The Music of the Spheres” by R.I

Iordanis Eleftheriadis

Matr.Nr.: 61800336 The Pythagorean-cosmological concept of the composition “The Music of the Spheres” by R.I. Langgaard.

Masterarbeit zur Erlangung des akademischen Grades

Master of Arts

des Studiums KMA Violine

an der Anton Bruckner Privatuniversität Linz

Betreut durch: Univ.Doz. Dr. M.A. Hans Georg Nicklaus Mag. Predrag Katanic

Linz, 1.5.2019

Index

1. Abstract...... 4 2. Preface...... 5 3. The Theory of The Harmony of the Spheres. 3.1. Pythagoreanism...... 6 3.2. Pythagorean Philosophy...... 8 3.3. Mental/Listening abilities of Pythagoras ...... 9 3.4. What was Music for the Ancient Greeks?...... 10 3.5. Pythagorean Harmonic...... 11 3.6. Tetractys...... 13 3.7. Aspects of Harmony in Ancient Greece...... 14 3.8. Dualism...... 15 3.9. Pythagorean Astronomy...... 16 3.10. The metaphysical side of the Harmony of the Cosmos...... 18 3.11. Pythagorean models of Harmony of the Spheres...... 18 3.12. Important followers of the Harmony of the Spheres...... 19 3.12.1. Plato...... 19 3.12.2. Boethius...... 22 3.12.3. The first musical example of Music of the Spheres...... 24 3.12.4. Johannes Kepler...... 25 3.13. Philosophical extensions of The Music of the Spheres...... 27 4. The “Music of the Spheres” by Rued Langgaard. 4.1. Rued Immanuel Langgaard...... 28 4.2. Works...... 29 4.3. Langgaards’ „Music of the Spheres“...... 31

4.4. Performances and reviews by critics and papers...... 33 4.4.1. First Performance...... 33 4.4.2. Second Performance...... 36 4.4.3. Versions of the piece after 1922...... 36 4.4.4. Third Performance...... 38 4.4.5. Later Performances...... 38 4.5. Instrumentation...... 40 4.6. Song Text inside the Piece...... 41 4.7. Analysis of the piece...... 42 4.7.1. Episode 1...... 46 4.7.2. Episode 2...... 48 4.7.3. Episode 3...... 50 4.7.4. Episode 4...... 52 4.7.5. Episode 5...... 53 4.7.6. Episode 6...... 53 4.7.7. Episode 7...... 54 4.7.8. Episode 8...... 56 4.7.9. Episode 9...... 57 4.7.10. Episode 10...... 59 4.7.11. Episode 11...... 60 4.7.12. Episode12...... 62 4.7.13. Episode 13...... 63 4.7.14. Episode 14...... 64 4.7.15. Episode 15...... 64 4.8. Conclusion of the Analysis...... 69 5. Bibliography...... 70

1. Abstract

The main object of this Thesis is the composition of R. I. Langgaard, “The Music of the Spheres”. The same title was first used by Pythagoras as a philosophical theory. Although a few classical analyses of this composition were made by musicologists, the attempt of this thesis is to view it from a different perspective: A more philosophical one. After exploring the limited-saved original excerpts of the Pythagorean School, a comparison is made with Langgaard’s composition, to investigate if any evidence of this theory can be traced in this music.

2. Preface

I became very interested in Pythagoras’ life and work, especially when I first read about his view of world harmony and his Theory of Music of the Spheres. I tried to read as much as possible in order to understand this theory. I believe that because this philosophical theory is so connected to music, it led me to discover (by-then unknown to me) the great composition of R. I. Langgaard: “The Music of the Spheres”. After listening to the piece, I was certain that I needed to set it as my main focus for this Thesis, since its character and energy was so captivating. The form of my Thesis is shaped in a way, that a philosophical frame of the Pythagorean’s Theory is foremost established, and then an investigation begins, where it is examined if a connection between Pythagorean’s Philosophy and Langaards’ “The Music of the Spheres” exists. What I am very keen about, is the fact that what I present about that composition, is not merely an analysis from the musicological view, but rather a philosophical one, if I may call it that way. The most important and credible source used in this case, is that of Diels/Kranz in which, original fragments of the Pythagorean School are displayed in Greek. It was a privilege to be able to read and understand the excerpts in original and to research about this specific theme.

3. Theory of The Harmony of the Spheres

The person of interest in this first part of my thesis, came from Samos of Greece. A boy born in about 570 B.C., the child of a prosperous tradesman and a clever woman, who was by birth, dedicated to the Gods. His name was Pythagoras. He had a burning zeal for knowledge. As an adult he went to Egypt and studied in the College of Priests at Memphis or Diospolis, where he learnt and mastered the secrets of Egyptian science and religion. After moving on to Babylon, he also acquired some Indian and Persian philosophy.1

By the time of his return to Samos at 535 B.C., he was not only attracted and sort after by the Ionian School (a School of philosophers focusing on proving the geometrical proportions of all particular instances) a school he came across priorly in his childhood, but also interested in the systems of religion of the different cultures he came across, in comparison with the philosophical speculations of Thales about Nature and the form of the World.2

Before his migration to Cicely, where his work for which he is famous had been made, he had already gained big fame, recognition and influence as an intellectual. In about 529 B.C., he settled in Croton.3

3.1. Pythagoreanism

Soon after the defeat of Croton by a rival city, many reformations needed to be made and Pythagoras came at the right time. His personality and mind attracted attention by the Senate of the city, which later gave him permission to formulate an order, whose purpose was cleansing and restoration of public life. Pythagoras was the absolute ruler of the Brotherhood, which in the beginning had mainly religious character, but later on had educational, ethical, social and scientific facets. It is interesting to know the fact that women had the same place as men inside his, as nowadays called “religious cult”.4 Theano of

1 Rouse (1915), p. 5-6. 2 Rouse (1915), p.6. 3 Ibid., p. 6. 4 Ibid., p. 6.

Croton, the wife of Pythagoras, is considered a major figure in early-Pythagoreanism. She was noted as a distinguished philosopher and in the lore that surrounds her, is said to have taken over the leadership of the school after his death. 5 Pythagoreanism as a religious community relied on oral teachings and worshiped by Pythian Apollo. They preached an austere life, believing that the highest reward for a human was to avoid reincarnation to another body after their death, by leading the soul to live next to the Gods. Their strict rules in their everyday life to reach purity, could be explained as a punishment of the soul until it reached purity.6

The brotherhood of the Pythagoreans, whose thinking was different from that of the general population, led eventually to opposition and hostile events, which resulted to a political tragedy of the Order. After Pythagoras’ death, in about 501 B.C., the ruined Order transformed itself into a philosophical Society, whose doctrines affected the works of famous mathematicians and philosophers, like Hippocrates, Euxodus, Socrates and Plato.7

The Pythagoreans were very secretive about their lives and did not document their doctrines and philosophy. In the next translation of the text of the Neoplatonic philosopher Porphyry, this can clearly be stated:

“When the Pythagoreans died, with them also died their knowledge, which till then they had kept secret, except for a few obscure things which were commonly repeated by those who did not understand them. Pythagoras himself left no book, but some little sparks of his philosophy, obscure and difficult to grasp, were preserved by the few people who were preserved by being scattered, like Lysis and Archipus. The Pythagoreans now avoided human society, being lonely, saddened and dispersed. Fearing nevertheless that among men the name of philosophy would be entirely extinguished and that therefore the gods would be angry with them, they made abstracts and commentaries. Each man made his own collection of written authorities and his own memoires, leaving them wherever they

5 https://en.wikipedia.org/wiki/Pythagoreanism, 12.02.2019. 6 Ibid., 12.02.2019. 7Rouse (1915), p. 6.

happened to die, charging their wives, sons and daughters to preserve them within their families. This mandate of transmission within each family was obeyed for a long time.”8

3.2. Pythagorean Philosophy.

Because of the secrecy of the Pythagorean School, the only way that we can find information about what Pythagoras did teach, is from his students, the “Mathematicians”, who further developed the studies of their master. Some of those were: Hippasos of Mantapont, Alkmaion of Croton, Philolaos of Croton, Archytas of Tarent , Hiketas and Ekphantos of Syracuse. Although during the time of Pythagoras, all the theories, his life and his school of thought was secretive and not documented, these students wrote about them in their later years and that is how we now have fragments of the Pythagoras’ life and philosophy, which will be used later throughout this thesis.

According to Pythagoras, the purpose of the human life is to become in accordance with God’s will and work, which is the Order of the Cosmos.9 This Order of the Cosmos is the “Harmony and Number”, whose true being can be found in the secrets of the numbers, in which Arithmetic, Astronomy and Music have a connection to each other.10 The Harmony fits inside the body (through the number) and is therefore qualified, to realise and synchronise itself with the Creator. That is the purpose of Harmony in the World. In order for a human to realise it, he must put himself in a state of cleansing his body and soul, which will gradually give him access to wisdom. The body can clean the soul, only with the study of Music and Philosophy. This human soul comes from a godly origin of higher level, into our human level. This soul is immortal and changes bodies in the human world as she wanders around the existence, by either going upwards into a spiritual shape or downwards in the animal/plant-based existence. Its highest and final form is reached when the soul becomes a star in the skies where its true destination is.11

8 J. James (1993), p. 24. 9 Schavernoch (1981), p. 36. 10 Ibid. 11 Ibid., p. 37.

The connection between Heaven and Soul, or between Creator and Humans, was tied to the experience of the planetary sounds, which in the later years took the name Harmony of the Spheres. In the time of Pythagoras though, the word Spheres was first spiritual and then got a more realistic meaning of ball-shaped planets, whose movement in the skies was the centre of discussion and Pythagorean thought. Also, the idea of Harmony had a different meaning to the harmony we now know which has a musical meaning of the seven notes of the Octave.12

3.3. Mental/Listening abilities of Pythagoras.

Due to the lack of written testimonies and documents from the time of Pythagoras, indirect sources like Iamblichus of Chalcis wrote: “Pythagoras by focusing his listening and mind, could dip himself in the harmonies of the World. According to him, he was the only person, who could listen and understand the harmonies and the symphonies of the spheres and that of other planets. The universal music was much more excessive and superior than all mortal melodies, composed of different elements and multicoloured sounds, which come from ‘bodies’, whose speed, size and position differ a lot. These ‘bodies’ exist in space in relation to one another, based on musical proportions, producing a melody, which vibrates through the beautiful movement and the melodical twirl of the sky.”13

Pythagoras was trying to transfer and imitate the Harmony of the Spheres, by playing the Lyre, so that his students could listen and understand.14

According to Empedocles about the Harmony of the Spheres:

He (Pythagoras) had very sharp senses and that is how his genius and perception could be explained. 15

12 Ibid. ,p. 38. 13 http://users.uoa.gr/~hspyridis/kallipateira.pdf, 16.02.2019. 14 Ibid. 15 Ibid.

The Harmony of the Spheres cannot be heard by the human ear, because the psychical harmony of the believers, synchronised with the cosmic music, has been distorted by the long-term entrapment to one body.16

3.4. What was Music for the Ancient Greeks?

Music was for the Greeks, as Walter F. Otto wrote, not only a godly gift from the Creator to Humans, but belonged to the eternal order of the beings of the world.17 The name “music”, came from the Muses, the daughters of Zeus, also Goddesses "with the whole meaning of the word”.18 Music was therefore a godly owned figure, like in the Power of Music by Orpheus, Arion and others.

