam traditions. After Chrysanthos' redefinition of Byzantine chant according to the New Method (1814), the scales of echos protos and of echos tetartos are usually soft diatonic, those of the tritos echoi and the papadikan echos plagios tetartos enharmonic (phthora nana), and those of the devteros echoi chromatic.[23] Whereas modern Western music is ultimately based on two different scales (major and minor), and the Latin octoechos on eight diatonic modes, four basic scales are used in the different Orthodox traditions of monodic chant today:

Notes

References

  1. ^ The numerical order of Byzantine echoi is the 4 kyrioi echoi, then the 4 plagioi echoi, in Carolingian tonaries it is tonus primus (first authentic tone), tonus secundus (first plagal tone) etc.
  2. ^ The echoi cycle on a dily basis during Easter Week.
  3. ^ The fourteenth-century manuscript is Paris, Bibliothèque nationale, fonds grec, ms. 360 and was edited by Jørgen Raasted 1983, an earlier fragment dates back to the twelfth century and was edited by Johann Friedrich Bellermann (1972).
  4. ^ Peter Jeffery (Jeffery 2001, 186f) believes that certain paraphrases – like Raasted 1983, §8, p.16 – are polemics against the 16 echoi of the Asma, the modal system of the Constantinopolitan cathedral rite.
  5. ^ Harold S. Powers, "Mode, §II: Medieval Modal Theory, 1: The Elements, (ii) The Byzantine Model: Oktōēchos" (Powers), see also Jeffery 2001 and Werner 1948.
  6. ^ Neubauer 1998.
  7. ^ German translation by Neubauer 1998, 378f.
  8. ^ According to Charles Atkinson (2008: p.177) the commentary was inserted by "author δ", the compilator of the fourth layer.
  9. ^ Gerbert 1784, 139.
  10. ^ The octave can be transposed, but if the tetartos octave for example is G-g, it has f sharp.
  11. ^ Hannick & Wolfram 1997: pp.84f.
  12. ^ Raasted 1983, §6, p.14.
  13. ^ Book 4, chapter 15 of Boethius' De institutione musica, see Bower's translation in Harold Powers' article "mode" (Powers, II:1:i, section "The Hellenistic model: tonus, modus, tropus").
  14. ^ Charles Atkinson (2008: p.149f).
  15. ^ See Atkinson (2008: ex.4.5, p.157) or ex. 2 in Harold Powers' article "mode" (Powers, II:2:i:a "The System of Tetrachords"). The different letter systems used in the notation of theoretical and liturgical chant sources are described by Nancy Phillips (2000).
  16. ^ Huglo (1971).
  17. ^ Michel Huglo (2000) refers to an episode which was described long ago by Oliver Strunk (1964).
  18. ^ Aurelianus Reomensis: "Musica disciplina" (Gerbert, 1784, 42).
  19. ^ Ibn al-Munadjdjim (in French)
  20. ^ Sources Arabes sur la Musique (in French)
  21. ^ The Mnemonic Verses: A Quick and Easy Guide to the Byzantine Tones, J. Suchy-Pilalis, accessed 2010-02-15.
  22. ^ The Byzantine Tones, Part I, accessed 2007-06-06.
  23. ^ Chrysanthos of Madytos 1832
  24. ^ The Byzantine Tones, Part II, accessed 2007-06-06.

Editions of Theoretical Octoechos Treatises

Greek Treatises

Hagiopolites
Dialogue Treatises
Papadikai
New Method

Latin Treatises

Translation of Harmonikai
Carolingian Music Theory
Tonaries

Studies

Related articles

Persons

External links