Klara Mechkova's books on Tetraphony and Triphony

n_antonov

Nikola Antonov
Dear friends, I would like to present to you two books by Bulgarian researcher musicologist and professor of music history Klara Mechkova.

Over the last decade, she has published two books on Tetraphony and Triphony as the major systems of the Byzantine music.

1. The Oktaechon System of the Byzantine Music in the Theoretical Texts Sources. The Tetraphony (2009). The book follows strictly the medieval Byzantine sources. The researcher examines in detail key issues of Byzantine music theory, makes a detailed and in-depth analysis of the St. John Kukuzel's wheel (Τροχός). She pays special attention to terms and issues such as φωνή, ήχος (functional theory of the echos), the discrepancy between the order and naming of the Ancient Greek scales and Byzantine scales, the relation between music and theology in the medieval Byzantium.

2. The Triphony in the Tetraphonic Musical System and in the Life of the Byzantine Oktaechon (2018). The book is a continuation of the first with an emphasis on the Triphony as a subsystem of the Byzantine music. The author makes a detailed analysis on the graphic of John Plusiadinos (Η σωφοτάτη παραλλαγή). Also, in this book she translates and analyzes the δοξαστικό Θεαρχίω νεύματι by various Byzantine sources. She pays special attention to terms such as φθορά, νανά, λέγετος, νενανώ and others key concepts. The question about the tonal system is also addressed in this book. She mentions the testimony of Chrysanthos about the three types of tonal intervals and traces the connection with the sources of Arabic music in the Middle Ages. It suggests that Arab musicians may have borrowed the idea of the intervals from the medieval Byzantium (there is no direct evidence, so this remains only a scientific assumption and hypothesis).

The Klara Mechkova's research focus is on the musical systems, functional analysis and the way these major components of music work, following strictly Byzantine music sources. In addition, she has deep knowledge and gives credit to the Three Teachers' reform. On one hand, she traces the continuity between medieval Byzantine music and the music of The Modern Times (the Three teachers' reform). On the other hand, she does not make the mistake of fully identifying or completely negating any connection between the Middle Ages and Modern Times (as many Western researchers make).

Unfortunately, Klara Mechkova's books are only available in Bulgarian for the time being.
 

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n_antonov

Nikola Antonov
The Oktaechon System of the Byzantine Music in the Theoretical Text Sources. The Tetraphonia (2009).

Main Topics:
Capture1.PNG
  • The theological background related to the specifics, contents and time of appearance of the Byzantine theoretical texts
  • The idea of phone in the Byzantine music system and medieval treatises
  • Phone and the accompanying terms in the texts sources
  • Phone - the definition
  • The quality of the note and phone
  • Phone and Tetraphonia
  • The melos of the note
  • The melos of the note and the polysyllabic naming of the notes
  • The melos of the notes and the interval matter of phone
  • Tetraphonia and genus
  • Metrophonia and parallage
  • The functionality of tetraphonia. The Oktaechia.
  • The tetraphonia features: 1) the tetraphonia as a hypostatic union; 2) the principle of the corresponding pair phone-tetraphonia; 3) the principle of the circular motion-tetraphonia; 4) the common operations ot the both principles
  • The tetraphonia and mastering of the acoustic space
  • The Oktaechia: 1) the principle of the corresponding pairs; 2) the tetraphonia and the filling of scales of the echoi
  • The principle of the circular motion in the Oktaechia
  • The Wheel of the St. John Koukouzelis: 1) the meaning of the small circles; 2) the meaning of the Tree; 3) the optimal variant of the circular motion in the Wheel and the small circles of the Wheel; 4) the second element of the Wheel; 5) the maximal variant of the circular motion in the Tree and the Wheel; 6) the spiral motion in the Tree; 7) the central body of the Wheel; 8) about the Wheel as a musical incarnation of the theological idea about the "saved space"
  • The Ancient naming of the scales and Byzantine echoi in the treatise of Agiopolitis. The principle of the circular motion. The treatise Vaticanus Graecus 871. The principle of the corresponding pairs echoi in to the Koukouzeli's Wheel.
  • A functional theory of the echoi: the historical and theological background; the meaning of the term ήχος; the theological aspect of the terms κύριος and πλάγιος.
  • The main ideas in to the treatise of the Monk Gabriel (Codex Lavra 610): γνωριστική and δηλωτική idea; mesos, diplasmos, naos.
 