For the Pythagoreans, the power of music had psychotherapeutic and psych-hygienic meaning. According to their beliefs, specific melodic motions could have an influence on the soul and the power to direct it accordingly.19

According to Iamblichus, Pythagoras with the help of music, could teach and heal his students:

“Believing that the care of human beings must begin on the journey through sensory perception, seeing beautiful forms and figures, and listening to beautiful rhythms and melodies, he assigned music first to education, education by certain sages and rhythms that worked to heal the nature and affections of man. The forces of the soul were returned to their original, harmonious balance. So, he devised various means to contain and cure ill and mental illnesses. Yes, what deserves even more attention: for his companions, he sensibly put together the so-called music for provocation by using the music of a daemon to create mixtures of diatonic, chromatic and enharmonic modes, by which he could easily reverse the emotions of the soul and turn them into the opposite, as long as these were still born and raised in the people in a completely new and unconscious way, he was able to cause a stir in the sense of virtue, by the appropriate musical methods, as well as by medicinally

16 Ibid. 17 Otto, p.27. 18 Ibid. p. 28. 19 Schavernoch (1981), p. 40.

mixed remedies. In the evenings, when his disciples went to sleep, he freed them from the confusing reverberation of the day, completely cleansing their thoughts, enveloped in the waves of arousal, and creating peaceful sleeps filled with good, even prophetic dreams. When he got up, he freed them from sleep drunkenness, slackness, and drowsiness through certain peculiar songs and melisma performed in unmixed form, either by lyre or purely vocal.”20

For the first time in the history of the World, the Pythagorean philosophy gave a Unitarian harmonic design to the cosmos. The Universe was an organic whole, comprising of different parts and components of their final summation. Pythagoras, in order to explain the unity of cosmos, had to establish a single principle, that lies in the root of everything in the World and constitutes the original cause of Being. This principle (αρχή) was the number (αριθμός).21

3.5 Pythagorean Harmonic

The Pythagoreans and especially Pythagoras did not conclude their experiments the same way the scientists are now conducting. They did not conduct exact measurements on tensed strings, but only interpreted the experiences of everyday life, which had to do with observation of string and wind instruments. These observations led Pythagoras to discover the number proportions of the Octaves, fourths and fifths. 22

The results about Harmonics, that Pythagoras and some of his students like Archytas, Hippasos and Philolaos concluded were23:

1. To every note belongs a number. To two same notes (pitch), belong equal numbers and to two different tones unequal numbers. 2. Same intervals correspond to the same number proportions. 3. Symphonic intervals are produced by (w+1): w, and their multiples from w : 1.

20 Ibid., p. 41. 21 Berghaus (1992), p. 44. 22 Schavernoch (1981), p. 41. 23 Ibid., p. 42.

Pythagoras managed to discover the proportions of the symphonic intervals by experimenting on the monochord.

As the legend states, one day, Pythagoras walked by a blacksmiths’ shop, from which he heard the sounds of differently weighted hammers beating iron out of the smiths’ anvil. Pythagoras was amazed, as the sounds were sounding in total harmony between themselves. Intrigued as he was, he tried to reproduce the effects of these consonant sounds. That led him to invent the monochord. A monochord is an apparatus with one string stretched across its board. The string is divided in two parts as a movable bridge supports the string from beneath. The purpose of the movable bridge is to divide the string into different lengths.24 The movable bridge can specifically change the ratios of the string and produce different tones. These tones (Octave, Fourth, Fifth), which are in proportions to each other, also have the characteristic of sounding harmonious! They sound ‘together’.25

By the division of the monochord into two parts, exactly in the middle, he discovered the Octave, which has a proportion of 2:1. With the division to one third of the monochord, the Fifth tone was produced, as a ratio of 3:2, where 3 depicts the whole length of the string and 2, the two thirds. Lastly, by the division of the string to 4 parts, the tone produced by the third quarter, gives the Fourth (proportion of 4:3).26

The above-mentioned proportions of 2: 1, 2: 3, 4: 3, refer to the relations of the lengths of the strings, in contrast with today's opinion, which suggests that the tones depend on the number of oscillations of the strings.27

For the Pythagoreans, only these three intervals were the symphonic ones, which seemed to be produced by the first four numbers 1, 2, 3, 4, the sum of which built the famous Pythagorean Tetractys (1+2+3+4=10).28

24 Blackstone (2011), p. 8. 25 Blackstone (2011), p. 8.

26Schavernoch (1981), p. 43. 27 Ibid. 28 Ibid., p. 44.

3.6 Tetractys

According to Pythagoras, the whole Cosmos is based on the numbers 1,2,3,4. This tetrad is the ideogram of the whole creation.29 Pythagoras created the Iera Tetractys (Holly Tetractys) and he is considered to be the God of the Tetractys, because he was the only person able to” hear "and realise it mentally.30

Tetractys, was a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical representation of the fourth triangular number. It was one of the most important symbols of the Pythagorianism and had a mystical and secretive meaning in the Pythagorean Order. The Tetractys symbolises:31

1. The first four numbers symbolize the musica universalis32 and the Cosmos as: a. (1) Unity (Monad). b. (2) Dyad – Power – Limit/Unlimited (peras/apeiron). c. (3) Harmony (Triad). d. (4) Cosmos (Tetrad). 2. The four rows add up to ten, which was unity of a higher order (The Decade).33 3. The Tetractys symbolizes the four classical elements—fire, air, water, and earth. 4. The Tetractys represented the organization of space: a. the first row represented zero dimensions (a point). b. the second row represented one dimension (a line of two points). c. the third row represented two dimensions (a plane defined by a triangle of three points).

29 Ibid. 30 http://users.uoa.gr/~hspyridis/kallipateira.pdf, p. 7, 15.02.2019. 31 https://en.wikipedia.org/wiki/Tetractys, 15.02.2019. 32 The meaning of musica universalis will be explained later. 33 Berghaus (1992), p. 45, ” It is through number that unity as primordial principle of Being, extends into the material world an becomes multeity. But the material world, being a physical entity, must have a limit. This limit is inherant in the numbers 1,2,3,4. They create the point, the line, the plane and the volume. Adding up these dimentions, 1+2+3+4= 10, we exhaust the limits of physical extention. There is no number following 10 that is not encapsulated in the tetrad. Nothing can be added that does not already exist as a combination of these four numbers. Tetrad and decad are therefore the numbers of perfection. They create unity out of multeity, and multeity out of unity. They originate in the unlimited, absolute world, but when they extend into the physical world , they create a limited, yet perfect, unified system, a universe.”

d. the fourth row represented three dimensions (a tetrahedron defined by four points).

The realisation that the ratios of the numbers of Tetractys produce only harmonic intervals, gave Tetractys divine importance. In the Pythagorean School, every freshman who wished to enter the Order had to swear on the name of the Holy Tetractys. 34

Ratio Musical interval 2:1 Interval of Octave 3:2 Interval of Fifth 4:3 Interval of Fourth 3:1 Interval of Octave plus Fifth 4:1 Interval of two Octaves

3.7. Aspects of Harmony in Ancient Greece

Harmony does not necessarily involve number or measurement. It simply meant “fitting together” and the main conception was that the existence of two or more distinguishable elements, were somehow capable of mutual adjustment.35

From what Pythagoras found, by the word harmony in music, one understood the octave as the scale with help of the Lyre (with seven or eight strings). This term appeared, because the order of the notes in ancient Greek music was based on the tetrachord comprising from the fourth. The tone sequence of this tetrachord was upwards, from A over G, F to E. By adding a second tetrachord from above (E ', D', C ', B) one got the octave. Harmony is therefore a combination, the result of which is the scale, the octave, which in turn also contains the

34 http://users.uoa.gr/~hspyridis/kallipateira.pdf, 16.02.2019. 35 Lippman (1963), p. 3.

other two symphonic intervals, the fifth and fourth.36 The Pythagoreans referred to this Harmony and the scale as” divine”, because she has a godly-perfect nature.37

“Harmony” in mythology.

Harmonia, was the daughter of Ares (God of War) and Aphrodite (Goddess of beauty and love), while in the Attic version, Harmonia was not only the daughter of Zeus and Atlántida Elektra, but also the Mother of the Muses (taking therefore a musical perception).38

The meaning of Harmony changed through time:

Etymologically, Harmony (Armonia), Ar or Har enters a variety of verbs in the Indo-European languages, signifying the unification of conflicting elements into an ordered whole. Verbs in early Greek literature beginning with this etymon have a broad range of application and encompass not only the performance of music or the tuning of the instrument, but a physical and mental fitting together and pacification.39

Homer used ararisko (=connect), aresko (=adapt, reconcile, satisfy), arasso (=slam together, strike, play the lyre), and harmozo (=fit together). The last verb harmozo, has a physical meaning by Homer, but in later times it gained a diversity of meanings like (marry, arrange, administer, tune, kiss), according to Pindar, Herodotus, Plato, Aristophanes and Euripides. Harmonia developed not only as a physical “connecting link”, but also a mental “agreement”.40

3.8. Dualism

Pythagoreans used the principle of Dualism to describe and explain the world, according to which the principles of opposites are behind the construction of the world. Through the power of harmony, which is a cosmic-metaphysical ordering force, the world became a

36 Schavernoch (1981), p. 44.

37 Ibid. 38 Lippman (1963), p. 3. 39 Ibid., p. 4. 40 Ibid., p. 5.

meaningfully merging whole, the cosmos. Thus, harmony is born out of opposition: from the union of the opposite.41

The table of the opposites according to the Pythagoreans: 42 limited unlimited odd even unity plurality right left male female rest motion straight crooked light darkness good bad square oblong

3.9. Pythagorean Astronomy

For the Pythagoreans, and in particular for Archytas, the science of Geometry, Astronomy, Arithmetic and Music were very close to each other, since they deal with the being, the number and the size. In few words, the Pythagorean Astronomy is derived from the structure of Geometry and can be counted from the numbers of Arithmetic being further mastered by Music. The knowledge of Astronomy comes therefore from the knowledge of the Harmony of the Planets.43

Cosmos was seen by the Pythagoreans geometrically. They believed that the stars were spherical and that they moved in circular orbits. For them, both spheres and circles were connected to the Godly-element. The beginning and end of a circle are connected and

41 Schavernoch (1981), p. 46. 42 Anonymous Pythagoreans: Fragment No. 5, {Diels (1903), p. 281}. 43 Schavernoch (1981), p. 47.

therefore connected with the never-stopping and immortal existence, and all sides of a sphere are equidistant to its centre, so that makes them also equal and never ending.44

For Pythagoras Earth was the middle of the cosmos, around which all other “divine and eternal” seven planets were moving in circular orbits.45

Pythagoreans were the first ones who determined the order of the planets from Earth, according to their speeds, where the faster ones circled closer to Earth and the slower ones, with Saturn being the most distant, orbiting further away from Earth.

