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WALENTYNA WĘGRZYN-KLISOWSKA

THE ESOTERIC ROLE OF NUMBERS IN THE CREATION OF MUSIC

Contents of Article: Introduction, Pythagoreans on Numbers, Connections with the Greek, Phoenician, Canaanite Languages, Theory of Guido of Arezzo, Conclusion.

Attributing the role of symbols (gr. symbolon, sign, feature, prophecy, password) to numbers was a sensual representation of specific or abstract objects. It was also a way of representing relations, activities and characteristics. From all the symbols used in different cultures it was the numbers, being the most abstract, that grew to be the most important in science, art and religion. It is already known that in ancient religious cults numbers referred to either a single sign or a formula. Thanks to the hierarchy of numbers the Sumerian priests defined the importance of their gods and attributed to them the power over celestial bodies, elements and other natural phenomena (1).

The Sumerian system, created about four thousand years ago, was not the only one in antiquity. Similar systems that referred to the same assumptions were created later in India, Egypt and Greece (2). Numbers became essential for Greek philosophers to express the hierarchy of values, determine the origin of all things, and leave behind the chaos of our unawareness about the world and ourselves as its elements.

The fact that Pythagoras recognised the One, that is, the monad (gr. monas) to be the “origin of all things” also meant that defining a set of similarly featured multiplicities, using the number 1, was possible. The unlimited dyad (gr. aoristos dyas) was considered to be the natural base for the One. Boiling the symbol of unity down to a geometric shape, a circle divided into two parts by its diameter, enables us to understand the kabalistic system that defines the number 1 as the arche, the first sound, tone, an impulse which, to manifest itself, needs breath, that is, a principle characteristic for life, a motion expressed by the number 2. Together they form what was defined by some as logos. In this system, one and two form an inseparable whole. In this respect, number 2 is an aspect of number 1.

The Pythagoreans believed that the monad and the unlimited dyad, the unity that has two aspects is the source of numbers, and from numbers originate points (gr. semeia), labeled with the number 1, from points originate lines (gr. grammai), labeled with the number 2, from lines originate planes (gr. epipeda schemata), labeled with the number 3, and from them originate solids (gr. sterea schemata), labeled with the number 4. From solids originate the bodies, which we can sensually perceive (gr. ta aistheta somata) that they contain four elements: fire, water, earth and air. These elements intertwine, thus creating a rational, living world (gr. kosmos noeros, emsychos) in the shape of a sphere. Inside, according to the theory, lies the centre. As you can see, a circle can also be expressed using the number 1 and it is frequently used as a symbol of the sphere (3).

The Greeks also reached a conclusion that even numbers are finite and express opposing characteristics of things. The cosmogonic role of the number 1 represented for example in the form of a circle can be also interpreted as a circle divided into four equal parts that together constitute a unity expressed in the motion of the numbers 1 + 2 + 3 + 4 = 10. The aspect of motion and multiplicity in unity is represented by that operation. The number 10 symbolises a closed cycle of activity of the unity’s four basic elements (4).

In music it is the octave that represents the perfection of a circle. Defining intervals by dividing the octave into different parts was also represented by dividing the monochord, a kind of a whole, a unity, to create smaller particles. The representation of the godly order of the world in numbers was the cause of the creation of sequences – letters that could be represented in music by joining together different intervals, articulations and rhythmic models. Thus, the fully created codified system came to be the most basic catalogue of esoteric meanings. It was first expressed in the rhetorical-melodic relation and then in the melodic-rhythmic structures of numerical carriers formed on the basis of the accent of words. They also had the character of meanings used to express magical content, mostly used in rites and liturgy.

The meaning of ornamental figures created in such a way, along with their proper intonation and ways of using them, as well as combining them, formed the esoteric knowledge transmitted from master to apprentice in circles of priests of different religions. The believers that took part in rituals were not acquainted with the meaning of the catalogue of formulas used depending on the occasion by the priest-scholars. Such experiences came to the Roman Church, and then to the Byzantine Church from the ancient East and Greece. The esoteric speculations that appeared during the Middle Ages favoured the creation of different abstract theoretical systems. It was them who had a basic impact on the development of professional music. The Greek theory of ethos was also very significant (5).

