Linos G. BENAKIS

UDC 781.4:1/14 Linos G. BENAKIS

BYZANTINE MUSICAL THEORY (HARMONICS)*

Abstract

Harmonics was one of the four mathematical sciences in the Byzantine higher education curricu- lum, together with Arithmetic, Geometry, and Astronomy (what was called quadrivium in the West). Our knowledge of Byzantine harmonics is rather limited, as only two or three of the relevant treatises have been published in new editions. In this paper a systematic approach is attempted, while, at the same time, keeping distances from the well-studied practical aspect of , i.e. ec- clesiastical music. Furthermore, the tradition of Greek musical theory (both Pythagorean and Aris- toxenian), which the Byzantines developed further from a dual, both textual and educational, interest, presenting us at the same time with some original contributions.

Keywords: Byzantium, greek music, Harmonics, Quadrivium, pythagoreans, canonists, harmo- nists.

In recent years, a wealth of scholarly and Greek harmonies (the kinds of octaves) and Byz- layman’s books have been written on Orthodox antine musical scales (the system of the eight ecclesiastical music, its character, and history. modes - oktōēchos), or does Byzantium represent There is intense interest in Orthodox church a new starting point with eastern roots? music in and abroad, and thankfully our For a more systematic approach to this sub- knowledge keeps expanding. ject we would naturally need to draw a clear-cut Yet when it comes to Byzantine musical distinction between music as it was practiced in theory, i.e. harmonics as a branch of science and Byzantium and Byzantine musical theory. Musi- philosophy in the Byzantine era, things are quite cal practice, the songs of the ancient world, of different. Here we are faced with a number of which we also know very little, was absorbed difficulties: although many critical editions, into Christian liturgical music and was overlaid commentaries, and detailed hermeneutical works by it, as with geological strata. Thus, by the time have been published on theoretical of Justinian (6th century AD), when Byzantine works on Music, the same cannot be said about ecclesiastical had come into its own the relevant Byzantine theoretical works. Several as a discrete art form, practiced by magnificent crucial scholarly issues remain unresolved; for Christian melodists such as Romanos, ancient instance: are there direct links between ancient Greek music was long dead. A Neoplatonic commentator of Aristotle, Olympiodorus of Al- th * In a short form published in Mousikos Logos exandria tellingly claimed in the 6 century that (Μουσικός Λόγος), Athens 1 (2000) 4sq. while enough ancient testimonies survive on the 98 WISDOM 1(10), 2018 98 99 WISDOM 1(10), 2018 Byzantine Musical Theory (Harmonics)

UDC 781.4:1/14 sciences of the ancients, such as arithmetic, ge- Byzantine era; this suggests an interest in copy- Linos G. BENAKIS ometry, and astronomy, precious little is known ing, studying and employing texts of ancient about ancient melody; in this case, a Homeric musical theory as teaching material. Interest for BYZANTINE MUSICAL THEORY (HARMONICS)* verse aptly captures the situation: ἡμεῖς δὲ κλέος teaching purposes eventually led to a dynamic οἶον ἀκούομεν οὐδέ τι ἴδμεν (“but we hear only a and original reception and integration of ancient rumor and know nothing” Il. 2.486). Olympiodo- Greek musical theories in Byzantine teaching Abstract rus further adds that he only has access to theo- practices, and the composition of music text-

retical works on ancient music. books; this is not confined to the field of har- Harmonics was one of the four mathematical sciences in the Byzantine higher education curricu- Thus we need to draw a fundamental dis- monics as part of the quadrivium or tetractys of lum, together with Arithmetic, Geometry, and Astronomy (what was called quadrivium in the Latin tinction: we should not confuse the musical prac- the mathematical sciences taught in Byzantine West). Our knowledge of Byzantine harmonics is rather limited, as only two or three of the relevant tices of the Orthodox Church, what we call Byz- higher learning institutions: these texts were treatises have been published in new editions. In this paper a systematic approach is attempted, while, antine music, with Byzantine non-ecclesiastical sometimes also put to use in the field of ecclesi- at the same time, keeping distances from the well-studied practical aspect of Byzantine music, i.e. ec- (thyrathen) music theory, i.e. the science of har- astical music. clesiastical music. Furthermore, the tradition of Greek musical theory (both Pythagorean and Aris- monics. The latter preserves several elements of Thus harmonics, as taught in Christian By- toxenian), which the Byzantines developed further from a dual, both textual and educational, interest, ancient musical theory and continues its scien- zantium in the context of ‘general education’, or presenting us at the same time with some original contributions. tific tradition. what we would describe as the thyrathen classi-