They also taught that the distances and the periods of time of the planets reacted according to the numbers. Each one of them represented a tone, building a certain Harmony, ito comprise the seven notes of a scale. The proportions of the orbit-distances of the seven planets and their relations of speeds form the intervals of this scale.46

The periods of planets were measured as whole numbers, which were showing that after some time, the seven planets were again in their original positions. This period of orbital rotation was called “Big Year” and the term played a very important role in the Pythagorean thought. The meaning of this “Big Year” was basically, the repetition of the same. The Octave, was an example of this repetition, which was seen as divine, because the same sound was produced, but not really the same, as it was in a different, higher pitch. This realisation was for them, a result of a great secret.47

Two more cosmic models were developed by the Pythagoreans, the first of which came from Philolaos, who believed that the Earth and the Moon, together with the other planets, were rotating around a central fire and secondly, from Hiketas and Ekpantos of Syracuse, who believed that the Earth is constantly moving in the middle of the cosmos with its own axis.48

Pythagoras and the Pythagoreans were the representatives of the observation and realisation of the natural phenomena, since they focussed on the Form and Shape of the

44 Ibid. 45 Ibid., p. 48. 46 Ibid. 47 Schavernoch (1981), p. 49. 48 Ibid.

World, and on the Unity of which the different parts of the world are made of. The shape of the world was found in the numbers and in Harmony. “The whole Sky = Harmony and Number”.49

3.10. The metaphysical side of the Harmony of the Cosmos.

It seems that they believed that in the Earth but also in the whole cosmos, Harmony exists in proportions and in symmetry and reveals Beauty and Eternity. The Harmony in Nature was also believed to extend to the Harmony of the soul of the human life and it’s interaction with the Harmony of the cosmos, through the relation of numbers and could bring someone to spiritual well-being, which was the purpose of Pythagoreanism. The extension of the Harmony of the Soul, could also lead to an internal understanding of Harmony, with a purpose of transformation and cleansing (catharsis) of the soul and the extraction of the internal divine-harmony. The Creator, who makes the planets and the stars rotate with specific rules, led people to follow that specific direction, the same that the Pythagoreans followed and proclaimed: Follow God.50

3.11. Pythagorean models of Harmony of the Spheres.

Pythagoreans and all those who succeeded them developed the harmony of the spheres from antiquity till modern years. They all tried to define the order of the planets and to assign them to the notes of the octave. This order changed a lot through the years, giving even opposite results as to the planets’ tone assignments.

The order of the planets seen in the following table according to Nicomachos, was determined by the planets’ rotating speed, which showed Saturn as the slowest planet and therefore the furthest away from the Earth and the Moon, with its fastest speed, the closest to Earth. In the middle was the Sun, as it was proven in the later years.51

49 Ibid. 50 Ibid., p. 50. 51Schavernoch (1981), p. 52.

Moon Venus Mercury Sun Mars Jupiter Saturn

3.12. Important followers of the Harmony of the Spheres

Pythagoras was the first person who, with the Harmony of the Spheres, tried to connect music and astronomy. He was the first person who, through geometric beauty, speculated the roundness of the world. According to him, all planets were moving around Earth with constant speeds, following orbits, which represented the same relationship of the musical scale with them, resulting in the sounds which were mentioned efore. This analogy, which is expressed from the Harmony of the Spheres, was the tool for discovering the secret of the cosmos.52 After Pythagoras, famous personalities of the Antiquity also believed in his theory and based their philosophies or sciences in the original Pythagorean theory, developing, explaining it or taking it to another level. Some of those followers are mentioned below.

3.12.1. Plato.

Plato modelled in his work “Timaeus”, an immense image of cosmology, which has its roots in the tradition of Socrates. The narrator in this dialogue-formed work is Pythagorean Timaeus, a fictional character of Plato narrating the story of creation of the world. God, whom Plato understands as Demiurge (Creator), whose essence is good, creates a visible cosmos according to the eternal archetype, directing the existing irregular and unorganised movements into one order. He made only one world, with the will that everything in this universe would remind Him of Himself as much as possible. The Creator formed the body of

52 Proust (2011), p. 358.

the Cosmos from the four elements, which relate to each other in geometric proportions, giving the ultimate spherical form, which is the most complete and perfect shape of all. The soul of the universe was created with the help of mixing, dividing and putting together, always in accordance to proportions, which as will be displayed later on, constitutes the Timaeus-scale. 53 The same proportions were used for the distance of the planetary-orbits to the Earth and between the planets themselves, so the intervals that came up referred in this musical harmony not only as the substance of the World Soul, but also the orbits of the planets that it included.

The Creator enclosed the World Soul with two circular and connected ribbons, like in the shape of X(chi), in two places. He left the outside circle undivided and turned horizontally to the right, while the inner one he divided in seven unequal circles as the orbits of the planets and turned diagonally and to the left.

The cosmos was created such that the sky and the heavens could be seen by people, but the Soul of the World could be only felt by thinking and Harmony.

Then God, after the creation of Sky, also created Time. Sky and Time were created in connection, as before Sky there could not be any days, nights, months and years and they pass by together.54

First came the Earth, then the Moon, the Sun, Venus, Mercury and other three planets. In that way, days, nights, months and years were created.55 These were used as a tool of time and therefore set in orbits.

The Creator used the four elements, which the world contains, which were Fire, Earth, Air and Water. He mixed these elements and in proportion created all the Stars and Planets, which seem to exist intelligently. Since God put the soul to the body and intelligence to the soul, all these planetary bodies must be Gods.

According to Timaeus, the order of the universe came from the development of the original idea of the Tetractys. There are two lines of numbers, banded together and starting from

53 Schavernoch (1981), p. 67. 54 Ibid. 55 Ibid., p. 68.

number 1. The left line derives from the three results by powers of 2 (1 2 4 8) and the right line from the three results by powers of 3 (1 3 9 27).

In total these 7 numbers refer to the number of the planets and the number of the strings of Lyra. The three symphonic intervals connect the parts together. The octave, seen three times (2 : 1, 4 : 2, 8 : 4), the Fifth (3 : 2) and the Fourth (4 : 3). Platon, through the number proportions, wanted to give the harmonic structure of the World Soul and also the relation to its planetary-orbits. Music from these Spheres, as an audible experience was not his purpose. These proportions would help Kepler later in about two thousand years to buid a Harmony, in which the Soul and not the ear, senses and hears.56

According to the numbers of Tetractys, music historians have built a planetary musical scale, like in the following example of Moberg, given in Schavernoch’s book57:

Planet Distance from Earth Interval Note Moon 1 Moon-Sun 6 Whole- f #’’’’ Tones. Sun 2 Sun-Venus 3,5 f #’’’ Tones. Venus 3 Venus-Mercury 2,5 H’’ Tones. Mercury 4 Mercury-Mars 6 f #’’

56 Ibid., p. 70. 57 Schavernoch (1981), p. 70.

Whole-Tones. Mars 8 Mars-Jupiter 1 f #’ Whole-Tone. Jupiter 9 Jupiter-Saturn 9,5 A Tones. Saturn 27

3.12.2. Boethius

One of the greatest followers of the Harmony of the Spheres was Boethius (477-524). 58

According to him, in his Book “De Musica”, he states that there are 3 types of music59. This was the first try, to put together the thoughts of ancient Greeks about music, in a more articulated way. According to him, there is 1) the unheard music of the spheres or celestial harmony (musica mundana, sometimes referred to as musica universalis)60, 2) the music that unites the body and the soul in a harmonious whole (musica humana)61 and 3) the music that we are all used to listening, which is the music produced by instruments or voice and the human ear is capable of listening (musica instrumentalis).62

1) The first type of music is the music that is produced by a celestial machine which moves so quickly, yet silent to our ears (explained with plenty of reasons). It can also be seen by the combination of the elements or changing of the seasons. This celestial machine works in such a perfect way, that although it contains extremely fast-moving and large bodies, it produces no sound whatsoever. Although each celestial body travels in higher or lower orbits, yet they all turn with equal force in a way that these dissimilar paths form one harmonious unity. When this celestial model is so perfect, then music, which comes from the proportions of the planet’s orbits, is also perfectly ordered and harmonious. The diversity on Earth generates a variety of seasons and fruits and forms the shape of the year,

58 Proust (2011), p. 360. 59Boethius: De institutione musica, I.2, p. 187, in: https://en.wikipedia.org/wiki/Musica_universalis#cite_note-6, 11.05.2019. 60 Ibid. 61 Ibid. 62 Ibid.

as we know it. But if the variety would disappear from the world, then everything would perish and lose their consonance. The same in music could be regenerated, if we loosened the low strings, making them even lower until there is no more substance, or if we put more tension to the higher strings, making them even higher until the strings would break. Therefore, everything in the universe and in the same way in case of music was made appropriately and fitting to perfection. The music of the Spheres suggests, that nothing is excessive and nothing goes beyond itself.63

2) The second type of music according to Boethius, the musica humana, is the type of music that someone can feel by focusing on himself and looking inside. A certain harmony is able to mix a non-corporal reason with the physicality of the body, as different elements of higher and lower tones, produce a well-balanced mixture of consonance. This type of harmony, since it is made of rational and irrational parts, is able to connect the different parts of the body with the soul.64

3) The third type of music, is the music which involves a certain number of instruments or voices. These are activated by either putting pressure on strings, winds, or aulos, or by water as in the hydraulic instruments, or by striking as in percussions. All these different methods of sound production create different sound characteristics of this musica.65

The relation of musica mundana and musica humana:66

“The divine mind descends through the hierarchies of the universe and carries the nature of its components into the human body. Thereby, the microcosmos is made to correspond to the macrocosmos. The octave is the tie by which God links the musica mundana to the musica humana. The decreasing degrees of spirituality are ordered in three diapasons, which reflect, the threefold division of the human soul: the spiritual sphere corresponds to the nine angelic hierarchies; the intermediate, or rational, sphere to the four elements. The descent from God to the human body, goes through six stages. A. pure mind, B. intellect, C. rational spirit, D. middle soul, E. vitalistic forces, F. the body as receptible for all things.”

63https://www.cengage.com/music/book_content/049557273X_wrightSimms_DEMO/assets/ITOW/7273X_01 _ITOW_Boethius.pdf, p. 1, 20.02.2019. 64 Ibid. 65 Ibid. 66 Fludd, Robert: Utriusque cosmi maioris scilicet et maioris metaphysica, physica atque technica historia. Vol 2, Oppenheim, 1619, p. 93. In: Berghaus (1992), p. 47.

3.12.3. The first musical example of the Harmony of the Spheres.

“The first musical example of the Theory comes from a Hymn written in the 7th Century, named Naturalis concordia vocum cum planetis, whose composer is not known and the manuscript uses a two-octave planetary scale, the first about the stars and the second about the happy beings (cherubim, seraphim ect.)”67.

67 Proust(2011), p. 361. With the term “happy beings”, the author most probably refers to the unearthy eternal creatures who directly attend to God according to Abrahamic religions. 68 http://www.17thcenturyideas.com/muziekw/scr/1/fvho.html, 21.02.2019. 69 https://www.google.com/search?q=Naturalis+concordia+vocum+cum+planetis&newwindow=1&source=lnms &tbm=isch&sa=X&ved=0ahUKEwizociO4czgAhXDC- wKHXbRCGwQ_AUIDigB&biw=1366&bih=625#imgrc=AZ5qoXyt4Ej22M, 21.02.2019.