The esotericism of sacred knowledge was the cause of creation and use of a different form of writing by ancient priests to express opinions about magical and religious knowledge. It was at first a syllabic writing restricted to two or three signs, the transcript itself included only consonants. It was impossible for the uninitiated to read this writing, for only adding vowels to the transcript gave it magical power, meaning and the proper way of pronouncing it. We can find marks of such usage in the book of Yetzirah, where the world is formed by three Sephirot. The first one defines sound – that is, intonation. The second one – closely connected to the first one – breath (life), that is providing a semantic form. Only the two Sephirot joined together become a word-body, a rhetorical-melodic formula – expressed by the number 3. The words Bereishit (in the beginning) and Berashith (He created) could be used here. The formula created that way could finally express what it was based on. However, without using vowels you could only create a framework of the denoted meanings. It is expressed in its fullest in the mentioned book of Yetzirah – also known as the Kabbalah (6).

Making the Greek alphabet dependant on Hebrew, Phoenician and Canaanite bound the understanding of the numerical interpretation of formulas in a pecular way, and that was included in the order of the world. The three highest Sephirot of the Hebrew Kaballah: presound – breath – logos, formed a conventional language that can be called the priests’ sacral language. Thereby, the thousands of names of God can be boiled down to three basic numbers understood as the beginning, the duration and the decay. Sound has these features. The basic values represented by letter-numbers reflect also musical divisions. That is how the basic notions of consonance, dissonance, harmony and disharmony were created, and the number, as the principle that ruled the world, was boiled down to unity. Its multiples and divisors provided different dimensions of reality. Dividing the octave into seven parts and dividing the circle left, however, fractions impossible to level. But the correspondence with musical phenomena was real. The Greek notions of point and line can be understood as a sound – melody, surface as a process and volume as a spatial form in motion. Together they formed a religious-magical system, providing the age to come with vital bases for the creation of music.

Attaching importance to melodic-rhythmic formulas existed in the whole of ancient East (ragas, maquams, sharakhans, nomos). They were noted as well within small groups that defined accents and the direction of melody. The music that was inseparably related with the religious cult was wholly based on a tradition expressed by letter-numbers and that is how it developed. It is because special care was given to the magical efficiency of prayers and following the proper structure. For example, it was characteristic to believe that changing a word caused a change of the formula. The Christianity adapted many of such formulas along with their symbolic meanings. All the melodies that appear in the Gregorian chant have their numerical equivalents in the sense of a letter code. Alleluia – 10, Amen – 6, Sanctus – 7.

Another significant fact is that the authors that wrote about music emphasised the great importance of understanding the singing. Such understanding was based on a profound esoteric knowledge that was fulfilled above all by a perfect understanding of the special transcript and the meanings and symbols it represented. The biblical “Songs of Songs”, psalms, lamentations etc. had special rhythmic-melodic models, maxims used to play them. Some of their names survived, like nginot, gittit and hanchilot, noted in the Hebrew language (7). The original transcript of the Lamentations of Jeremiah the Prophet also survived, it had special markings of word-letters on the headings. After some time the particular words acquired their own melodic-rhythmic structures, which could be joined into various melodies (8). Numerical interpretations from the Greek theory made their way to treatises from the Middle Ages. Boethius calls music a mathematical knowledge, very closely related to the soul of the universe. He also used Greek musical notation and some Greek terms to name musical formulas: tonos (9), tropos (10).

Alchemy, both in antiquity and the Middle Ages treated as magic (Egypt, Greece), was another source of esoteric knowledge. Many esoteric schools, based on the Pythagoreans’ and Plato’s teachings and often called hermeticism, were based on knowledge only for the initiated (11). A similar case appeared in the Middle Ages, where an allegorical form of transfer was popular (12). The mystical tradition raised from the Greek sources made possible the creation of a new, rationalistic way of creating music. From all the medieval theoreticians of music, the most prominent one was a Benedictine friar Guido of Arezzo (992 – about 1050).

