Spherical harmony

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As harmony of the spheres or spheres of music (after ancient Greek σφαῖρα sphaira "ball") is defined as originating from ancient Greek idea that in the movements of celestial bodies and their supporting transparent balls ( spheres ) tones arise, the amount of which depends on their distances and speeds. The tones result in a harmonious harmony (Greek symphōnía ), which, however, is usually not audible for people. This idea comes from Pythagoras of Samos or his followers, the Pythagoreans , and forms an essential element of Pythagorean cosmology . This was based on the conviction that the cosmos is a whole that is optimally ordered through mathematical proportions and that therefore the same principles are shown in astronomy as in music. In a figurative sense, the term “music of the spheres” is also used today for the transfer of proportions from astrophysics into musical relationships.

Astronomical requirements

The basis was the geocentric view of the world, represented by the vast majority of astronomers and philosophers in antiquity, with the earth as the resting center of the universe around which all celestial bodies revolve. This was associated with the idea of ​​“spheres”. This was understood to mean transparent, uniformly rotating hollow spheres arranged concentrically around the center of the world, to which the stars are attached. According to the model, this attachment means that the celestial bodies are kept in their constant circular paths. So your movements are a result of the rotation of the invisible spheres. The outermost sphere is that of the sky of the fixed stars; all fixed stars are attached to it. In addition, there are the spheres of the five planets known with the naked eye, Mercury, Venus, Mars, Jupiter and Saturn, as well as those of the sun and moon, so a total of eight concentric spheres. However, the inadequacy of a model limited to eight spheres was already in the 4th century BC. Obviously, since many of the observed movements could not be explained with it. Therefore, the astronomer Eudoxus of Knidos assumed additional spheres with the same center but different axes of rotation. In his system he needed three each for the sun and moon and four each for the five planets, that is, together with the fixed star sphere 27. The composite movement of the celestial body resulted from the different spherical movements. However, like his student Callippos of Kyzikos , who introduced seven other spheres, he did not regard these spheres as physical reality, but only as a conceptual construct for the purpose of geometrical illustration. Aristotle, on the other hand, understood the spheres as real crystal balls.

The Pythagoreans did not hold a uniform view in astronomy; whether Pythagoras himself, who in the 6th century BC BC lived, already had an elaborate astronomical doctrine and what this possibly looked like is unknown. In the second half of the 5th century, the Pythagorean Philolaos assumed a central fire invisible from the inhabited part of the earth in the middle of the universe, which is orbited by all celestial bodies including the earth. Whether an acoustic heavenly harmony was provided in this system is debatable. The concept of celestial harmony was apparently part of the oldest Pythagorean model, widespread before the middle of the 5th century, which included a non-rotating earth as the center of the world. It is unclear whether the early Pythagoreans in the 6th and 5th centuries assigned spherical shells to the individual planets; presumably they only assumed a sphere for the fixed star sky and considered the planets, to which they also counted the sun and moon, to be freely movable. In this case the term "harmony of spheres" is misleading. In any case, the early sources speak neither of music of the spheres nor of harmony of the spheres, but only of heavenly harmony. The planetary spheres were only mentioned explicitly in the 4th century BC. At Eudoxus of Knidos.

Physical concept

The oldest evidence for the concept of heavenly harmony among the early Pythagoreans comes from the 4th century BC. Chr .; it is information from Aristotle and an indirect reference in a fragment from a lost work by the Pythagorean Archytas of Taranto . Furthermore, indistinct traces of it can be seen in Plato's cosmology.

According to Aristotle, the underlying train of thought was physical. The starting point was the experience that fast movements of large bodies on earth are associated with noises. The Pythagoreans therefore assumed that the movements of the much larger and faster celestial bodies must cause much louder noises. So every planet produces a sound. It was assumed that the pitches depend on the speeds and the distances to the center of the world, the earth. It was assumed that the distances between the planetary orbits result in the proportions whose acoustic result is musical harmony. The starting point for these considerations were observations on the monochord - allegedly invented by Pythagoras - with an adjustable bridge (called "canon" at the time). It can be used to show the inversely proportional dependence of the pitch of a vibrating string on its length, with which the musical harmony can be expressed as a mathematical proportion. From the proportions of the string lengths and their effects, analogous properties and phenomena in the distances between the planetary orbits were concluded. The Pythagoreans attached great importance to the mathematical correspondence of the musical with the cosmic harmony, since their worldview assigned a central role to the numbers and their proportions.