3.12.4. Johannes Kepler (1571-1630).

J. Kepler was the greatest follower and developer of the Pythagorean philosophy at the time of the Renaissance. He was intrigued by the Harmony of the Spheres of Pythagoras, which mainly had a metaphysical concept, and he wanted to discover the connection between music and astronomy by himself. After publishing the “Mysterium Cosmographicum” (The Mystery of the Cosmos), he devoted much of his time, trying to explain the key of the true nature of Cosmos. In 1619, Kepler published the “Harmonices Mundi” (Harmony of the Worlds), positing that musical intervals and harmonies describe the motions of the six known planets of that time. He believed that this harmony could be heard by the soul, and that it gave a feeling of bliss and a feeling closest to imitating God. In his “Harmonices Mundi”, Kepler supported the argument that the creator connected geometry, astronomy and music and that the planets were arranged intelligently. “Harmonices Mundi” is split into five books, or chapters. In the first two books, he explained his idea that the five famous solids from the antiquity, define the orbits of the planets and their distances from the sun. In Book three, he focuses on musical harmonies, defining consonance and dissonance, intervals, problems of fine tuning, relations of intervals to strings’ length and what could be characterised as pleasurable. In the next Chapter, Book No. 4, he presents a metaphysical side of his system, with arguments for why the harmony of the world appeals to the intellectual soul in the same manner as the harmony of the spheres appeals to the human soul. Here he used this view of harmony to explain his argument of heliocentrism. In the last Chapter, Book N. 5, Kepler describes in detail the orbital motion of the planets and how this motion nearly perfectly matches musical harmonies. Furthermore, by focusing on the angular speeds of each planet, he discovered that the ratio of their maximum and minimum speed equals to a consonant musical interval. Taking it into the next step, by combining the planets together, these intervals generate more mathematical harmonies. The fact that these angular speeds, explain the orbit of every planet and together they move in harmony, made Kepler believe in a heavenly creator.70

Although, Kepler believed that the Harmony of the World was inaudible, he gave his theory in which every planet produces a tone, which is shown in the next Picture. The difference of

70 https://en.wikipedia.org/wiki/Musica_universalis, 22.02.2019.

Kepler's connection of every planet to a musical tone, was that, to him, each planet produced a polyphony by itself, since planets with larger eccentricities have a greater variation in speed, they produce more notes. For example, Earths’ maximum and minimum speeds, are in ratio of 16 to 15, or that of a semitone, shown below. Venus’ orbit is nearly circular, and therefore produces only one note. Mercury, which appears to have the largest eccentricity, has at the same time as the largest musical interval, that of minor 10th, or that of ratio 12 to 5.71

Kepler's’ music system according to the Solar system, was that the universe can be written in the musical score as, Saturn and Jupiter singing two Bass notes, Mars alone as Tenor, Venus and Earth as 2 Altos and Mercury the Soprano voice. This system, he believed to have sung in perfect concord in the beginning of time and there was still potential for future accordance. He was certain of the link between musical harmonies and the harmonies of the heavens that he mentioned “man, the imitator of the Creator, had emulated the polyphony of the heavens so as to enjoy the continuous duration of the time of the world in a fraction of an hour.”72

Kepler was a man of belief. He was so convinced of the existence of the Creator and his “proof” that the elliptical speeds of planets produce harmonious intervals, that although he led himself to mathematical inaccuracies (since he figured out that the ratios of Mars and Jupiter do not create a consonant interval), he brushed aside this problem by making the argument explained by his other theories in “Mysterium Cosmographicum”, that the values for the dimensions of the solids and the angular speeds would have to differ from the ideal values. This was, according to Kepler, the Creator’s way to compensate with the irregularities (since according to him, geometry and music were truly connected).73

71 Ibid. 72 Ibid. 73 Ibid.

3.13 Philosophical extensions of The Music of the Spheres.

If motion produces music, it becomes impossible to deny that all things that move, and therefore exist, have their own music-making. The chamber music of the stars becomes the concerto Grosso of existence. The music of the Spheres becomes an universal symphony, in which everything that walks, crawls, swims, flies, agitates is a performer, living by music and for music. Because, everything that lives, moves and everything that moves, creates sounds and eventually music. All existence is motion, all motion is music and therefore all existence is music. The Harmony of the Spheres is the place where science, religion and philosophy of Pythagoras meet.

Since every kind of movement, with the force of friction, produces a sound, it is reasonable to believe that planets also with their constant motions produce sounds. Of course, all sounds are not musical, as music that appears as noise in the beginning, after a period of time, can become lucid and harmonious to our ears. According to this view, progress in music consists of a continual extension of its frontiers over the world of dissonance. The noise can be eventually be perceived by our minds as harmony. To conclude, it is therefore possible that all audible sounds can become eventually music.

The Pythagorean tradition in music is capable of another extension. A poet named Rainer Maria Rilke focused entirely on experimenting in finding the way to the knowledge of God. He was convinced that human beings and their affairs are used in an instrumental way by the Creator. His discovery was that the Creator, to whom many nouns were given, like law- giver, judge, an embodiment of power and wisdom, a lover, was as a matter of fact a Creator of Song. This Creator was the primal musician, with his own melody, who was able to communicate to every creature, a motif that was the clue leading to the unravelling of the secret of His own obsession.

The conclusion of the Pythagorean tradition and of the Harmony of the Spheres, is that both in natural and supernatural orders, music is the medium in which the evidence of the artists’ soul lies in the artists’ work and the evidence of the Creator lies in the world of his creation.

If that creation transforms into motion, and that motion into a musical sound, then one concludes that the Creator is Himself a musician.74

4.The Music of the Spheres by Rued Langgaard.

4.1 Rued Immanuel Langgaard (28 July 1893 – 10 July 1952) was a late-Romantic Danish Composer and Organist, son of two pianists Siegfried Langgaard and Emma Langgaard. He showed musical talent from a very young age since, after taking piano lessons at the age of 5 with his parents and private teachers, he was able to quickly reach a very high level and compose his first pieces for piano and organ. Additionally, he also studied the organ and the violin.75

Already at the age of 13, Langgaard managed to publish his first compositions and was taught music theory and counterpoint by the famous composer Carl Nielsen. At the age of 18, Langgaard managed to achieve great honour and opportunity, when his First Symphony, “Mountain Pastorals”, was performed by the Berlin Philharmonic at a concert in Berlin.76

After the death of his father (1914) and his mother (1926), Langgaard married a young woman named Valborg Constance Olivia Tetens (known as Constance).

From the age of 18 until 59, Langgaard was appointed only temporarily as an organist of various Cathedrals and although he received a state grant at the age of 30, many of his works and job applications were rejected by the establishment. Due to this, he withdrew himself to Ribe, the oldest city of Denmark, and served as the permanent Organist of the Cathedral there. He died at the age of 59 totally unrecognised as a composer.77

74 Bennet (1945), p. 198-199. 75 The New Grove Dictionary of Music and Musicians, Volume 14, p. 243-244. 76 https://en.wikipedia.org/wiki/Rued_Langgaard, 10.03.2019. 77 Ibid.

4.2 Works78

Symphonies • Symphony No. 1 "Klippepastoraler" (Mountain Pastorals) (1908-09/1910-11), BVN. 32 • Symphony No. 2 "Vårbrud" (Awakening of Spring) (1st version 1912–14) • Symphony No. 2 "Vårbrud" (Awakening of Spring) (2nd version 1912-14/1926-33), BVN. 53 • Symphony No. 3 "Ungdomsbrus (La Melodia)" (The flush of youth (La Melodia) (effectively a piano concerto in one movement of about 30 minutes, 1915-16/1925- 33), BVN. 96 • Symphony No. 4 "Løvfald" (Leaf-fall) (1916/1920), BVN. 124 • Symphony No. 5 (1st version, 1917-18/1926), BVN. 191* • Symphony No. 5 "Steppenatur" (Nature of the Steppe) (2nd version, 1917- 18/1920/1931), BVN. 216*. • Symphony No. 6 "Det Himmelrivende" (The Stormy Sky) (1919-20/1928-30), BVN. 165 • Symphony No. 7 (1st version, 1925–26), BVN. 188 • Symphony No. 7 "Ved Tordenskjold i Holmens Kirke" (By Tordenskjold in Holmen's Church (2nd version, 1925-26/1930-32), BVN. 212 • Symphony No. 8 "Minder ved Amalienborg" (Memories at Amalienborg) (with mixed chorus, 1926–28/1929-1934), BVN. 193 • Symphony No. 9 "Fra Dronning Dagmars By" (From Queen Dagmar's City) (1942), BVN. 282 • Symphony No. 10 "Hin Tordenbolig" (Yon Hall of Thunder) (1944–45), BVN. 298 • Symphony No. 11 "Ixion" (1944–45), BVN. 303 • Symphony No. 12 "Helsingeborg" (1946), BVN. 318 • Symphony No. 13 "Undertro" (Belief in Wonders) (1946–47), BVN. 319

78 Ibid.

• Symphony No. 14 (Suite) "Morgenen" (Morning) (with mixed chorus, 1947-48/1951), BVN. 336 • Symphony No. 15 "Sørstormen" (Storm at Sea) (with bass-baritone solo and male chorus, 1937/1949), BVN. 375 • Symphony No. 16 "Synflod af Sol" (Deluge of the Sun) (1951), BVN. 417

Other orchestral works • Drapa (On the Death of Edvard Grieg, 1907–09), BVN. 20 • Heltedød (Death of a Hero) (1907–08), BVN. 24 • Sphinx (Tone Poem) (1907–13), BVN. 37 • Saga blot (A Thing of the Past) (1917–19), BVN. 140 • Symfonisk Festspil (Symphonic Festival Play) (1917–20), BVN. 166 • Prelude to "Antikrist" (original version, 1921–23), BVN. 170:1 • Music for "En Digters Drøm" (A Poet's Dream) (1923–26), BVN. 181 • Musernes Dans paa Helikon (The Dance of the Muses on Helicon) (Concert Ouverture, 1925/1939), BVN. 185 • Prelude to "Fortabelsen (Antikrist)" (Perdition (Antikrist)) (1921-23/1926-30), BVN. 192:1 • Prelude to "Komedien om Enhver" (Comedy of an Everyman) (1921-23/1936), BVN. 232 • The Danish National Radio (Fanfares, 1948), BVN. 351 • Mistèrio "Dødssejleren" (The Phantom Ship) after Liszt (1931–32)

Concertante works • Concerto (in one movement) for Violin and Orchestra (1943–44), BVN. 289 • Interdikt for Organ and Orchestra (1947–48), BVN. 335 • Søndagssonate (Sunday Sonata) for Violin, piano, organ and orchestra (1949–50), BVN. 393 • "Fra Arild" (From Arild), concerto for piano and orchestra freely adapted from compositions by Siegfried Langgaard (1935–37)

Chorus and orchestra • Drømmen (The Dream) (Sinfonia interna) (1915-16/1945), BVN. 98

• Hav og Sol (Sea and Sun) (with soprano or mezzo-soprano; version with chorus by Mike Cholewa after the composer's sketches, 1915/1940s), BVN. 102 • Sfærernes Musik (Music of the Spheres) (soprano or mezzo-soprano solo & choir, 1916–18), BVN. 128 • Fra Dybet (From the Deep) (soloists and choir, 1950–52), BVN. 414