While constructing his theory, he was greatly influenced by the ideas of Odo, the abbot of St. Maur. He was the first one to use a new musical notation that had its origins in the Greek way of transcribing instrumental music (letters). By changing their position and a set of combinations he obtained eighteen signs to register different notes and figures. Like his predecessors, he also used a syllabic transcript of the text by introducing the so-called phtongs that encircled the scale of the male’s voice. Nonetheless, the basis of his system was the phenomenon of vowel shifting. He got the idea from a Greek theoretician Nicomachus and adapted it to the Latin alphabet in the form of five vowels: a – e – i – o – u. As in the Greek theory, the first “a” took the central position as the symbol of the sun.

With the use of all the vowels, he created the solmization system, completed only in the 12th century by the Franco-Flemish school by adding the syllable “Si”. When writing the famous hymn “Ut queant laxis”, already based on this principle, he followed the letter-numerical rules. The whole hymn can be represented by the number 11, which is a symbol of the Holy Spirit and Christ. In the seventeenth chapter of his treatise “Micrologus”, Guido of Arezzo creates a sort of a handbook for the students of the schola cantorum, which he affixes with a significant commentary: “Everything that is spoken can be sung” (13). Neither syllables nor words can exist without vowels. When arranging vowels with their letter equivalents of the musical scale Guido of Arezzo obtained 15 sounds:

A – B – C – D – E – F – G – a – b – c – d – e – f – g – a

According to the further instructions of Guido of Arezzo, the interval skips can be filled with transition sounds. The creation of a whole system of vowel-based sounds by Guido was not only a handbook of composition, it is also a proof that the basis of constructing pieces were not the scales, but formulas based on letter-numbers. The composer’s task was to match these formulas with the wanted text, whose next vowels were used in the arrangement of sound equivalents of a defined pitch coming from the accepted scale.

Melodic-rhythmic sequences created on the basis of these principles survived in the Gregorian chant, and through it they transferred to the profane professional music, but still traditionally serving the liturgy. Since then, when they were used, they were always strongly related with the order of the liturgical year and a specific text, thus fulfilling the requirement of the full accordance of meaning – letter – number. It was the beginning of creating music on the basis of a widely understood tradition.

Completing the solmization system by using all of the vowels made the use of a diatonic scale possible. According to arithmetic, the basic number of a shiftable series was 4. It encircled the basic vowels a – e – i – o. The full system based on 5 vowels, after adding the “u”, was presented by Guido of Arezzo in the above mentioned treatise, at the same time creating a complete sound system needed to compose music:

a – e – i – o – u – a – e – i – o – u – a – e – i – o – u – a

e – i – o – u – a – e – i – o – u – a – e – i – o – u – a – e

i – o – u – a – e – i – o – u – a – e – i – o – u – a – e – i

o – u – a – e – i – o – u – a – e – i – o – u – a – e – i – o

u – a – e – i – o – u – a – e – i – o – u – a – e – i – o – u

| – A – B – C – D – E – F – G – a – b – c – d – e – f – g – a

a – e – i – o – u – a – e – i – o – u – a – e – i – o – u – a

e – i – o – u – a – e – i – o – u – a – e – i – o – u – a – e

i – o – u – a – e – i – o – u – a – e – i – o – u – a – e – i

o – u – a – e – i – o – u – a – e – i – o – u – a – e – i – o

u – a – e – i – o – u – a – e – i – o – u – a – e – i – o – u

Many years later, Guido of Arezzo was known as the inventor of music. He was the first and the only one to create a system for composing music based on the ancient numerical symbols and the rationalism. The religious efficiency of the compositions obtained was related to the usage of proper accents. Following the handbook of composition, speculative treatises on music were written to describe scales that were later matched with the already existing formulas. They varied along with the historical development, taking more and more interesting shapes, depending on the reigning style, techniques and executive possibilities. The religious-philosophical basis, however, remained common, it had strong Asian, Egyptian, Hebrew and the most perfect Greek roots.