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n_antonov

Nikola Antonov
The Triphonia in the Tetraphonic Musical System and in the Life of the Byzantine Oktaechon (2018).
Capture2.PNG
Main Topics:


  • The Triphonia in to the contemporary science and the medieval text sources
  • The basics of Triphonia: 1) definition; 2) the functionality of the triphonia and tetraphonia; 3) a functional relationships between the triphonia and tetraphonia; 4) the melodic "holdingness" and "unholdingness" as a prerequisite for a functional "holdingness" and "unholdingness"
  • The Triphonia as a phtora: 1) different kind of modulations in the echoi; 2) the double parallage
  • The "turnover" of the Triphonia: 1) the monophonia; 2) an extended (compound) triphonia
  • Acoustic parameters in to the Byzantine music system: 1) the hypothesis; 2) the idea of the "unequal fourths"; 3) the "unequal fourths" in to the context of the Byzantine echoi
  • Nana, nenano, legetos
  • The Triphonia in to the didactic aids: 1) "Η σοφοτάτη παραλλαγή" of John Plousiadenos; 2) the method of John Laskaris
  • The Triphonia in to the manuscripts
  • The Byzantine music system by the example of the sticheron "Θεαρχίω νεύματι".
 
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Daidalos

Μέλος
Dear Nikola

I thank you for a more competent translation (the English abstracts at Bulgarian Musicology are still somehow rhapsodic):
Buleva, Mariyana. «Клара Мечкова: “Трифонията В Тетрафоничната Музикална Система И В Живота На Византийското Осмогласие.” Българско Музикознание n. 1 (2019): 102–5.
https://www.ceeol.com/search/article-detail?id=777078
 

n_antonov

Nikola Antonov
Here are some highlights related to the Byzantine music term phone (φωνή) by the book of Klara Mechkova about the tetraphony.

I'm still working on the translation of the whole chapter. The text below is still a draft, just to have an idea.

The Byzantine notion of the smallest building block of the musical system – phonē (ἡ φωνή) – is specific and radically different from the acoustic perception to note (tone) in Antiquity and in the Western Middle Ages which is the basis of the modern theory of music. Probably, the fact that the notion of “note” in Byzantine musical practice has not been substantially understood by modern scholars is the first hindrance for the reconstruction of the theoretical system of the Byzantine Oktoechos. We will begin with a very revealing text: “The beginning, the middle, the end and the system of all the signs of the psaltic art is the ison, for without it there is no phonē. It is called aphona not because it has no sound, but [because] it sounds but is not measured" [Codex Barberinus Graecus 300 - Tardo, 151]. This quotation holds the key to a unique understanding of phonē. It is evident that ison "sounds," i.e., that the Byzantine musician and theorist had both the hearing and the understanding of tonality, of a single note as an acoustic phenomenon. At the same time, the "sounding" ison is called "aphona", i.e. soundless. At this stage of the analysis, we come upon a seeming contradiction, which will find its logical explanation. The question is: why is the "sounding" (which is specifically emphasized in the text) ison "soundless"? The text itself gives a clear answer: because "it is not measured". What does this mean? For the Byzantine musician, it is not the note as a tone itself that is informative, but the note, which is achieved by another note by moving in ascending or descending direction. This is also clearly communicated in the above quotation - the ison is not measured, but the phonē is produced by it.
The lack of instruments in medieval musical practice gives us a substantial reason for interpreting and defining phonē differently from our usual modern notion of both note and interval. For the Byzantine musician, the note is not a building block of music, if it is not achieved through an interval; in other words, the presence of an "interval" transforms a reached pitch into a musical phenomenon (a building block of the system). Therefore, the musician in Byzantium did not have an abstract notion of a single, individual note as the micro-structural material of musical language in the same sense in which Antiquity understood note as embodied through the string organs. It is this understanding that became standard in the West (also due to the influence of keyboard instruments). Of course, in perceiving music, the hearing ability of a man registers individual notes of a certain pitch (as was already noted in interpreting the above quotation). However, in Byzantine music, the notes are mere sub-elements - not autonomous building blocks of the language of music. The question, therefore, is not whether the note is heard, but what in a given musical practice is a building block, i.e. an atomic unit. According to Hieromonk Gabriel, “...an element is that from which something arises, as from a beginning, and in which it breaks down, as an in an end” [Codex Lavra 610 - Tardo, 187]. How does this thought reflect the idea of phonē? For the musician, who is performing only with his voice (i.e., vocally only), the musically informative note is the note that is achieved by an interval.
[...]
 