Thus, we do not know much about Byzan- cism of the Byzantines, allows us to follow how Keywords: Byzantium, greek music, Harmonics, Quadrivium, pythagoreans, canonists, harmo- tine musical theory. Until recently, interest in issues and scientific trends that emerged in Late nists. this field was limited to special philological Antiquity continued to occupy the thought of

and exclusively musicological research. There writers in the following centuries. As we shall

are but a handful of works written from a theo- see, Byzantine harmonics is also chiefly preoc- In recent years, a wealth of scholarly and Greek harmonies (the kinds of octaves) and Byz- retical and philosophical perspective. Byzan- cupied with the tonal systems and their mathe- layman’s books have been written on Orthodox antine musical scales (the system of the eight tine works on the subject were of interest to matical underpinnings, as it attempts to calcu- ecclesiastical music, its character, and history. modes - oktōēchos), or does Byzantium represent modern scholars only insofar as they helped late their elements. By manner of introduction, There is intense interest in Orthodox church a new starting point with eastern roots? them decode , apply the tonal what we need to underline again is that the sub- music in Greece and abroad, and thankfully our For a more systematic approach to this sub- system, and study its historical development - ject of harmonics was cultivated solely in the knowledge keeps expanding. ject we would naturally need to draw a clear-cut i.e. as secondary sources for Byzantine ecclesi- higher schools of the empire and almost exclu- Yet when it comes to Byzantine musical distinction between music as it was practiced in astical music. sively by the erudite philosophers who taught theory, i.e. harmonics as a branch of science and Byzantium and Byzantine musical theory. Musi- Notwithstanding the lack of modern edi- the relevant class on harmonics in the context of philosophy in the Byzantine era, things are quite cal practice, the songs of the ancient world, of tions, however, of all Byzantine works on har- the quadrivium: arithmetic; geometry; harmon- different. Here we are faced with a number of which we also know very little, was absorbed monics, and the absence of relevant treatises, it ics; astronomy. difficulties: although many critical editions, into Christian liturgical music and was overlaid is certain that in this field we can detect an im- To describe the content of Byzantine musi- commentaries, and detailed hermeneutical works by it, as with geological strata. Thus, by the time th pressive continuity between ancient and later cal theory we need to become acquainted with have been published on ancient Greek theoretical of Justinian (6 century AD), when Byzantine Greek musical theory. This thesis can now be the ancient and late antique theoretical musical works on Music, the same cannot be said about ecclesiastical hymnology had come into its own supported more methodically on the basis of discussions and debates that continued during the relevant Byzantine theoretical works. Several as a discrete art form, practiced by magnificent more recent assessments about specific musical Byzantine times. One of the main currents in an- crucial scholarly issues remain unresolved; for Christian melodists such as Romanos, ancient theory works in the most recent of all the rele- cient Greek musical theory stems from the doc- instance: are there direct links between ancient Greek music was long dead. A Neoplatonic vant studies (see Troelsgard, 1988). We should trines of Pythagoras, as expounded by Pythago- commentator of Aristotle, Olympiodorus of Al- th stress the fact that many manuscripts containing rean philosophers throughout the ages. At its exandria tellingly claimed in the 6 century that texts on harmonics are present throughout the core lies the notion of numbers as the essence of while enough ancient testimonies survive on the 98 99 99 WISDOM 1(10), 2018 Linos G. BENAKIS