Chamber music • String Quartet No. 1 (1914-15/1936), BVN. 68 • String Quartet No. 2 (1918), BVN. 145 • String Quartet No. 3 (1924), BVN. 183 • String Quartet No. 4 "Sommerdage" (Summer Days) (1914-18/1931), BVN. 215 • String Quartet No. 5 (1925/1926-38), BVN. 189 • String Quartet No. 6 (in one movement, 1918–19), BVN. 160 • String Quartet in A flat (1918), BVN. 155 • Violin Sonata No. 1 "Viole" (1915/1945), BVN. 94 • Violin Sonata No. 2 "Den store Mester kommer" (Behold the Master Cometh) (1920– 21), BVN. 167 • Violin Sonata No. 3 (1945–49), BVN. 312 • Violin Sonata No. 4 "Parce nobis, Jesu!" (1949), BVN. 376 • Septet (for winds, 1915), BVN. 95 • Humoreske (sextet for winds and drum, 1922–23), BVN. 176

Opera • Antikrist

4.3 Langgaards „Music of the Spheres“.

The „Music of the Spheres“ was composed between December 1916 and February 1918. It is important to our analysis and end results of this paper that, the detailed course of development of this piece is not known. After the first completion of the piece which was signed by the composer himself on December 1916, Langgaard wrote a letter to the music historian Godtfred Skjerne, asking for a reference to a presentation of Pythagoras’ thought

concerning the Harmony of the Spheres. He wrote “I know a little about the subject, but not as much as I would desire”.79

Emma Langgaard, the composers’ mother, states in a letter dated 16 January 1917, that the last piece named “Music of the Spheres” was to serve as an “instrumental introduction” to the scenic symphony “Sinfonia interna”, and partly to an independent piece named “Tone Symbol”. Emma Langgaard wrote “A work like this – I don’t understand how it has come about – but – when I now see it standing there, it seems to me to be an impossibility. Such a work can only be created once, and never again. All of it is like a heavy shower that falls on one’s head.”80

On January 1917, Rued Langgaard sends a letter to the Head of the Royal Danish Orchestra asking him to check his new piece with the possibility of performing it. Rued Langgaard stated “[…] As a kind of introduction to ‘Interna’ I have composed a piece of music that is called: ‘Music of the Spheres’ – I would very much like to show you this; perhaps you would consider playing it at a concert by the Royal Orchestra […] The piece – although I say it myself – might well command your interest – for it is even stranger than Debussy’s: Sirens! […].” He mentioned “Sirens” because this was last performed by the orchestra from the time that he sent the letter.81

After the completion of the piece for the first time and with the assumption that Langgaard read more in detail about the Pythagorean way of thought and the Theory of Harmony of the Spheres, he revised some details of the piece and configured it from an instrumental composition to a choral work also. In autumn 1917, the piece features under the title “Music of the Spheres, an echo for solo voices, choir and orchestra” (1916-1917). Although the contract for publishing the piece by the Wilhelm Hansen’s Music Publishing House came in December 1917, the final date that Langgaard himself finally signed the piece was February 1918, meaning that the piece was most probably expanded and different elements or corrections had been placed.82

79 Nielsen(2016), p. 5. 80 Ibid. 81 Ibid. 82 Ibid., p. 6.

4.4 Performances and reviews by critics and papers.

4.4.1. First Performance

The first performance of the piece had been scheduled for 1st of October 1918 by the Royal Danish Symphony Orchestra, but the performance was cancelled a few days before. The real reason of cancellation was unknown and there were two possible reasons. The first was because of the dangerous “Spanish flu”, that was expanding at the time, the National Board of Health forbid all public concerts in order to minimise the risk of flu-expansion. The other reason was because the Head of the Orchestra approved the piece and set it in the program to be performed without taking the approval of the program committee of the orchestra (which most probably did not like the composition) and therefore cancelled the whole performance.83

The actual premiere of the piece took place in Karlsruhe in 1921, after the German conductor Hans Seeber van der Floe accepted to perform it in his home town, inside a collection of pieces under the title “Nordic concert”. Floe travelled to Fredensborg in August 1921 to go through the work together with the composer, who spent the summer there. The concert was to take place in the Konzerthaus in Karlsruhe on 26 November 1921:

Karlsruher Zeitungs’ review on 28 Nov. 1921:84

“The effect of this wild orgy of notes on the audience was simply devastating. One saw individual members almost ﬂeeing from the concert hall. As if pursued by Erinyes. And when the composer was ﬁnally allowed to show himself, one can probably say is that he was not understood. The applause was for the orchestra and the conductor, who applied themselves to the work with admirable dedication.”

“[…] Langgaard absolutely follows his own path as a composer. The listener has to free himself completely from generally accepted musical conceptions, otherwise he will gain no rapport with this kind of “music”. He will otherwise be confronted with an insoluble riddle.

83 Ibid., p. 7. 84 Karlsruher Zeitung 28 Nov. 1921 under the heading Konzert-Wochen-Rückblicke. Signature: P. In: Nielsen(2016), p. 8.

[...] The composition remains a grotesque attempt. The title “The Music of the Spheres” or the subtitle “A Fantasy of Life and Death” convey nothing at all. During this music one can imagine everything and nothing. Even so, the climax, with the erupting cry of the choir, the eerie song of the bells and the horriﬁc booming of the drums has a shattering eff ect. A sinister dread breaks out from these sounds, as if announcing the Day of Judgment. If this climax could have been organically separated from the work, if the composer had striven to achieve a greater concentration, if he had explored more in depth than in breadth, one would not have been able to deny his work a certain recognition. In its present state, however, it is unbearable. It is the music of an arbitrary nature, the expression of a ﬂoundering, feral phantasy, one that one can neither excuse nor explain by such slogans as expressionism, futurism or cubism. [...]”.85

According to Karlsruher Tagblatt:86

“[…] Among the weirdest things one has heard in a concert hall for a long time was the ﬁ nal work “The Music of the Spheres” by Rud Langgaard. [...] “The Music of the Spheres” is of a completely different nature. Langgaard intentionally places himself outside what one understands by music. No real melody, no harmonic contexts – just notes, squeezed into shapes by a fanatic will, which are then meant to be a mirror of what Langgaard regards as life and death. This gives rise to a series of images, or mood pictures – but they do not elate or elevate. Through uniformness, frequent repetition of what has already been stated, too great lengthiness the listener becomes exhausted. Admittedly, quite a lot seizes and grips one despite all that is strange and bizarre. And one recognises in this work a quite distinctive personality, an artist who is passionately steeped in what he feels must be expressed in his own way. And the honesty of his creation is something one has to allow him. But the violently primitive nature of his language (just listen to what the women sing!), the often tormented and far-fetched nature of this music that seldom produces any bright, joyous sounds, has more of an oppressive than an exhilarating effect on the listener. In spite of this, one must thank Seeber van der Floe for having familiarised us with this idiosyncratic work. He involved himself with all the force of his personality as an artist in “The Music of the

85 Ibid. 86 Karlsruher Tagblatt, 29 Nov. 1921 (No. 330), ﬁ rst issue, under the heading Nordisches Orkester-Konzert. Signed H. Wck. In: Nielsen(2016), p. 9.

Spheres”. One had the feeling of his being completely permeated by the task of bringing to life a valuable creation. His contribution as a conductor was fabulous. The powerful ﬁnal climax – probably the best feature of the work – he brought out with full force. [...] The reception of “The Music of the Spheres” was (as could be predicted) divided. On the basis of the applause, Rud Langgaard was able to appear several times on the podium alongside his interpreters.”

Anton Rudolph from Badische Presse:87

“Pure music: no, – - Art, yes. Our inner eye gazes – with the individual sections into cosmic expanses and scenes and only through their clarity are rays reflected back into the mind. The ear as an eye – the influence of Wagner in this piece. He received the descriptively clear from the word, i.e. from poetry, the modern composers receive it from painting. The consequences must make an impact – the person that knows this can extract respect, even admiration, from this fantasy of Langgaard. Is anyone who has heard it able to deny that compared to the shallowness of Sibelius it has character and a will to express, i.e. artistic potency? As such, to be completely fair, we must consider it to be valuable product of our age. The reception was divided. That is understandable. Not everyone is prepared to take up the fight which, despite everything is so interesting and captivating as some phenomenon of nature.”

In Denmark, in the periodic “Musik and Politiken”, the work received the following two reviews:88

“ […] German criticism [would seem] to offer certain surprises. It is, for example, claimed that Arnold Schönberg pales alongside the atonal composer Langgaard, whose double orchestra conjures up what is a highly potent witches’ sabbath. It is hardly this kind of radicalism that until now has been most noticed by his fellow-countrymen.”

“[…] The work, which is extremely modern in form and content, was hardly understood by its listeners – local criticism writes – but Langgaard’s “incredibly powerful, often beautiful fantasy – and vivid orchestral ability” is the subject of many words of praise. It is felt that

87 Badische Presse 28 Nov. 1921, Abendausgabe. Signed A. R. [Anton Rudolph]. In: Nielsen(2016), p. 9. 88 Musik, vol. 6, no. 1, 1 Jan. 1922, p. 13. Unsigned. In: Nielsen(2016), p. 9.

“Arnold Schönberg” pales alongside Langgaard when it comes to ﬁnding new “possibilities for expression” – and it is said that here one is perhaps standing at the beginning of a new direction in music.”

4.4.2. Second Performance

On 10 of May 1922, after the bad critics, Langgaard attempted to present the piece one more time in Germany and particularly in Berlin. The concert was under the patronage of Queen Alexandrine, and comprised “Sphinx”, Symphony No. 2 and, after the interval, The “Music of the Spheres”. Immediately after the concert, at 11.21pm, Rued Langgaard sent a telegram home to his mother in Copenhagen with the single word “Prachtvoll” (magniﬁcent).89

Following the last performance, the Allgemeine Musik-Zeitung in Berlin wrote:90

“But then the gifted young musician lapsed into brooding over world and soul, death and resurrection, Christ and Antichrist, and sought new paths that express everything in music. And thus, there arose a horrific monster in terms of both content and form – unfortunately extremely down-to-earth non- music. One can already see this on glancing at the explanations: they contain no less than 15 different so-called themes [...]. Despite this apparent richness of inventiveness, however, one cannot deduce any gift of invention. These aphorisms are devoid of any suggestive expressiveness and capacity for development; once pronounced, they are finished. Their correlation is purely kaleidoscopic, without inner necessity they are strung together with the aid of a highly muzzy poetical-philosophical programme that even with the explanations to hand is impossible to grasp clearly. The huge apparatus is not sufficiently mastered, since the composer lacks any finer sense of sound or any economy in the use of the means at his disposal [...]”

4.4.3. Versions of the piece after 1922.

Langgaard continued to work on the piece even after the initial performances in Germany, writing a piano reduction in 1923. One year later, he presented a shortened and exclusively

89 Nielsen(2016), p. 9. 90 Allgemeine Musik-Zeitung, vol. 49/1922, 19 May 1922, p. 423. In: Nielsen(2016), p. 11.

instrumental version of the work, to the Royal Danish Orchestra, which rejected it. During the 1929-34 period, new versions of the work appeared, none of which, however, has been preserved. In January 1934, Langgaard made a new version, this time based on the printed version and including the entire ensemble: soloists, choir, orchestra, organ and bells. It is mentioned in several sources under the title “Nirvana”, a title that also had been linked to an instrumental version. Although Langgaard continued to change the piece and its name throughout the years, he always returned to the original version of title and index.91

Some of the titles he gave to the piece were:

• A Fantasy of Life and Death for solo voices, choir, large orchestra and a distant orchestra. • Titanic. • Fantastic Fantasy for Soloists, Choir, Orchestra and Organ. • The Abyss (Instrumentation Fantasy) • The Bruges-la-Morte-Bells (referring to Georges Rodenbach’s novel Bruges-la- Morte, 1892).