n_antonov

Nikola Antonov
“Phonē” is a term used to denote the smallest, meaningfully indivisible musical space that is the building block of the system. It contains within itself three levels, which we will call "sub-elements":

  1. A fixed basic note from which the movement will be started (i.e. a reference point to achieve the note sought);
  2. Crossing the exact interval at which the sought note is separated from the base note - we will call this the "interval part" of the phonē;
  3. The achieved note in which the previous two levels are reflected.
The last of the three sub-elements has two unique properties: to be a kind of "target" in the unfolding of phonē, so that the impression of the preceding note (the underlying note) is erased or fades away because it is only a point of reference; to be a self-sufficient representative of phonē, whereby it stores in itself the "memory" of the other two sub-elements. It follows that phonē cannot and should not be identified with the term interval in the modern sense, the definition of which (ratio between the pitches of two notes) rests on two real-sounding (in sequence or simultaneity) numerically fixed notes. Phonē is also not a whole tone in the modern sense, because it is not an unambiguous acoustic measure (see below), but a note absorbed in the process of live music-making at a certain distance from the preceding neighbor. Phonē is also not a “sound” in the Western European sense, because even in its appearance as a single sound through the third sub-element, it is always present in the musical consciousness precisely through the three.
 

n_antonov

Nikola Antonov
It is a credit to Bulgarian musicology that for the first time, this idea was brought out in its historical-cultural aspect and generative sense by the eminent musicologist Elena Toncheva: “In the West, as early as the so-called second period in the development of neumatic notation (according to Bruno Steblein this is the period from 1050 to 1200) the attempt for visuality placed the neumatic signs on lines, thereby achieving unambiguity in tone-pitch and emancipates the individual note. In the East, the attempt for diastematicism also was realized with the advent of the so-called Middle Byzantine notation (c. 1150). But this is a diastematicism of a completely different type (the idea of linearity remains entirely alien to the East): the Middle Byzantine notation also achieves unambiguity, but this unambiguity concerns not the single note but the single melodic interval (sub. m., K. M)” [Toncheva: 2001, 6].

If at the beginning of our considerations, it was necessary to start from the ison in order to discover the idea of phonē, it is now possible, through the defined notion of phonē, to specify the fundamental meaning of the ison. Literally and figuratively it encodes the idea of musical space: on the one hand, through its sense of sign - each preceding sign in relation to the next is in the role of an ison, i.e. a starting point for a reading of the phonē - and on the other hand, through “...the aesthetics of the ison-bourdon in the Orthodox monody - the fullness, the strength (power) of the monotonous bourdon sound...” [Toncheva: 2001, 9]. “The ison does not have phonē neither ascending nor descending, but for all notes it is consonantal. And it brings uniformity, and equality for the sound that starts again... The ison exists everywhere. From it we derive the name, for [the name] would be found in the sharpness of the sound or in the lows of those sounds. From it (from the ison) is derived the phone” [Codex Vaticanus Graecus 872 - Tardo, 170]. On this basis, we suggest that it is the phonē as a foundation for psaltic art that is being referred to by the metaphor “name”. This exclusively important function of the ison, whose flat sound recalls the golden background of mosaics in St. Sophia, was realized by medieval musicians, which is why it was named “king of all signs” [Codex Constantinopolitanus 811 - Thibaut, 161] and given a special place in the neumatic classification.
 