the universe. For the Pythagoreans, harmony re- influenced by eastern mysticism; and, finally, sults from a synthesis of opposites; this holds Proclus in the 5th century composed valuable true both for the cosmos as a whole and the soul, commentaries on Plato and Euclid. In this direc- as well as in the regular (albeit unequal) distribu- tion, and for all the philosophers mentioned, but tion of melodic intervals in the tonal system. This also for many more, the purpose of mathematics is the direction of the so-called Canonists. Ex- and music/harmonics is to elevate man from the amples of Canonist musicians and philosophers material world of the bodies and transport him to are Archytas (430-360 BC), the single most im- the Domain of the Ideas (or Forms), a realm of portant exponent of the theory, and later Pythag- absolute beauty and perfect harmony. Mathemat- oreans until the time of (108-168 AD) ics, and the related sciences, astronomy and har- and the Neoplatonic philosophers. The other di- monics, exert a purifying and edifying influence rection is that of the School of the Harmonists; on the soul. More specifically, harmonics as a they were supporters of , the eminent philosophical and scientific field is founded on 3rd century BC philosopher, who originated from the imitation of divine harmony. Taras, but lived and taught in Athens. His work Under such presuppositions and in its pure- Elements of Harmony is extant, together with ly theoretical character, the study and cultivation fragments from another one called Elements of of harmonics during this period engendered a Rhythm. certain disdain and neglect for everyday lay mu- Following a rather long hiatus, from the 2nd sical practices. On the contrary, the Church Fa- century BC to the 1st century AD, Pythagorean thers, having embraced the Greek understanding musical theories (those of the Canonists) flour- of music’s nature as an imitation (mimēsis) of ished again, thanks to the great mathematician divine harmony and a tool for promoting psychic and astronomer Claudius Ptolemy. Ptolemy ded- health, welcomed the use of music in divine wor- icated much of his studies to musical theory. His ship as it allowed people to listen to and compre- work Harmonics represents a philosophy of mu- hend the message of the Holy Scriptures more sic, a study of the proportional nature of tonal clearly. Thus musical practices not belonging to relations, a proportionality that is echoed in the continued to be sidelined in the human soul and heavenly bodies. Ptolemy’s following centuries, although later there is evi- Harmonics has been described as Antiquity’s dence for the use of songs in the rituals and cele- most insightful and most comprehensive synthet- brations of the Byzantine imperial court and in ic work. Ptolemy’s rational, systematic treatment popular festivities. of harmonics is of equal value to his astronomi- Throughout the Byzantine period, harmon- cal work. The direction of the Pythagoreans was ics or musical theory was cultivated and taught also adopted by Neoplatonic philosophers, i.e. as a mathematical science, which in turn be- the continuators of Plotinus’ (205-270 AD) longs to the supreme science, philosophy. Its thought: Porphyry wrote in the late 3rd century a subject-matter is chiefly the mathematical rela- Commentary on Ptolemy and discussed the logi- tions between tonal intervals. After all, the in- cal distinctions between the quantity and the corporation of harmonics in the four subjects quality of tones; Iamblichus, active in the 4th cen- (the so-called quadrivium) taught in the higher tury, dealt with symbolic numerology and was learning schools of Byzantium deflects interest