The medieval theoreticians’ interpretations greatly darkened the image of “music creation” by perceiving music scales to be the base, even though they actually came into being as secondary phenomena. A great many of other consequences and interpretations are the cause of that kind of thinking that continues even today. Every musical analysis omits this vital aspect of the process of the creation of a musical piece, its identity, proper genesis of the basic melodic material and its development. Despite the great changes caused by the theory and the medieval interpretation of musical phenomena, the way of thinking of the “inventor of music” – Guido of Arezzo, was not fully discarded.

The principle of creating music that he constructed was still used during the Baroque as one of methods of formal structuration. An example of its use is the “Conclave Thesauri magnae artis musicae” from the year 1719, written by a Cistercian friar from Prague – Mauritius Vogt (14). Like Guido of Arezzo, he created a system of magical melodic-rhythmic formulas that could be freely shifted. Some traces of the Greek tradition-based way of thinking also appear in modern music. The presence of magic squares in the works of Roman Haubenstock-Ramati, the works of Edgar Varese, being a reference to a crystal structure and most of the works of Anton Webern are proof of that. Esoteric number symbolism, operating with rhetorical-melodic and rhythmic structures and models, can also be found, amongst others, in the works of Karlheinz Stockhausen (15) and Luciano Berio (16). Despite the great stylistic changes that took place during the development of music, the traditional mechanics of melodic-rhythmic formulas can be seen everywhere. Their shape, structure and the message they convey are deeply rooted in the ancient patterns led by the perfect Greek models.

PRZYPISY

(1) Cf. Rudolf Ranoszek (1988), „Religie Mezopotamii”, in: „Zarys dziejów religii”. Praca zbiorowa, red.: Józef Keller, Wiesław Kotański, Witold Tyloch i Bogdan Kupis, Warszawa, pp. 237- 259.

(2) Cf. Georges Ifrah (1990), „Cyfry i litery”, s.158-167; „Litery, cyfry, magia, mistyka”, pp. 168-172; „Indie – kolebka współczesnej numeracji”, pp. 200-222, in: „Dzieje liczby czyli historia wielkiego wynalazku” („Les chiffres ou l’histoire d’une grande invention”), transl. by S. Herman, Wrocław, Warszawa, Kraków, Gdańsk, Łódź

(3) Cf. Jamie James (1996), „Muzyka sfer. O muzyce, nauce i naturalnym porządku wszechświata” („The Music of the Spheres. Music, Science, and the Natural Order of the Universe”), transl. by Mieczysław Godyń, Kraków, pp. 45-46, 51-64. Juan Eduardo Cirlot (2000), „Kula”, in: „Słownik symboli”, transl. by I. Kania, Kraków, pp. 214-215.

(4) Juan Eduardo Cirlot, „Liczby”, in: „Słownik symboli” („Diccionario de símbolos”), op. cit., pp. 224-229.

(5) John Gray Landels (2005), „Muzyka w życiu, poezji i dramacie Grecji”, in: „Muzyka starożytnej Grecji i Rzymu” („Music in ancient Greece and Rome”), wyd. II, transl. by M. Kaziński, Kraków, pp. 17-40, 61, 129-148.

(6) Juan Eduardo Cirlot, „Litery”, in: „Słownik symboli”, op. cit., pp. 231-235. Cf. „Księga Jecirah. Klucz Kabały”, translation, introduction and commentary by M. Prokopowicz, Warszawa 1994.

(7) Cf. Curt Sachs (1981), „Muzyka w świecie starożytnym” („The rise of music in the ancient Word”), transl. by Z. Chechlińska, Warszawa, s. 82.

(8) Ibidem, s. 85.

(9) Ibidem, s. 218, 236, 276.

(10) Ibidem, s. 218, 236, 240, 271, 273, 276; Cf. też: „Tropus”, in: „Riemann Musik Lexikon, Sachteil”, red. Wilibald Gurlitt i Hans Heinrich Eggebrecht, Mainz 1967, pp. 996-997.