n_antonov

Nikola Antonov
This notion of phonē is realized in two possible ways: in the ascending and in the descending direction, each of the movements gives the achieved note (i.e., the third sub-element) a different quality into which the particular form of the first two sub-elements is shown, and which in theoretical texts is brought out precisely by the expression quality of the sound of phonē. Let us first trace the source texts:


  • “... as regards the echoi, we must bear in mind that we do not name the quantity of the notes, but their quality, because for notes usually we use expressions such as 'height', 'lowness', 'shortness', 'completeness' and 'clarity'. All these things refer to the content side of the note; not of what magnitude, how big it is, but rather of what kind it is note. The purpose of the echoi is not to be enumerated, but to represent the sound quality (emphasis mine) of the melody” [Codex Parisinus 360 - Raasted, §30, 38];
  • “The same note gives another impression to the sense of hearing at the ascent and another at the descent. The ecclesiastical musicians, therefore, gave to the same note another name at the ascent and another at the descent. For example, the 'pa' in relation to the "ni" was pronounced ‘annanes’, but in relation to the ‘vu’ it was pronounced ‘aneanes’. This is what is called quality of the notes (emphasis mine)” [Great Theory..., §238].
  • “The 'pa' said 'annanes' in ascent and 'aneanes' in descent; the 'vu' in ascent is said 'neanes', in descent 'necheanes'; the ‘ga’ "nana" in ascent, "aanes" in descent; the ‘di’ ‘agia’ in ascent, ‘neagie’ in descent...” [Great Theory..., §73].

From these few quotes - the first from the dawn, the other two from the zenith of the Byzantine science of music - it is understood that each tone as a third sub-element within the category of phonē was achieved ascending (“height”) or descending ("lowness"). Depending on where the sound is attacked (from above or from below), it acquires a different quality, for which the direction of the melodic movement is decisive. The possibility that the achieved note of phonē could be realized in two ways - ascending and/or descending - in Byzantine music is denoted by the terminological phrase quality of the note of phonē.
 

n_antonov

Nikola Antonov
The basic structural unit of the Byzantine musical system is called τετραφωνία (tetraphony), τετράφωνος (tetraphonos - the verbal adjectival form of the noun tetraphonia). Hieromonk Gabriel: “It is called tetraphonos because it occurs in the four phonē of the melos” [Codex Lavra 610 - Tardo, 198]. The entire musical space of Byzantine music is "graphed" by the tetraphonic unit just as (to make a connection with the logical level at which we are working) the modern musical system is "graphed" into octaves, or as The Ancient Greek Greater Perfect System into tetrachords. It should be immediately and clearly emphasized that the term tetraphony, as well as the underlying “phonē”, is unique to Byzantine music, has no analog in European music, and is neither a tetrachord nor a pentachord [...]