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the universe. For the Pythagoreans, harmony re- influenced by eastern mysticism; and, finally, away from music as artistic performance (musi- the time of Bardas (863). Leo the Mathemati- sults from a synthesis of opposites; this holds Proclus in the 5th century composed valuable cal act), refocusing it on the theoretical study of cian, or Philosopher, taught there, while import true both for the cosmos as a whole and the soul, commentaries on Plato and Euclid. In this direc- mathematical relations between sounds, har- educators such as Photius, Arethas, a.o. were as well as in the regular (albeit unequal) distribu- tion, and for all the philosophers mentioned, but monic calculations, and the relevant theoretical active there. During this period, and with the tion of melodic intervals in the tonal system. This also for many more, the purpose of mathematics analyses. Therefore, music, as a science and a support of an erudite emperor, Constantine VII is the direction of the so-called Canonists. Ex- and music/harmonics is to elevate man from the practice, was marginalized in education (both in Porphyrogenitus, authorial output increased amples of Canonist musicians and philosophers material world of the bodies and transport him to terms of textbooks and teaching activity) and in significantly and many ancient literature works are Archytas (430-360 BC), the single most im- the Domain of the Ideas (or Forms), a realm of the intellectual life throughout the Byzantine were being copied, several of which were dedi- portant exponent of the theory, and later Pythag- absolute beauty and perfect harmony. Mathemat- lands and throughout the western middle ages. cated to the subject of harmonics. In 1970, E. oreans until the time of Ptolemy (108-168 AD) ics, and the related sciences, astronomy and har- To be precise, this was the case until the Euro- Pöhlmann demonstrated that the work known as and the Neoplatonic philosophers. The other di- monics, exert a purifying and edifying influence pean Enlightenment, when new ideas led to the Introduction to the Art of Music by Bacchius rection is that of the School of the Harmonists; on the soul. More specifically, harmonics as a emergence of the view that music is a mimetic Sennex is dedicated to Constantine VII, and not they were supporters of Aristoxenus, the eminent philosophical and scientific field is founded on art and a creative activity. Around that time, to Constantine I, as was earlier believed. 3rd century BC philosopher, who originated from the imitation of divine harmony. musical theory as a branch of mathematics One of the earliest works on harmonics Taras, but lived and taught in Athens. His work Under such presuppositions and in its pure- slowly began to disappear from the curricula of from the Byzantine era is by Gregory Elements of Harmony is extant, together with ly theoretical character, the study and cultivation European higher schools. Aneponymous Syntagma eusynopton eis tas fragments from another one called Elements of of harmonics during this period engendered a A more systematic overview and more tessaras mathēmatikas epistēmas, and was Rhythm. certain disdain and neglect for everyday lay mu- works on the position of musical theory in the composed between 1008 and 1040. It was for- Following a rather long hiatus, from the 2nd sical practices. On the contrary, the Church Fa- context of Byzantine education are much need- merly ascribed to the great philosopher and pol- century BC to the 1st century AD, Pythagorean thers, having embraced the Greek understanding ed now. Following the relocation of the capital ymath Michael Psellos, but nowadays we have musical theories (those of the Canonists) flour- of music’s nature as an imitation (mimēsis) of of the Eastern to Constantino- at our disposal an excellent edition of this work ished again, thanks to the great mathematician divine harmony and a tool for promoting psychic ple, the city evolved into a great educational by the great Dansh historian of ancient mathe- and astronomer Claudius Ptolemy. Ptolemy ded- health, welcomed the use of music in divine wor- center, comparable to Hellenism’s once famed matics J. Heiberg, Anonymi Logica et Quadriv- icated much of his studies to musical theory. His ship as it allowed people to listen to and compre- centers of learning. In the time of Theodosius ium cum scholiis antiquis, Copenhagen 1929). work Harmonics represents a philosophy of mu- hend the message of the Holy Scriptures more (425 AD), the Imperial University of Constanti- It is important to note that in 1750 one of sic, a study of the proportional nature of tonal clearly. Thus musical practices not belonging to nople (Pandidakterion) had 30 chairs; among the pioneers of modern musicology R. Mizler relations, a proportionality that is echoed in the Christian liturgy continued to be sidelined in the the courses taught we find Harmonics, always (†1778), a German professor and publisher of a human soul and heavenly bodies. Ptolemy’s following centuries, although later there is evi- in conjunction with Arithmetic, Geometry, and musicology periodical in Leipzig, attempted to Harmonics has been described as Antiquity’s dence for the use of songs in the rituals and cele- Astronomy. During the reign of Heraclius (610- publish Gregory’s Music (harmonics) along with most insightful and most comprehensive synthet- brations of the Byzantine imperial court and in 641), in addition to theological sciences, this a German translation of the text. This is because ic work. Ptolemy’s rational, systematic treatment popular festivities. ‘Ecumenical’ school, as it was dubbed, also of- Mizler, imbued with the rationalism of the great of harmonics is of equal value to his astronomi- Throughout the Byzantine period, harmon- fered instruction on Greek sciences. These natu- Christian Wolff, sought to find arguments that cal work. The direction of the Pythagoreans was ics or musical theory was cultivated and taught rally included mathematics and harmonics. Two would allow him to promote music as a branch also adopted by Neoplatonic philosophers, i.e. as a mathematical science, which in turn be- centuries later, we hear of the studies and the of mathematics (musica more geometrico) in the continuators of Plotinus’ (205-270 AD) longs to the supreme science, philosophy. Its pursuits of the great dogmatist of the Eastern university curricula. Thus Mizler singled out and thought: Porphyry wrote in the late 3rd century a subject-matter is chiefly the mathematical rela- Orthodox Church, , who highlighted the Prologue by that distant 11th cen- Commentary on Ptolemy and discussed the logi- tions between tonal intervals. After all, the in- “was taught... mathematics, music, etc.” tury Byzantine author, where he claims that “the cal distinctions between the quantity and the corporation of harmonics in the four subjects Higher learning experienced a phase great harmony of the cosmos is borne out in Music”; quality of tones; Iamblichus, active in the 4th cen- (the so-called quadrivium) taught in the higher development following the establishment of that “Harmonics are grounded on the fact that tury, dealt with symbolic numerology and was learning schools of Byzantium deflects interest University of the Palace Hall of Magnaura in harmony is the synthesis of diverse tones in a