The reason why we do not hear anything about it is given by the Pythagoreans that a perception only reaches our consciousness if the opposite or the absence of what is perceived can also be experienced. Accordingly, people do not notice the heavenly harmony because it sounds continuously and thus the contrast to an opposite silence is unknown. Archytas found another reason; he said that the human ear canal is too narrow for such a powerful sound. However, since some followers of Pythagoras ascribed superhuman abilities to the master, they trusted him to still hear the heavenly harmony. Walter Burkert connects this with the “shamanism” that he adopts in Pythagoras. Cicero said that we are "deaf" to the sound of the sky, just as people who live near the Nile cataracts do not notice the constant noise of the water. Aristotle had already made a similar comparison with blacksmiths who no longer perceive the noise after getting used to it.

Since it was assumed that all planets move uniformly on their circular orbits, it had to be concluded that each planet only ever produces a single unchangeable tone and that all tones always sound at the same time at a constant volume. Therefore the harmony of these tones could only be thought of as a single constant mixed tone. Accordingly, the celestial harmony is, strictly speaking, not “music” in the common sense of this term, but rather it consists of the one constant chord that results from the harmony of the planetary tones. In the Roman Empire, however, the term mélos (song, melody) appeared in their description , and there was talk of an “extremely musical” ( mousikōtatos ) proportion and diversity that Pythagoras had singing and imitated with musical instruments. Apparently it was assumed that Pythagoras could perceive the individual components of the heavenly tone separately and that this therefore presented itself to him as a musical variety. Since the stars were considered divine and because of the assumed perfection of the celestial mechanics, the celestial harmony was imagined as a unique euphony.

Mythical concept

Plato let himself be drawn from the ideas of the Pythagoreans, which he had already on his first trip to Italy in 388/387 BC. Got to know a concept of the harmonious structure of the cosmos, which he presented in the dialogues Politeia and Timaeus . Its spherical harmony is based on eight tones emanating from the seven planetary spheres and the fixed star sphere. He arranged the planets in the order Moon, Sun, Venus, Mercury, Mars, Jupiter, Saturn; He considered Saturn to be the slowest planet because of its proximity to the counter-rotating fixed stars. In contrast to the Pythagoreans, whose teachings Aristotle described, Plato did not give the movements of the stars as the physical cause of the heavenly sounds. Rather, in the tenth book of the Politeia, he had the mythical narrator Er report that the authors of the harmony of the spheres were eight sirens , mythical figures who were assigned to the eight spheres and rotated with them. According to the narrator, each of the sirens makes a constant single sound; together they create a scale of eight tones, the consonance of which results in a harmony. Thus Plato presented the idea of ​​the harmony of the spheres not as a physical hypothesis, but in the form of a myth.

Plato's version may be linked to an old, original myth. In this case, the physical justifications given in the 4th century were only attempts to reinterpret the myth from a scientific point of view and to explain it in this way. This is supported by the fact that in the 2nd century AD Theon of Smyrna ascribed the connection between the planetary tones and the sirens to the Pythagoreans. An ancient Pythagorean saying passed down by Iamblichus of Chalkis points in this direction : “What is the oracle of Delphi ? The Tetraktys , that is the harmony in which the Sirens are. "Here the oracle wisdom is equated with the Tetraktys (" Fourth "), a key term of the Pythagorean numerical theory, and it is indicated that this term also opens up the understanding of the Siren Harmony, which obviously means the heavenly harmony. The background is the fact that the tetraktys (the totality of the numbers 1, 2, 3 and 4) contain the numbers that express the basic harmonic consonances ( octave 2: 1, fifth 3: 2, fourth 4: 3, double octave 4: 1).

reception

The doctrine of the heavenly harmony has been received in many ways both in natural philosophy and literary terms since ancient times. As an aesthetic expression of a well-ordered cosmos, this idea found and is particularly well received in circles that regard the universe as a uniform manifestation of a mathematical order of divine origin. In the course of European cultural history, a purely spiritual interpretation has replaced the physical interpretation.