Langgaard about The Music of the Spheres, which was the title he finally settled with:

“In The Music of the Spheres I have, in night and despair, completely abandoned everything that is normally understood as motifs, intensive study, form and context. It is “Music” wrapped in black veils and impenetrable death mists. [Karl] Gellerup’s words ﬁt this “Music”: “– rest ocean of the world, the great silent sea that resounds deeply in the music of the spheres: – The melody of life faded blissfully away into the resting chord of eternity”.92

In addition to the title, he stated that the new motto was: “It may seen that the stars signal to us in friendly fashion, but the writing of the stars is cold and without mercy”.93

91 Ibid., p. 11. 92 Ibid., p. 12. 93 Ibid.

4.4.4. The Third Performance.

Ligeti about the piece:

The Third Performance of the piece (Stockholm in 1968) did not come until 46 years after the Berlin Performance and after Langgaards’ death. The rediscovery of the piece was accredited to the Danish composer Per Nørgård. He was a member of the selection committee under the Swedish organisation Rikskonserter (National Concerts), together with the famous composer Ligeti. As Nørgård describes, he attempted to put the additional copy of the “Music of the Spheres” in the pile of music scores that the committee had to examine and vote in the end, which pieces would to be performed in the Rikskonserter. When Ligeti took the score of Langgaard, he examined it thoroughly and then said: “Gentlemen! I did not know that I am – a Langgaard imitator”.94 Ligeti had observed the striking similarity in composition between “The Music of the Spheres” and some of his own works, written 40 years later – not least his “Atmosphères” from 1961. Additionally, he commented: “Truly an interesting score, a discovery. He has sound surfaces like the ones that were written in the 1960s. He makes use of a cluster technique – not chromatically but diatonically and with the same effect. At certain points he has two separate tempi – like a kind of present-day aleatoric music. Special instrumental effects: glissando on the piano’s strings. [...] But it is deﬁnitely late-Romantic as well – Wagner, Debussy...95.

4.4.5. Later Performances

The piece was performed finally for the ﬁrst time in Denmark during the Aarhus Festival Week on 14 September 1969 and in 1971 in one of the Danish Broadcasting Corporation’s Thursday concerts, with John Frandsen as the conductor.96

94 https://www.youtube.com/watch?v=0OX_4cJyhgI, 11.3.2019. 95 Nielsen(2016), p. 13. 96 Ibid.

4.5. Instrumentation

Main orchestra • Four flutes (doubling: piccolo) • Three oboes (doubling: cor anglais) • Three clarinets • Three bassoons • Eight horns • Three trumpets • Three trombones • Bass tuba • Timpani • Percussion • "Glissando-piano" (string piano) • Organ • Soprano soloist • Strings

Distant orchestra • Two flutes • Oboe • Two clarinets • Horn • Timpani • Harp • Strings

Choir

Organ

Solo Voice

4.6. Song Text inside the Piece

The author of the text was Ida Lock (1882-1951), whose name was only mentioned in the Berlin Performance (not mentioned at all in the original or in the publishers’ copy). In a printed copy of the score, however, Langgaard does hint who the author is, for he has added the initials I.O. after the song text. These initials were for Ida Ohlson, a student of Langgaards’ father. Ida Ohlsen married the Swedish shipmaster Martin Lock, but after as she became mentally sick, her mind was clouded as it was said and she was hospitalised. Ida Lock, then, was not a professional writer and did not publish anything. The poem must have been originally written in Danish, but no manuscript is known to exist, nor is there any certainty regarding the date of its composition.

The text which is sung in German is given below, together with the English translation:

“Wenn ich tauch‘ meine Seel‘ in die Tiefen von Schmerzen und Freud‘, in einem Blick, mir scheint es, als höre ich Töne einer fernen verklärten Musik, als ob wiederhallte der Luftkreis von Tönen voll Schmerzen und Qual, wie ein Echo von Seufzer und Klage aus dem irdischen jammernden Tal, wie die duftende klingende Welle, wie die lebende tönende Flut aus dem Lande vom Leid und Freude wo die Seele träumet und ruht.”

“When my soul is submerged in an ocean of tears and smiles from an eye, it would seem to have caught the music of a glorious symphony, the air seems charged with rhythm conceived in sorrow and pain transmitting its sad, sighing longing, and the sound of its haunting refrain through billowing waves of fragrance down a winding rippling stream from the ocean of tears and laughter from the souls’ ecstatic dream.”

4.7. Analysis of the piece

In the following part of the paper, a closer look will be taken inside the composition in order to detect, whether there are the elements that prove the existence of the Pythagorean Theory and to answer the questions that arise whether he was influenced by the theory, and if so, how and why. This will be presented in the conclusion of the Analysis. The basic tools that will be used for that kind of analysis, will be the proportions, or analogies and ratios since, as explained in the first part of the paper, these were the tools of Pythagorean philosophy. In the whole extend of the Analysis, the original fragments from the writings of the followers of Pythagoreanism given in the book of Diels/Kranz (1903), will be taken into account, to explain and shine light to the piece „Music of the Spheres “.

From the complete score of the piece, which is given additionally in the binder, I use coloured lines and shapes on specific excerpts, in order to make my arguments as clear as possible. Before every excerpt, I will always mention the pages in the complete score, in which my arguments can be found and be looked at in detail. In other words, I would advise the reader to have in their hands the complete score while reading my Analysis, because a more complete view of the piece is necessary.

A general overview

The composition lasts for about 35 minutes. It is a symphonic piece with choir, solo voice, organ and a second orchestra at a distance. It is not written in movements, instead in small episodes, if I may call them so, each one following the other without breaks or interruptions. There are 15 of these Episodes, the beginning of which is given by the composer as in the following photos, but also marked in the complete score.

1. Like sunbeams on a coffin decorated with sweet-smelling flowers 2. Like the twinkling of stars in the blue sky at sunset 3. Like light and the depths 4. Like the refraction of sunbeams in the waves 5. Like the twinkling of a pearl of dew in the sun on a beautiful summer's morning 6. Longing - Despair - Ecstasy 7. Soul of the world - Abyss - All soul's day 8. I wish ...! 9. Chaos - Run - Far and near 10. Flower wither 11. Glimpse of the sun through tears 12. Bells pealing: Look! He comes 13. The gospel of flowers - From the far distance 14. The new day 15. The end: Antichrist - Christ

Before we enter each and every Episode of Langgaards’ Music of the Spheres, we already detect the analogies, with which he titles the work. Most of them reveal their similarities to something else, which cannot even be expressed, and therefore he marked most of theme beginnings with the word like. So, these titles are not to be taken literally, but analogically, or in proportion (already a clue of Pythagoreanism).

Episode 1:

The first Episode consists of four similar events. With the term event, I characterise the shapes that appear in the whole extent of this composition. Each one of those have a clear beginning, middle and end (just as events in real life). In this Episode, the four events appear with a rhombical shape (beginning, middle, end). Our first clue in this research is showing itself by this number 4. According to Philolaos, the number 1 (in our case, our first Episode), is the unit of all things, so the unit of this Episode also.97 It unites together these four

97 Philolaos: Peri Fysios. Fragment No. 7. In: Diels/Kranz (1903), p. 252.

events, in which, number 4 was also considered as a highly important number for the Pythagoreans, according to the Tetractys, as mentioned before.98

The first event is shown in the next three Pictures.(Complete score: p. 5-6.)

The first event starts with eight divisi violins, then added by seven divisi violas, then the timpani comes in also to complete the fullness of the event and then slowly the seven divisi of the violas stop gradually one after another. Then violins do the same, until the moment only one violin voice plays.

98 https://en.wikipedia.org/wiki/Tetractys, 16.03.2019.

This event, when taken into a more microscopic view, seems that it begins with a cluster of eight different voices in the violins. The different tones of the cluster, which are included in the scale of E Flat Major, are heard all together in pp dynamic for three bars, as shown by the blue line. In the following 6 bars, the body that the first three bars created, is expanding downwards, as shown by the red line, step by step, in the key of E flat Major, increasing its density until the moment of tutti violins and violas playing for the first time together. The next six bars show the maximum volume/density and dynamic of the event, and right after, the body starts losing pieces of itself on a regular rhythm until it becomes so small in density and volume (which is shown in the third picture, where the violin 1 plays the e flat by itself).

This was the summary of the first event. But what is interesting for our research, is the fact that apart from the total symmetry that it has, even by just looking at it, it represents a big part of the Pythagorean philosophy because of proportions:

a. Speaking about voice density, the beginning eight voices (8), become sixteen (16) reaching the high point or climax (blue line), so proportion of 16/8= 2 (or double as many) and in the end only one remains, leaving a proportion of 1/8, than that of the beginning. b. From a time-point-of-view, the body of the high point lasts also twice as long (6 bars) than the body of the first 3 bars, giving again a proportion in time, that is 6/3=2. After the high point, the body loses material and recedes upwards, with double the tempo than the downwards expanding, giving once again a proportion of 2 (expands by whole notes, recedes by half notes). c. Dynamically, exactly the same proportions occur.

To sum up, before we continue to the other element of the Pythagorean philosophy, in the first event: Density, time and dynamic appear in proportions of 2.

The expansion and shrinking of this symmetrical body, depicts a Sphere. This Sphere increases itself very smoothly and symmetrically, becoming double and then shrinking by 16 times until it becomes a small point.

According to the original fragment No. 7 of Philolaos, he writes: “το πράτων αρμοσθέν, το έν, εν τωι μέσωι τας σφαίρας εστία καλείται” in which the number 1 (έν) is in the middle of

the Sphere of fire.99 Marked with the red line. We observe a descending scale starting from Violin 8 playing an e flat and then step by step down the scale after 6 bars. We hear the base e flat (also in proportion of an octave), which is the Tonic of the scale. Another way we could show the Tonic would be I. In other words, the Tonic (e flat) is heard in the middle of the event when it reaches its maximum density and then lasts for 6 bars. The last thing that seems to originate from the Pythagorean philosophy, is the fact that the scale marked with the red line reaches its destination (I) and completes its body, in bar 10. The number 10 is also an important number for Pythagoras, because it is the sum of all elements (1+2+3+4=10) which make the absolute perfection, or as Philolaos wrote” The true effect and nature of the numbers is hidden in the number 10.”100

To move on, the Sphere-shape that we described appears again in the next three times of the Episode, in different volumes and duration but always with the spherical expanding- shrinking shapes in complete symmetry.

To conclude, I believe that the first Episode is formed exactly according to the Pythagoreans and as Archytas wrote: There are three proportions in Music. A. The Arithmetical, b. The Geometrical and c. The Harmonical.101 As I analysed before, the whole Episode is written according to all these three proportions.

Episode 2:

Similarly in the second Episode, the circular motives shown in the following pictures in the green circles are moving in small orbits around changing points while connecting with each other through heterochronic entrances, while other voices ascend-descend, increasing and shrinking the body of this particular Sphere very symmetrically, in the voices of flutes and clarinets. (Complete score: p. 8-9.)