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certain order”; and that the “purpose [of harmon- ‘music’, ‘’ and others, as well as the prob- ics] is to study the constitution and the arithmeti- lems of employing string instruments in ecclesi- cal relations between the symphonic intervals”. astical musical practices). Of course, today we know more about this Now, we will very briefly provide an over- early work of Byzantine musical theory, and view of Byzantine authorial output in the field of that its treatment of harmonics follows, up to a harmonics from the 11th century to the dissolu- point, Aristoxenus’ school (the Harmonists) and tion of the . Michael Psellos, not that of Pythagoras (the Canonists); Mizler the head (literally “chief”) of the school of Con- had failed to notice this. At any rate, the core of stantinople ( tōn philosophōn) was also this work, i.e. its doctrine on the intervals, relies known for his part in the reorganization of the on the Pythagorean conception of arithmetical curriculum in the “University of ” relations, as expounded by the brilliant mathe- after 1045. He also composed an Introduction to matician (1st-2nd century AD). Rhythmical Science and other minor works on In other words, at a critical point in the work, music; this reveals the important place music the Byzantine author switches from Aristox- held in the teaching of one of Byzantium’s most enus’ summation of intervals from sharp ele- prominent sages. In the lower grade of the new ments to the Pythagorean calculation of the University, Grammar, Rhetoric and classical au- arithmetical relations between the tones, i.e. his thors always formed part of the curriculum; the analysis of harmonics unfolds simultaneously higher grade featured the quadrivium subjects on two levels. Nonetheless, the core of the work and Philosophy (Logic and Natural Philosophy) is Pythagorean, and this feature characterizes all and, depending on the course of study elected by on harmonics. the student, Jurisprudence or Medicine. An inter- Certainly, scholarship in this area is lag- esting detail reflecting these teaching practices is ging both in terms of the degree of acquaintance preserved in a work by the 12th century author with the available material, and its proper eval- Nicholas Messarites. He describes how, in the uation. That is why contributions, such as the School of the Saint Apostles in Constantinople, one mentioned above by Chr. Troelsgard, are pupils received instruction on and extremely valuable. His study also confirms the “in the enclosure” (these were first grade stu- mixed nature of Byzantine harmonics (Tro- dents); higher grade students, however, who took elsgard, 1988, pp. 230-232); interestingly, he classes “in the courtyard”, were taught harmon- further notes that works on ecclesiastical music, ics. Thus it is once more clear that musical prac- such as that by Hagiopolites, the earliest (12th tice (hymns, songs) was separated from musical century) extant text of its kind (Hagiopolites, theory, which was taught in the context of “sci- 1983), we find elements of ancient harmonics entific” disciplines. that are deemed useful in determining the ap- In the Palaeologan period (1261-1453), propriate level for teaching ecclesiastical music. Byzantium’s last period of flourishing in arts Other extensive and systematic works on har- and letters, the subject of harmonics was widely monics by Pachymeres and Nikephoros Bryen- taught in the “University”, the Patriarchal Aca- nios can provide evidence on the features of demy, and in other higher-learning schools; al- musical practice (here of interest are the terms most all of the erudite philosophers of these two