Antiquity

Aristotle rejected the celestial harmony hypothesis. He argued that the planetary motion could not cause any noise because it was not a proper motion of the planets, but only a result of the rotation of the spheres. To explain this, he stated that an object that is in a moving body does not produce any noise if it moves with the body without friction; Individual parts of a moving ship that are at rest relative to their immediate surroundings move silently with it, and the ship also makes no noise when it glides along a river with the current. In addition, Aristotle thought that such powerful tones must have far more violent effects than mere auditory perception; they would have to be louder than the thunder and would smash solid objects.

Despite the criticism of Aristotle, the idea of ​​heavenly harmony prevailed in wide circles. It met a widespread need to decipher the secrets of the cosmos with mathematical means and thereby to show it as an orderly overall system in which earthly and heavenly music obey the same recognizable laws. In addition to the Platonists, the doctrine of heavenly harmony also spread among the Stoics. In the 3rd century BC, their stoic followers included Chr. Kleanthes , Eratosthenes of Cyrene and Aratos of Soloi . Eratosthenes compared the eight heavenly tones with the tones of the eight-string lyre of the god Hermes .

In the 1st century BC Alexander of Ephesus wrote a didactic poem in which he set out the assumed correspondences between the distances between the celestial spheres, the lengths of the lyre strings and the musical intervals according to whole and semitones. Even Marcus Terentius Varro treated the subject in the music dedicated part of his work on the liberal arts . The most famous exponent of the sky harmony concept was then Cicero ; he described it in the part of his dialogue De re publica known as Somnium Scipionis . He assumed eight spheres surrounding the earth, but only seven tones, since Venus and Mercury produce the same tone; He regarded the moon as the slowest planet with the lowest pitch, and assigned the highest speed and pitch to the sphere of fixed stars. Although Plato's concept was his starting point, he believed motion to be the immediate cause of the sound. The order of the spheres was the dominant one at that time: Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn, fixed stars. He saw the relationship between heavenly and earthly music (like many later authors) as that of an archetype to an image. The idea behind the idea that human music imitates heavenly music was originally based on the idea that Pythagoras had given mankind this possibility because he was the only one who could hear heavenly music. Cicero assumed a majority of people who were capable of such perception.

During the Roman Empire, Pliny the Elder expressed himself skeptically; he said that nothing could be known about the harmony of the spheres. After all, he reported what he knew about the cosmic distances and their hypothetical assignment to musical intervals. The concept of spherical harmony was taken up and developed in detail by the Middle Platonists of the Imperial period and the Neo-Platonists , who were also New Pythagoreans. The Middle Platonist Plutarch and the astronomer Claudius Ptolemy tried in different ways to clarify the question of the mathematical determination of the relationship between the known musical proportions and the distances or speeds of the planets. The Jewish scholar Philo of Alexandria believed that if people could hear the harmony of heaven, they would forget about eating and drinking. He saw heaven as a musical instrument, the sound of which accompanies the hymns that are sung to glorify God. He held this instrument for the archetype ( Archetypon ) of human musical instruments; thus he brought the choir of the seven planets into connection with the seven-stringed lyre. The model of the New Pythagorean Nicomachus of Gerasa , whose music-theoretical views had a decisive influence on the treatment of music in lessons in later epochs, had the most lasting effect . Nicomachus reversed the previous assumption about the correspondence between the distances of the spheres from the earth and the notes of the scale. While it was previously assumed that the innermost planet produced the lowest tone and that the pitch rises with increasing distance from the earth, Nicomachus adopted the reverse order; with him the moon as the innermost planet produces the highest tone. This view is logical if one sees the distances of the planets from the center in analogy to the string lengths, since the longest string produces the lowest tone. Nicomachus also deviated from the standard model of Cicero with regard to the order of the spheres; its order was: Moon, Venus, Mercury, Sun, Mars, Jupiter, Saturn (although this may be an oversight). Like Philo, he assigned the heavenly bodies to the strings of a seven-stringed lyre. The names of the corresponding tones were: Nete (moon), Paranete (Venus), Paramese (Mercury), Mese (sun), Lichanos (Mars), Parhypate (Jupiter) and Hypate (Saturn).