99 Philolaos: Peri Fysios. Fragment No. 7. In: Diels/Kranz (1903), p. 252. 100Ibid., fragment No. 11, p.253. 101 Archytas: Armonikos. Fragment No. 2. In: Diels/Kranz (1903), p. 271.

An accidental coincidence or a symbol of Pythagoreanism is the fact that in page 10, the same Sphere as in the beginning is presented again without any alteration. It can mean therefore, that this symmetrically perfect Sphere once more comes right in the perfect moment (p. 10).

Example of symmetry and proportion is also the following (Complete score: p. 11):

In this example, Langgaard changes the nature of the sound by changing the timbre of this descending scale in violins playing tremolo, to violas with a deeper sound and lastly by the horns, proportionally half the tempo of the scale. This is another characteristic of what

Archytas wrote about Harmonics, that the high sounds move fast and with power, while the low ones slower and weaker.102In the previous example, the motif played in a high timbre by 8 violins, changes to lower 7-viola timbre and then to a 3-horn timbre, which is half as fast.

Episode 3:

The third Episode is full of circular repeating motives and melodies moving around varied points in rhythmical variations, always in triads. Variations are of course another tool of proportions and analogies. The first motif alone by the Violin 1, spreads itself in the other instruments in different times and slightly changed, by always following the same analogy of circular orbits (Complete score: p. 12-13.):

One level in this Episode is the rhythmical repetition of the 4 timpani voices in every bar throughout the Episode as seen right below:

The element that brings “harmony” to the four different voices of the timpani is the fact that the sum of all notes in every beat is always adding up to 6, although they appear in

102 Archytas, fragment No. 1. In: Diels/Kranz (1903), p. 269.

totally other rhythmical places. This symmetry of the repeated timpani motif binds the whole Episode together from beginning to end.

In the same way this Episode goes on and on, but there is only one more important moment for us, when after the entrance of all these unexpected triads of circular motion, the 4 violas playing marcato point out the result, which is the Emphasis on the Fifths (2:3) (Complete score: p. 15.):

Episode 4:

This Episode starts with an interesting repeated rhythmical pattern between 4 flutes and 3 Horns, giving the impression of two motives {a. Three-note descending (Flutes) and b. Two- note ascending (Horns)} working in harmony together in relation to one another. They still form a wavy or half circular orbit in the first two and a half bars of this beginning just like in the previous Episodes (Complete score: p. 17.):

In the following 5-bar phrase, absolute proportion creates the expansion and shrinking of a circular phrase in triplets throughout its 5-bar duration. The circled motif (marked in orange) appears in each of those 5 bars, settling the basis of this excerpt, which builds up until the middle {addition of its mirror motif and its parallel (one third below)}, and gradually from the middle to the end, the added motives are removed (shrinking) leaving the original motif alone again. This excerpt has a proportion of 3:1 (as far as the density of circular motions) in the middle compared to its beginning and ending. This little circular event is depicted in perfect symmetry and proportion once again (Complete score: p. 18.):

Episodes 5-6:

In these two Episodes, the previous phrase: breaks into proportionally smaller and faster pieces, appearing unexpectedly from triads of instruments. At the moment they start to deviate from the pattern (usually by chromatic scales), another triad of instruments takes over, representing the same phrase but in a different rhythm (proportion in rhythm) and at different beats in the bar (proportion in time). (Complete score: p. 19.)

After the repetition of all these smaller pieces reappearing again and again, the rhythmical proportion changes again and becomes bigger, this time in the violins (whole bar has 6 quarter notes, so proportion of 3:2) playing (Complete score: p. 21.):

Episode 7:

The title of this Episode is “Soul of the World- Abyss- All Souls’ Day”.

In a few words this long Episode uses thematic material of sextuplets and timpani voices. The sextuplets are moving fast and in circles in chromatic and step-by-step motions, always around their own centre. They multiply themselves and they complex the whole Episode, giving a vague and mysterious character which evolves and wanders around constantly, without order and pause. The timpani voices, are constant throughout the Episode and they lead to an event where all of these never-ending irregular voices stop suddenly and the 4 divisi timpani voices take over, changing the whole Episodes’ nature.

The green lines of the first picture depict the gradual ending of the complex lines, which then give place to the timpani event of the next pictures (Complete score: p. 29-30.):

Proof of Pythagoreanism can be found in this Episode leading to the Abyss, if we consider that the connecting voice (timpani) represents this vibrating and mysterious earthquake, the Abyss. The souls of this World, move endlessly and without order through the sextuplets until they stop and they find themselves in the Abyss, produced by the 4 divisi Timpani. According to Archytas, the earthquake used to symbolise the gathering of the Dead, for the Pythagoreans.103

103 Anonymous Pythagoreans: Akousmata kai Symbola. Fragment No. 2. In: Diels/Kranz (1903), p. 290.

Episode 8:

The background of the eighth Episode is set by the successive alternation of two augmented chords (e #-d #).

The main incident though, happens by the Choir, which appears for the first time in the composition, repeating the same phrase 14 times. The choir sings a melody based on the proportional discoveries of Pythagoras. The melody consists of intervals of 4th (ratio of 3:4),

5th (2:3), semitone (256:243)104 and the previously mentioned notes of whole-tones (8:9).105 The interesting thing here is that by singing the mentioned intervals, they actually speak do- re-mi-fa-sol-la, giving a symbolic relation to the title of the piece which is … I wish! (Complete score: p. 31)

104 http://demonstrations.wolfram.com/SemitonesInPythagoreanTuningAnd12ToneEqualTemperament/, 13.5.2019. 105 Philolaos: Peri Fysios. Fragment No. 6. In: Diels/Kranz (1903), p. 252.

Episode 9:

For the first time the Orchestra in the distance makes its appearance. It is basically a smaller ensemble of the orchestra, something like a miniature orchestra playing from a distance in the concert hall and not directly on the stage. Because of its size it has a very distinctive sound.

Langgaard sets the Impetuoso character with the orchestra at a distance playing firstly alone. After the listener is adapted to the distance and character of this sound source in the hall, he lets the main orchestra in the middle of the stage play exactly on top of the distant one. It is very interesting, in this way, he practically puts together two different events in the hall which are presented one inside the other, or better, one in proportion or in direct reference to the other. This sound-alloy now created can be interpreted as the outcome between the original here-there, now-then, or as the title marks far-near. This musical interpretation of dualism allows him to explore physically, the dualism of Pythagorean philosophy.106

Additionally, Langgaard writes about the orchestra at a distance notation:” This composition (orchestra at a distance) is supposed without time, but is conducted with beats for each seventh eighth in the chief orchestra at which the orchestra at a distance gets 3 beats in a 4/4 time.”

Very clearly, it is said then, that the orchestra at a distance plays in relation to the normal beats and has a proportion of ¾, in relation to its 4 beats/bar. (Complete score: p. 39):

106 Philolaos: Peri Fysios. Fragment No.5. In: Diels/Kranz (1903), p. 251.

Episode 10:

This Episode, titled “Flower wither”, translates the negative effect of the word withering, from # to ♮ in its whole extent. In the introduction of the Episode, the withering is expressed by the notes of c# - c♮. (Complete score: p. 42):

The c# - c♮ relation becomes narrower: , which by double as fast notes (proportions 2:1) and by transposition to intervals of 4th and 5th (transposition

according to Pythagorean proportions), creates melodies as: . The circled intervals of 1) f# - f♮ and 2) g# - g♮ are now the intervals expressing the withering of nature. The same effect happens in the cadenza-like event at the end of this Episode, where the descending chromatic scale, marked with blue, is interrupted by the imperfect 5- (diminished) interval followed by its perfect 5th:

In a few words, it is concluded, that the deterioration of nature happens in this Episode by the imperfection of the Pythagorean proportion 3:2 (Fifth), which appears first diminished and then to its perfect condition. That exact perfection in nature will be easily understood in Episode No. 13, where nature is expressed through the perfection of the Pythagorean intervals.

Episode 11:

The first 8 bars of this Episode show its way of development. This 8-bar phrase is divided into 2 similar moving four-bar phrases, whose intervals are moving proportionally in the same directions.

Each of the following coloured lines move proportionally between the first 4 bars and the next 4 (Complete score: p. 44):

The same method of proportionally moving intervals creating similar melodies can be shown in the following example. Here, the created melodies enter in different times, creating a complex mixture of orderly-moving patterns:

Episode 12:

Here, symmetry is once again the purpose of Langgaard.

The title gives a clue of duality once again since it is marked as:” Look! He comes!”. That is another way to give a double location in space. One location is the “stable-here”, where the observer looks, and the other location is the “moving-there”, travelling and getting closer to the first one. The “stable-here” seems to be the introduction of the timpani 3-bar phrase, giving the excitement of the title “Look!”. The “moving-there" is represented by an 8-bar phrase, made by fast moving quarter notes, played for 8 non-interrupted times (symmetry), passing through the keys of D-Major/E-Major/F #- Major to end up in f-minor. It is travelling through these different tonalities, maintaining its original form and shape, upto the point where it reaches its destination which seems to be again the timpani 3-bar phrase, giving a sense of arrival and a complete symmetrical shape of the whole Episode. (Complete score: p. 49):

Episode 13:

The focus is given to the solo Singer for the first time in the work. The Singer sings allegorically the text, which was given earlier in this paper. The index of the text has no clear meaning, but it rather mentions many different details, which do not necessarily connect together, because their meaning is too broad. But, with this method the proportional- connection of the text can be linked together, creating a unity.

The title of this episode is “The Gospel of Flowers- From the far distance”. Here, the introduction-theme played by the Violins of the distant orchestra and the melody of the song, seem to be both based on ascending and descending intervals of 4th and 5th , around which different notes are put to only complete the melodies. (Complete score: p. 53):

The introduction-bars (Red=5th, Orange= 4th):

Likewise, in the Singers’ voice:

The title gives away the index of the Episode referring to nature. Pythagoras was observing nature and conducted experiments in order to understand and explain the whole cosmos. The whole principle of the cosmos can be found in nature as mentioned in the pages about Philolaos’ life: “ά φύσις δ’ έν τωι κόσμωι-πάντα”.107The experiments on the monochord is

107 Diogenes: Fragment No. 1 about Philoloas’ life. In: Diels/Kranz (1903), p. 243.

an example of observing nature, which led him to discover the ratios of the perfect intervals. Back to this Episode now, it can be assumed that Langgaards’ way to imitate the perfection hidden in nature and in cosmos through his music can be achieved by the extensive usage of the Pythagorean intervals of 4th, 5th, 8va .

In the same way, trying to create the Episode 14, titled “The new day”, he continues using the basic intervals that this “new day” is made of. (Red=5th, Orange=4th, Green=8va). (Complete score: p. 57):

Episode 15:

In the final Episode of the composition, dualism plays a big role. With the title Antichrist- Christ, Langgaard once again gives the relation of the opposites like limited-unlimited of the Pythagoreans.108

108 Philolaos: Peri Fysios. Fragment No. 1. In: Diels (1903), p. 249.

Although in the whole composition, we once again meet the philosophy of dualism, this time Langgaard chooses to express it with Christ and Antichrist. In the Pythagoreanism and specifically in Philolaos’ work, there is a reference to Demonic and Godly things.109 The good versus evil that Langgaard expresses with Christ and Antichrist gives a more present approach to the religious aspect of opposites.