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certain order”; and that the “purpose [of harmon- ‘music’, ‘chant’ and others, as well as the prob- centuries composed textbooks on harmonics. the number of original works on harmonics and ics] is to study the constitution and the arithmeti- lems of employing string instruments in ecclesi- The most important names of this period are: of the manuscripts containing earlier works sug- cal relations between the symphonic intervals”. astical musical practices). Nikephoros Blemmydes in Nicaea and Ephesus; gests the subject continued to be studied exten- Of course, today we know more about this Now, we will very briefly provide an over- George Acropolites in the School; sively. In these years, contacts with the West early work of Byzantine musical theory, and view of Byzantine authorial output in the field of Maximos Planoudes (1255-1310), who com- multiply, and Byzantium begins to exert increas- that its treatment of harmonics follows, up to a harmonics from the 11th century to the dissolu- posed a very extensive and unfortunately not ingly greater influence on the Latin-speaking point, Aristoxenus’ school (the Harmonists) and tion of the Byzantine Empire. Michael Psellos, extant Harmonics, where the astute author sums world; this phenomenon will reach its apogee not that of Pythagoras (the Canonists); Mizler the head (literally “chief”) of the school of Con- up the entire ancient Greek musical tradition; with the flight of scholars from Byzantine lands had failed to notice this. At any rate, the core of stantinople (hypatos tōn philosophōn) was also John Pediasimos; and, above all, the renown to Italy after the . The final this work, i.e. its doctrine on the intervals, relies known for his part in the reorganization of the . Pachymeres’ (1242-1310) testimony on Byzantine musical theory is a brief on the Pythagorean conception of arithmetical curriculum in the “University of Constantinople” Quadrivium has been thankfully published in a work by George Gemistos or Plethon, the great relations, as expounded by the brilliant mathe- after 1045. He also composed an Introduction to critical edition (Tannery, 1940). The section on philosopher of (1360-1452), and is enti- matician Theon of Smyrna (1st-2nd century AD). Rhythmical Science and other minor works on Music (harmonics) covers some 100 pages and tled Some Chapters on Musical Theory. His stu- In other words, at a critical point in the work, music; this reveals the important place music is supplemented by many illustrations. dent, the scholarly cardinal Bessarion, kept inter- the Byzantine author switches from Aristox- held in the teaching of one of Byzantium’s most From the 14th century onwards, Byzantine est in the science of harmonics alive, as revealed enus’ summation of intervals from sharp ele- prominent sages. In the lower grade of the new scholars become increasingly more interested in by the large number of the relevant manuscripts ments to the Pythagorean calculation of the University, Grammar, Rhetoric and classical au- ancient Greek works, and chiefly in Aristox- he bequeathed to the Biblioteca Marciana in arithmetical relations between the tones, i.e. his thors always formed part of the curriculum; the enus, Ptolemy, and other later authors on music. . analysis of harmonics unfolds simultaneously higher grade featured the quadrivium subjects A number of Byzantine commentaries on these As a conclusion, we can claim that as a on two levels. Nonetheless, the core of the work and Philosophy (Logic and Natural Philosophy) works are composed. The lengthiest and most higher learning scientific discipline, musical is Pythagorean, and this feature characterizes all and, depending on the course of study elected by complete work on harmonics was produced, theory/harmonics in Byzantium remained firm- Byzantine literature on harmonics. the student, Jurisprudence or Medicine. An inter- however, by Manuel Bryennios in ca. 13201. ly oriented towards the Pythagorean music Certainly, scholarship in this area is lag- esting detail reflecting these teaching practices is Bryennios’ work was preserved in a large num- theoreticians, Ptolemy, Nicomachus of Gerasa, ging both in terms of the degree of acquaintance preserved in a work by the 12th century author ber of manuscripts and in the late 15th century it Theon and others, who remained the authori- with the available material, and its proper eval- Nicholas Messarites. He describes how, in the became known in the West thanks to a Latin ties in the field of harmonics; their status re- uation. That is why contributions, such as the School of the Saint Apostles in Constantinople, translation by Franchinus Gaffurius. mained unchallenged. Beyond the main musi- one mentioned above by Chr. Troelsgard, are pupils received instruction on hymns and chants Another eminent philosopher and astron- cal commonplaces (topoi), which throughout extremely valuable. His study also confirms the “in the enclosure” (these were first grade stu- omer, Theodore Metochites (1260-1332) ana- the Byzantine era constituted a shared patri- mixed nature of Byzantine harmonics (Tro- dents); higher grade students, however, who took lytically defined the essence of harmonics; he mony in musical education (parallel to the the- elsgard, 1988, pp. 230-232); interestingly, he classes “in the courtyard”, were taught harmon- had studied under Manuel Bryennios. As a oretical and arithmetical orientation of Byzan- further notes that works on ecclesiastical music, ics. Thus it is once more clear that musical prac- Christian humanist, he pondered on the possible tine harmonics, with respect to relations be- such as that by Hagiopolites, the earliest (12th tice (hymns, songs) was separated from musical benefits to be had from the study of harmonics tween intervals), musical philosophers were century) extant text of its kind (Hagiopolites, theory, which was taught in the context of “sci- on one’s worldview: he argues that harmonics also well versed into Aristoxenus’ doctrines on 1983), we find elements of ancient harmonics entific” disciplines. can bring people closer to the miracle of the melody and rhythm; thus, Byzantine musical that are deemed useful in determining the ap- In the Palaeologan period (1261-1453), harmony of the heavenly spheres, and God’s theory was anything but monolithic. At any propriate level for teaching ecclesiastical music. Byzantium’s last period of flourishing in arts perfection and omnipotence. rate, practical music textbooks (the so-called Other extensive and systematic works on har- and letters, the subject of harmonics was widely In the final years of the Byzantine Empire, Papadikes) apparently continue precisely this monics by Pachymeres and Nikephoros Bryen- taught in the “University”, the Patriarchal Aca- practical (acoustic) method of Aristoxenus’ 1 This work has also received an important modern nios can provide evidence on the features of demy, and in other higher-learning schools; al- edition: Manuēl Bryenniu Harmonika: The harmon- school, albeit with a different purpose and in musical practice (here of interest are the terms most all of the erudite philosophers of these two ics of Manuel Bryennius (ed) G. H. Jonker (Gro- another context. Finally, it should be under- nigen 1970). 102 103 103 WISDOM 1(10), 2018 Linos G. BENAKIS