(11) Roman Bugaj (1991), „Hermetyzm”, Wrocław, Warszawa, Kraków. Cf. też: Franz Liessem (1969), „Musik und Alchemie“, Tutzing

(12) Roman Bugaj, „Średniowieczna alchemia europejska”, in: „Hermetyzm”, op. cit., s.139-165.

(13) Fragment pełnego tekstu brzmi: „Perpende igitur quia sicut scribitur omne quod dicitur, ita ad cantum redigitur omne quod scribitur. Canitur igitur omne quod dicitur, scriptura autem litteris figuratur…”. Curt Sachs podaje, że nabożeństwo w synagodze oparte na czytaniu Pisma świętego „było całkowicie przeniknięte muzyką”, Cf. „Muzyka w świecie starożytnym”, op. cit. s. 82. Były to antyfonalne kantylacje, kantora i gminy.

(14) Podaję za: Helmut Kirchmeyer, „Vom historischen Wesen einer rationalistischen Musik. Eine Studie über die Verwandlung der musikalischen Kombinationskunst von Guido z Arezzo bis zur Gegenwart”, in: „Die Reihe. Informationen über serielle Musik“, red. Herbert Eimert i Karlheinz Stockhausen, Wien 1962, pp. 20-21. Kirchmeyer podał tę informację za Scheringiem.

(15) Cf. Ryszard Mieczysław Klisowski (1999), „Rola improwizacji wokalnej w utworze »Stimmung« Karlheinza Stockhausena, in: „Wokalistyka i pedagogika wokalna”, „Zeszyt naukowy” nr 74, Akademia Muzyczna im. Karola Lipińskiego, Wrocław, pp. 50 -71.

(16) Cf. Ryszard Mieczysław Klisowski (2000), „Rola ezoterycznej symboliki w konstrukcji i realizacji utworu na solowy głos żeński – „Sequenza III” Lucian Berio”, in: „Wokalistyka i pedagogika wokalna”, „Zeszyt naukowy” nr 77, Akademia Muzyczna im. Karola Lipińskiego, Wrocław, pp. 164 -177.

NOTES

(2) Cf. Georges Ifrah (1990), „Cyfry i litery”, p.158-167; „Litery, cyfry, magia, mistyka”, pp. 168-172; „Indie – kolebka współczesnej numeracji”, pp. 200-222, in: „Dzieje liczby czyli historia wielkiego wynalazku” („Les chiffres ou l’histoire d’une grande invention”), transl. by S. Herman, Wrocław, Warszawa, Kraków, Gdańsk, Łódź

(4) Juan Eduardo Cirlot, „Liczby”, in: „Słownik symboli” („Diccionario de símbolos”), op. cit., pp. 224-229.

(7) Cf. Curt Sachs (1981), „Muzyka w świecie starożytnym” („The rise of music in the ancient Word”), transl. by Z. Chechlińska, Warszawa, p. 82.

(8) Ibidem, p. 85.

(9) Ibidem, p. 218, 236, 276.

(10) Ibidem, p. 218, 236, 240, 271, 273, 276; Cf. też: „Tropus”, in: „Riemann Musik Lexikon, Sachteil”, red. Wilibald Gurlitt i Hans Heinrich Eggebrecht, Mainz 1967, pp. 996-997.

(11) Roman Bugaj (1991), „Hermetyzm”, Wrocław, Warszawa, Kraków. Cf. też: Franz Liessem (1969), „Musik und Alchemie“, Tutzing

(12) Roman Bugaj, „Średniowieczna alchemia europejska”, in: „Hermetyzm”, op. cit., p.139-165.

(13) Fragment pełnego tekstu brzmi: „Perpende igitur quia sicut scribitur omne quod dicitur, ita ad cantum redigitur omne quod scribitur. Canitur igitur omne quod dicitur, scriptura autem litteris figuratur…”. Curt Sachs states that the service in the synagogue based on reading the Holy Bible „was completely pervaded with music”, Cf. „Muzyka w świecie starożytnym”, op. cit. p. 82. It consisted of antiphonal cantellation, cantors etc.

[The first version of this text was published in Heksis No. 1/1996, pp. 15-18.]