there are 4 phonē but five real notes, as the first one in ascending direction and the first one in descending direction (placed in brackets) sound but are not counted because they are "not measured", i.e. they are "aphona" (soundless – by the nice expression from Codex Barberinus Graecus 300 [Tardo, 151]). In this sense, tetraphony is not a pentachord (since the first of the five notes is not measured, i.e. it is not a phonē), but it is not a tetrachord either, since this same note, though an aphona, sounds in real. If we dare to express ourselves aphoristically: tetraphony is not a pentachord because it contains four phonē, and it is not a tetrachord because it contains five notes. This is what gives uniqueness to the phenomenon called 'tetraphony'. As a confirmation of what has been said, let us hear a remarkable passage from the Codex Lavra 1656, dedicated to the ison: “We stand before a high place as if we were measuring it. Therefore, we imagine a ladder and, raising ourselves, we call its steps one, two, three, and four. The ground on which the ladder is placed, and we stand ourselves, we do not account for. For it is the ground. By reflection we have found that only the ascending steps count, not the base”. [Tardo, 217]. This famous metaphor clearly shows that the ison, respectively the first note, is the base from which the phonē is pushed, that it is the "base", the "ground". Since the element of the system is phonē, we may say that the ison is the most important as the first sub-element of the first phonē of tetraphony, and hence for tetraphony as a whole (see Fig. 2, notes in brackets).

Organized in a system, the four phonē obey a certain logical sequence according to their acoustic magnitude (see below). This sequence is followed flawlessly regardless of which of the four phonē starts the sequence. This is also the difference between the abstract category of phonē and phonē in the system at the level of tetraphony. Here Byzantine music, therefore, contains another extremely interesting phenomenon called the "melos of the note". The melos of the note can include the various amounts of phonē (from one to four), whereby each note achieved through a melos can be recognized as a place in the system unit relative to the base, and hence to the note below and above it. The melos of the note is therefore unique phenomenon, analogous to the understanding of tone in modern musical thinking. We will propose the following definition for the introduced term "melos of the note": the combination of phonē necessary (in terms of acoustic, functional, and other parameters) to achieve each note sought in tetraphony with a certain quality (achieved "from below" or "from above"). This expression, which is astonishing, even absurd, from the point of view of modern musical concepts, actually expresses the sacred specificity of Byzantine musical thinking. In the manuscript Athens 2015, foll. 26v-27v [cited in Raasted: 1966, 53] the melos of the note is written in the old notation “κατὰ δε τοῦς παλαιοῦς, οὓτω” [...]
 

n_antonov

Nikola Antonov
In favor of the above concept of the melos of note come the polysyllabic combinations (annanes, neanes, etc.), which we believe were used to name the notes in tetraphony. This hypothesis is not widespread in the modern science of Byzantine music, since it is not expressed in this direct form in the medieval treatises which are the main sources. It is widely known that on these syllables (annanes and so on) were sung the vocal intonations (echemata), and the research interest in the echemata [Raasted: 1966], [Strunk: 1945] is even related to the origin of these “mysterious syllables” as a verbal phenomenon [Grand Theory... - §66]. However, the following fact is very interesting: unlike medieval treatises, where the vocal intonations were certainly sung on these syllables, Chrysanthos introduces them as notes of the Wheel: “These eight words are called notes of the Wheel” [Great Theory... - § 66]. And to this day, with the exception of Greek musical medievalism and in particular that of Gregory Stathis [Stathis: 2000, 79], it is accepted that in medieval Byzantine musical practice, the notes did not have independent names - a natural conclusion in the absence of more information on the problem in the source texts.

Let's present the notes in general: 1) annanes - a note that stands on one phonē ascending from the “base”; 2) neanes - a note that ascends on one phonē from annanes or two phonē ascending from the “base”; 3) nana - a note that is one phonē away from neanes or three phonē ascending from the “base”; 4) agia - a note that is one phonē away from nana or four phonē away ascending from the “base”. The abstract level of the term tetraphony as a structural unit implies the presence of these four notes, each tied to the other, without, however, implying which one comes first. The four notes can be thought of in descending terms, and then they are given the following names: 1) aanes - a note distant one phonē lower than agia; 2) necheanes - a note one phonē lower than aanes; 3) aneanes, a note one phonē lower than necheanes; and 4) neagie - a note one phonē lower than anaenes. Again, we are not referring to an initial base, but only a supposed four descending names, whichever comes first, follow in the order indicated. Hence the space of tetraphony as a structural unit (measure) can be “traversed” in the ascending or descending direction.
 