lined that the contemporary scholarly research, et Latin, 56 (pp. 228-238). comprehensive in its methods and goals, schol- Hagiopolites (1983). The Hagiopolites, A Byz- arly research needs to clarify a series of ques- antine Treatise on Musical Theory. In tions before we will be in a position to speak J. Raasted (Ed.), Cahiers de l'Institut with some degree of certainty about the great du Moyen-Âge Grec et Latin, 45. contributions of the Byzantines also in the field Tannery, P. (Ed.) (1940). Quadrivium de of music.2 Georges Pachymère. (E. Stephanou, Ed.). Vatican City. REFERENCES Bryennios, M. (1970). Manuēl Bryenniu Har- monika: The Harmonics of Manuel Troelsgard, Ch. (1988). Ancient Musical Theo- Bryennius (G. H. Jonker, Ed.). Gro- ry in Byzantine Environments. In Ca- nige. hiers de l'Institut du Moyen-Âge Grec

2 The core of this article predates the brilliant chapter “Musik” (in vol. 2, pp. 181-218) by Christian Han- nick in Herbert Hunger (Ed.) Die hochsprachliche profane Literatur der Byzantiner: Philosophie, Rhetorik, Geschichtsschreibung (Munich 1978). I would advise anyone with a keen interest in Byzan- tine music to use this as a starting point. 104 WISDOM 1(10), 2018 104 105 WISDOM 1(10), 2018