The beginning of the new and final Episode of the composition is easily understood by the entrance of the full choir in fortissimo dynamic shouting only the letter “a”. It can be divided into three smaller parts, in which, the part A, represents the Christ-part and B. the Antichrist-one. The C. is a calm part occurring after a great long tension between the two opposites A+B. (Complete score: p. 61):

In part A:

The Choir sings in Fortissimo dynamic, only singing the letter a, without any stop from the beginning until the entrance of the B part. It works as the connection link between the opposites.

The whole A is in ff and fff (maximum dynamic).

The motif, first introduced by the first violins: , changes into

many phases and appears altered like: , or:

but always in resemblance with the original first theme. Through A. all instruments, in different times, break these original motives into smaller repeated

pieces like: , multiplying the tension and density of the voices in the orchestra. It finally leads to an explosion, which is part B.

109 Philolaos: Peri Fysios. Fragment No. 11. In: Diels/Kranz (1903), p. 253.

In part B:

The part B, although highly important, is written in only one bar. This bar lasts for one minute, as the composer marks, with the constant strings' tremolo, timpani rolls and piatti in ffff dynamic. The proof that this part represents the evil-Antichrist part, is the fact that the bells, previously ringing extravagantly throughout part A, suddenly stop.

The strongest characteristic of the Pythagorean philosophy in this part is that part B. appears to have no borders or specific limits, thus expressing the unlimited. According to the fragment No.7 of anonymous sources of Pythagorean School: “το γαρ κακόν του απείρου, ως οι Πυθαγόρειοι είκαζον, το δ’ αγαθόν του πεπερασμένου”, the bad or evil was represented by the unlimited and the goodness from the limited.110

Relation of A and B:

This perfect example of opposition is understood by the duration of the two parts. According to Per Nørgård, the duration of the tremolo (part B) marked as 1 minute, if compared to the A part, one realises that the two parts are in fact equal (in relation to the duration they last and the maximum dynamic of sound), no matter their different notations given by the composer. If we explore this more in detail, although part A is written normally for each instrument separately and specifically, aiming to create a huge and complex volume, part B is written as one fermata-bar tremolo in ff dynamic lasting for one minute. When one checks the duration of part A, one realises that this part is composed in such a way that it lasts exactly 1 minute, just as part B. They are therefore equal and opposite.111 Getting deeper into the Pythagorean philosophy, we observe that the A represents the limited part, because it is clearly written. It progresses and develops in a natural way, by dividing the elements of its original theme and adding them successively in every instrument.

Part B is clearly the unlimited part, since there is no real structure and its duration can approximately last 1 minute, which makes it impossible to be precisely counted or measured.

110 Anonymous Pythagoreans, p. 282. 111 https://www.youtube.com/watch?v=0OX_4cJyhgI, 19.03.2019.

In conclusion, looking at it from the Pythagorean point of view, the goodness is used to represent the limited (part A), and the bad/evil the unlimited (part B).112

In Part C:

After the explosion of part B, the tension disappears with a general pause for one bar before the C. Adagio part starts. In this last part everything seems to come back to normal and in order. The marking is Adagio molto, piano e misterioso, creating a calmness on one hand, but also an exploring feeling of dropping harmonies of Dominant 5ths. In that way Langgaard goes through every harmony by simply following the Pythagorean proportion of circled-dropping-Fifths (2:3).

The harmony changes every half note as: A7 D7 G7 C7, (then repeats half for one bar) A7 D7, and then a bigger circle of dropping 5ths start) B7 Eb7 Ab7 Db7 Gb7 Cb7. The circle gets even bigger passing by more harmonies like: G7 C7 F7 B7 Eb7 Ab7 Db7 Gb7 and finally finishing and staying in Eb7, which is considered to be the original key that the Music of the Spheres begun with:

112 Anonymous Pythagoreans, Fragment No. 7. In: Diels/Kranz (1903), p. 282.

The piece finally ends with a mysterious cluster of notes, creating a big crescendo- decrescendo over 4 bars and disappearing into nothing.

4.8. Conclusion of the Analysis

In Music of the Spheres, Langgaard seems to have gathered together all the instrumental and vocal possibilities existing, in order to form and express a complete and ultimate meaning. In this composition, he combines the expressivity of an orchestra, a choir, the organ and solo voice with a very innovative idea: the orchestra at a distance.

Although with the title “Music of the Spheres”, one may believe that the composition’s purpose is to perhaps create the music that the different Spheres (planets) produce, Langgaard himself named the subtitles of the different parts of the composition, which have no relevance to planetary music. Most of the subtitles work in a kind of enigmatic way aiming to express a similarity to something else, or to project a deeper idea and that is why many of them start with the preposition like. Langgaard very smartly, even from the titling point of view, managed to give a hint of the purpose of this music, which connects seemingly irrelevant to each-other, pieces of life together, to create a unity or harmony.

The whole Pythagorean school of thought was trying to analyse and understand the harmony that the cosmos appeared to have.

Langgaard through his music not only used the idea of Pythagoreanism in focusing on Nature and how perfect Nature is, but also used the Pythagorean tools (proportions) to express it.

The direction of Music of the Spheres heads clearly to the biggest climax, in its 35 min. duration, which is in the last Episode. This Episode, titled Christ-Antichrist, seems to be the ultimate destination of the piece. The relation of the opposites, like Christ and Antichrist in this case, is the essence of Pythagorean Philosophy, and therefore where Langgaard wants to lead us through his music, in order to feel the dualism, which was the key of understanding the cosmos.

In conclusion, Langgaards’ Music of the Spheres, using Pythagorean philosophy, aims to create (musically), the harmonic perfection of the cosmos.

5.Bibliography

Bennet, Victor: Thoughts from Pythagoras. Music and Letters. Vol. 26, no. 4, 1945, JSTOR, www.jstor.org/stable/728030.

Berghaus, Günter: Neoplatonic and Pythagorean Notions of World Harmony and Unity and Their Influence on Renaissance Dance Theory. Dance Research: The Journal of the Society for Dance Research, vol. 10, no. 2, 1992, JSTOR, www.jstor.org/stable/1290654.

Blackstone, Lee: Remixing the Music of the Spheres: Listening to the Relevance of an Ancient Doctrine for the Sociology of Music. International Review of the Aesthetics and Sociology of Music, vol. 42, no. 1, 2011, JSTOR, www.jstor.org/stable/41228640.

Christensen, Erik: The musical Timespace. A Theory of Music Listening. Aalborg University Press, 1996, https://www.researchgate.net/figure/Graphic-symbols-representing-the- intervals-of-the-chromatic-scale-For-distinction-of_fig4_209436138.

Diels, Hermann/ Kranz, Walther: Die Fragmente der Vorsokratiker, Griechisch und Deutsch. Berlin, 1903, https://archive.org/details/diefragmenteder00krangoog/page/n298.

Godwin, Joscelyn: The Harmony of the Spheres: The Pythagorean Tradition in Music. Rochester, Vermont, Simon and Schuster, 1992, https://books.google.at/books/about/The_Harmony_of_the_Spheres.html?id=74qPQgAAC AAJ&redir_esc=y.

Harap, Louis: Some Hellenic Ideas on Music and Character. The Musical Quarterly, vol. 24, no. 2, 1938, JSTOR, www.jstor.org/stable/738976.

James, Jamie: Music, Science and the Natural Order of the Universe. New York, 1993, https://books.google.at/books/about/The_Music_of_the_Spheres.html?id=sVDqE3Qsd20C &redir_esc=y.

Kinkeldey, Otto: The Music of the Spheres. Bulletin of the American Musicological Society, no. 11/12/13, 1948, JSTOR, www.jstor.org/stable/829272.

Lippman, Edward A.: Hellenic Conceptions of Harmony. Journal of the American Musicological Society, vol. 16, no. 1, 1963, JSTOR, www.jstor.org/stable/829917.

Nielsen, Bendt Viinholt: Rued Langgaard, The music of the spheres (BVN 128). The Rued Langgaard Edition and Edition Wilhelm Hansen AS, Copenhagen, 2016.

Proust, Dominique: The Harmony of the Spheres from Pythagoras to Voyager. In: The Role of Astronomy in Society and Culture. Proceedings of the International Astronomical Union, IAU Symposium, Volume 260, Paris, 2011, http://adsbit.harvard.edu/full/2011IAUS..260..358P/0000358.000.html.

Rouse, W. W. Ball: Pythagoras. The Mathematical Gazette, vol. 8, no. 115, 1915, JSTOR, www.jstor.org/stable/3602290.

Schavernoch, Hans: Die Harmonie der Sphären. Die Geschichte der Idee des Welteneinklangs und der Seeleneinstimmung. Freiburg/München, 1981.

Solomon, Wyatt Jason: Spatialization in Music: The Analysis and interpretation of spatial gestures. Athens-Georgia, 2007, http://getd.galib.uga.edu/public/solomon_jason_w_200705_phd/solomon_jason_w_20070 5_phd.pdf.

Dictionaries

The New Grove Dictionary of Music and Musicians. Volumes 13/14/15/17. Macmillan Publishers Limited, London New York, 2001.

Videos https://www.youtube.com/watch?v=pTV9RM-7Xhg&t=25s https://www.youtube.com/watch?v=REqFSOu0Frg

Webpages https://en.wikipedia.org/wiki/Musica_universalis

https://en.wikipedia.org/wiki/Music https://www.futuresymphony.org/the-music-of-the-spheres-or-the-metaphysics-of-music http://users.uoa.gr/~hspyridis/kallipateira.pdf, translation from Greek language. http://www.jazzbluesrock.gr/h_mousiki_twn_sfairwn_1119, translation from Greek language. https://omadaorfeas.blogspot.com/2017/09/pythagoras-mousikh-sfairwn-sympantikh- mathimatikh.html, translation from Greek language. https://www.nea-acropoli-athens.gr/arthra/astrologia/229-i-mousiki-ton-sferon-kata-ton- kepler, translation from Greek language. https://www.gramophone.co.uk/feature/introducing-your-next-great-musical-discovery- rued-langgaard http://www.musicsalesclassical.com/composer/short-bio/rued-langgaard https://www.npr.org/sections/deceptivecadence/2010/09/12/129813223/classical-lost- and-found-rued-langgard-s-mystical-musical-universe https://en.wikipedia.org/wiki/Pythagoreanism https://pdfs.semanticscholar.org/998a/b5c0d628683e4f18226b498200e727e23332.pdf http://adsbit.harvard.edu//full/2011IAUS..260..358P/0000358.000.html http://demonstrations.wolfram.com/SemitonesInPythagoreanTuningAnd12ToneEqualTemp erament/

Eidesstattliche Erklärung

„Hiermit erkläre ich eidesstattlich, dass ich die vorliegende Arbeit selbstständig und ohne fremde Hilfe verfasst habe. Alle Stellen oder Passagen der vorliegenden Arbeit, die anderen Quellen im Wortlaut oder dem Sinn nach entnommen wurden, sind durch Angaben der Herkunft kenntlich gemacht. Dies gilt auch für die Reproduktion von Noten, grafische Darstellungen und andere analoge oder digitale Materialien. Ich räume der Anton Bruckner Privatuniversität das Recht ein, ein von mir verfasstes Abstract meiner Arbeit auf der Homepage der ABPU zur Einsichtnahme zur Verfügung zu stellen.”