n_antonov

Nikola Antonov
In order to further explain the phenomenon of “melos of the note”, we will return to the above-mentioned idea that the acoustic value of specific phonē in tetraphony is different. Because of the extreme importance of this problem, we will clarify: Chrysanthos, naming the polysyllabic notes monosyllabically (meaning us, pa, vu..., corresponding to the solmization syllables do, re, mi...), seemingly replaces the traditional idea of phonē with the Western European idea of the tone. For tone and for tone interval he uses the same term – τόνος (tonos – a tone). The approach Chrysanthos seems both different and new and modern in relation to medieval theory, but in fact, the theorist achieves a high degree of informativeness in relation to it and respectively to the term phonē. With the two meanings of tonos, he breaks down the unified nature of the medieval phenomenon of phonē, while nevertheless the monosyllabic fixation of note is accompanied by a mathematical expression of the magnitude of the intervals. These two procedures disentangle and give greater clarity to the medieval phenomenon. In many places, Chrysanthos emphasizes that “their own” intervals are not like European ones (e.g., §19, §217 - footnote, 226, 227, 228, and elsewhere where the numerical relations of the intervals are introduced within an octave, fifth or forth). Numerically expressed intervals between tones at Chrysanthos, corresponding to the ratios 9:8 (major tone), 12:11 (minor tone), and 88:81 (minimal tone) [Great Theory... - § 228], do differ from the numerical ratios and proportions in both ancient and Western European music. Thus, by determining their magnitude - the most natural consequence of the introduction of monosyllabic names of the notes, Chrysanthos for the first time announced the magnitude of the intervals, which had existed for centuries in church tradition as an oral practice. In other words, he reveals the intervallic nature of the term phonē, which continues its existence from here on “in the paradigm of continuity between orality and writing” [Toncheva: 2005, 7]. Therefore, in the magnitudes of major tone, minor tone, and minimal tone, he brings to light the magnitude of each phonē brought by tradition, and in particular its “intervallic part”. Here are the specific acoustic parameters.
 

n_antonov

Nikola Antonov
The tetraphony is diatonic. This statement we could not cover with a quotation from the source texts (like the hypothesis of polysyllabic names of notes). Therefore, in our reasoning on this point, we will draw exclusively on Chrysanthos' Great Theory. So: “Church musicians call τροχός (trochos - wheel) a method with which they ascend and descend the intervals of the pentachord diatonically with the eight words or polysyllable notes mentioned” [Great Theory... - § 67]. Chrysanthos deals mainly with the problem of the acoustic values of tones in three places in his Great Theory: Book 1, Chapter 6 “Concerning the intervals”; Book 1, Chapter 8 “Concerning the diapason system”; Book 3, Chapter 1, “Concerning the genera in music”. Individual examples in numerical values appear in other chapters of the work. The first information (§ 53) introduces three numbers: 12, 9, and 7, expressing the magnitudes of the three types of tones: major, minor, and minimal. For the sake of theoretical clarity, it should be remarked immediately that in § 52 Chrysanthos defines the term “tone” in advance as a sound of a certain pitch (“the place on a string where the tone is emitted”) and as the spacing between adjacent tones in the octave scale. Ostensibly, this coincides with the modern existence of the term “tone”. The difference is that today the intervallic notion of tone is associated with a major second, whereas Chrysantos means with this term all intervallic variations between two adjacent tones. What do the numbers 12, 9, 7 mean? It is the difference between the lengths of the strings (or the parts of a string) playing a major, minor or minimal tone. In abstract measure (the number of “positions” from fret to fret of the tambourine as explained by Chrysanthos), the difference between the lengths of the strings whose sounds are spaced on the major tone is 12 (12 “positions”); on the minor tone, the difference between the two lengths equals 9 (“positions” of the tambourine); for the minimal tone, it is 7. Chrysantos shows these intervals also in relation to each other. We should remark immediately that his numerical operations are non-standard and do not correspond to the operations with intervals performed by ancient Greek theorists and adopted by Latin medieval music theory. If, in the usual conceptions, the relation between two numbers shows a relation between two tones, in this case the relations indicate relations of intervals. Thus, 12:9 and 12:7 is the ratio of the major to the minor and minimal tone, 9:7 and 9:12 is the ratio of the minor tone to the minimal and major, and 7:12 and 7:9 is the ratio of minor to major and minimal. Due to the complexity of Chrysantos’ musical mathematics, we will not consider in detail his subsequent operations with fractions. It is not the exact interval value that is important for us and the mathematical logic of its derivation, but the musical information embedded in the numbers. The facts indicate:

  • there are three acoustic varieties of distances between adjacent tones in the diatonic Byzantine system;
  • they are specific and correspond neither to the Western European nor to the Ancient Greek;
  • they are all expressed terminologically by Chrysanthos by the term tone (τόνος ), and in the tradition of medieval theory by phonē (φωνή).
 

Kosmo Love

New member
Dear Nikola,
Thank you kindly for providing these remarkable excerpts! I recently attended a conference on music education in the middle-ages, and the general ignorance of Bulgarian musical culture, still less the periodic Byzantine diaspora, though predictable, led to frustrating attempts to work around the bias toward interpreting musical systems through the 'one-sided' perspective of 'note' as building block. Discussions of tonus/sonus/pthongoi were not able to develop in such a short space.
Are you intending to translate the whole book?
 

n_antonov

Nikola Antonov
Thanks for the kind appreciation of my humble attempts. This subject matter is complicated to translate, the terminology is strictly specific, and it is a huge challenge for me. Unfortunately, the Bulgarian reception of Byzantine music and its more recent version (the New Method) is deeply underestimated and unknown. As far as Klara Mechkova's research is concerned, I would very much like to find an international response. Perhaps I will be able to do a translation of her first book. I would very much like to translate the whole book, but I cannot find the time now.
 

Daidalos

Μέλος
Here are some highlights related to the Byzantine music term phone (φωνή) by the book of Klara Mechkova about the tetraphony.

I'm still working on the translation of the whole chapter. The text below is still a draft, just to have an idea.

The Byzantine notion of the smallest building block of the musical system – phonē (ἡ φωνή) – is specific and radically different from the acoustic perception to note (tone) in Antiquity and in the Western Middle Ages which is the basis of the modern theory of music. Probably, the fact that the notion of “note” in Byzantine musical practice has not been substantially understood by modern scholars is the first hindrance for the reconstruction of the theoretical system of the Byzantine Oktoechos. We will begin with a very revealing text: “The beginning, the middle, the end and the system of all the signs of the psaltic art is the ison, for without it there is no phonē. It is called aphona not because it has no sound, but [because] it sounds but is not measured" [Codex Barberinus Graecus 300 - Tardo, 151]. This quotation holds the key to a unique understanding of phonē. It is evident that ison "sounds," i.e., that the Byzantine musician and theorist had both the hearing and the understanding of tonality, of a single note as an acoustic phenomenon. At the same time, the "sounding" ison is called "aphona", i.e. soundless. At this stage of the analysis, we come upon a seeming contradiction, which will find its logical explanation. The question is: why is the "sounding" (which is specifically emphasized in the text) ison "soundless"? The text itself gives a clear answer: because "it is not measured". What does this mean? For the Byzantine musician, it is not the note as a tone itself that is informative, but the note, which is achieved by another note by moving in ascending or descending direction. This is also clearly communicated in the above quotation - the ison is not measured, but the phonē is produced by it.
The lack of instruments in medieval musical practice gives us a substantial reason for interpreting and defining phonē differently from our usual modern notion of both note and interval. For the Byzantine musician, the note is not a building block of music, if it is not achieved through an interval; in other words, the presence of an "interval" transforms a reached pitch into a musical phenomenon (a building block of the system). Therefore, the musician in Byzantium did not have an abstract notion of a single, individual note as the micro-structural material of musical language in the same sense in which Antiquity understood note as embodied through the string organs. It is this understanding that became standard in the West (also due to the influence of keyboard instruments). Of course, in perceiving music, the hearing ability of a man registers individual notes of a certain pitch (as was already noted in interpreting the above quotation). However, in Byzantine music, the notes are mere sub-elements - not autonomous building blocks of the language of music. The question, therefore, is not whether the note is heard, but what in a given musical practice is a building block, i.e. an atomic unit. According to Hieromonk Gabriel, “...an element is that from which something arises, as from a beginning, and in which it breaks down, as an in an end” [Codex Lavra 610 - Tardo, 187]. How does this thought reflect the idea of phonē? For the musician, who is performing only with his voice (i.e., vocally only), the musically informative note is the note that is achieved by an interval.
[...]
It was well studied by Maria Alexandru in her doctoral thesis. This is the concept of Papadike (basically a list of signs needed for psaltic art) and these signs are specified as phona and aphona, some which have sound and other signs which have not. Among musicologists Maria is the expert for the study of great signs (τὰ μεγάλα σημάδια), she started it with her critical edition of Mega Ison published among the CIMAGL, and then she did her doctoral thesis:
Maria Alexandru, Studie über die ‚großen Zeichen‘ der byzantinischen musikalischen Notation unter besonderer Berücksichtigung der Periode vom Ende des 12. bis Anfang des 19. Jahrhunderts [Study about the 'great signs' of the Byzantine musical notation with focus on the period between the 12th and the beginning of the 19th century] (PhD, University of Copenhagen, 2000).
The language is German, but it is full of Greek quotations taken from the original sources (without offering any translation). It has three volumes, but the second (appendix II) is simply a collection of lists of signs, how are the exact names and how are the subgroups classified:
Hagiopolitan classification, early Middle Byzantine classification, late Middle Byzantine classification, combination of late Middle Byzantine and Hagiopolitan classification, and Chrysanthine classification. Middle Byzantine refers to Papadike, the earlier Hagiopolites was the treatise preceding the tropologion (unnotated hymn books used until the 12th century), but some late Papadikai combine both classifications, Chrysanthos' classification is later and refers to his Theoretikon mega, published by his student Panagiotes Pelopides at Triest in 1832.

Unfortunately, Maria never published her thesis as a book like Klara, but if you are interested, I could upload this appendix here. She never abandoned the subject, because she is preparing together with Christian Troelsgård a critical edition of the huge corpus of Papadikai for MMB.

The phonic signs are subdivided as bodies (σώματα) and spirits (πνεύματα), but phone (ἡ φωνή) as a term means literally "voice", but refers to steps, since bodies move only one step, but spirits make them fly over several steps (αἱ φωναὶ). Thus, you get also larger intervals. As such φωνή refers to the movement between the tones, but the term for tone is taken from a musical art of memory and is phthongos (ὀ φθόγγος), and just means a kind of place where you define a certain tone such as πρῶτος, δεύτερος, τρίτος and τέταρτος. It could be fret on a keyboard of an instrument or a mnemonic place on the Koukouzelian wheel which is marked by an echema (τὸ ἤχημα).

The concept is still in use today, you can also not avoid these terms, when you teach today (as you know from your own experience), but it was already known in the Hagiopolites which divided the signs in groups known as τόνοι, ἡμίτονα, πνεύματα and μέλη, while Petropolitanus (refering to the National Library of Russia in Saint Petersburg, Ms. Gr. 495, f.1v-2) which she calls still "Hagiopolitan", is divided into τόνοι, πεύματα and ἡμίτονα.
 

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