In late antiquity, Macrobius put together a wealth of material on the subject in his commentary on Cicero's Somnium Scipionis (2.1.1–2.4.15). According to his report, according to "theologians" - by which he did not mean Christians - the nine muses took over the role that Plato had intended for the sirens. Eight of them were responsible for the eight spheres ( Urania for the fixed star sky and the highest tone), while the ninth, Calliope , supervised. Plutarch had already said something similar about the Muses. In the 5th century, Martianus Capella also dealt with the responsibility of the Muses for the planets in his encyclopedia The Marriage of Philology and Mercury . Since, in contrast to Macrobius Calliope, he assigned the planet Mercury, another muse, Thalia , remained with him superfluous; he assigned her an earthly abode.

The late ancient Neo-Platonist Simplikios rejected the conventional explanation, according to which people do not hear the celestial harmony because they are used to it. He argued that Pythagoras would not have been able to perceive them either. His hypothesis was that the ability to hear them depends on the soul vehicle, a heavenly, light-like body of the soul. According to a Neoplatonic idea, the soul brought this vehicle with it from the heavenly world, but its functionality is impaired due to earthly pollution during life in the physical body. Simplikios meant that whoever, like Pythagoras, purifies his senses through a favorable fate or good lifestyle and connects the soul vehicle with the physical body, will be able to perceive what remains hidden to others. He also considered the possibility that "hearing" ascribed to Pythagoras was a metaphor for understanding the mathematical foundations of musical harmony, and thus the thinking of harmony was meant.

In ancient Christianity, the reactions of the church fathers to the idea of ​​heavenly harmony were sometimes skeptical or even negative ( Ambrose of Milan , Basil the Great ), but they also met with general approval, especially among those Christians who were relatively open to the influence of Platonism . Gregor von Nyssa stands out among the supporters of the concept , who emphasized that cosmic music is by no means sensual, but only mentally perceptible. The biblical sentence according to which God arranged everything “according to measure, number and weight” ( Weish 11, 20) offered the Christians an important point of contact, since it seemed to confirm the Pythagorean basic idea of ​​a mathematically expressible cosmic order.

middle Ages

Folgenreich was the fact that in the final stages of Late Antiquity Boethius the musica mundana (World Music, cosmic music) in detail in his handbook of music theory ( De musica institutione ) treated, which was in the Middle Ages to a relevant textbook. He relied primarily on Nicomachus of Gerasa and gave his view of the pitch of the individual planets, according to which Saturn produces the lowest and the moon the highest. But he also reported the opposite view that he found in Cicero.

Since, in addition to Boethius, influential ancient authors such as Macrobius and Martianus Capella regarded the heavenly harmony as a fact, it was initially generally accepted in the medieval Latin-speaking scholarly world of Western and Central Europe. Pythagoras was considered to be the discoverer and at the same time the founder of music theory; Occasionally, however, the teaching was also traced back to Orpheus as the founder of music. In addition, there was the authority of some biblical passages considered relevant. Regino von Prüm († 915) pointed to the agreement between pagan philosophers and Christian authorities. "World music" - this term became common - became an integral part of medieval music theory, although it was mostly given relatively little attention due to its lack of practical relevance. In the quadrivium , the group of the four subjects to which music belonged, medieval students became acquainted with it.

The starting point was usually the representation of Boethius. A detailed elaboration of the theory, remarkable because of its originality, was created in the 9th century by the Neo-Platonist Johannes Scottus Eriugena in his main work De divisione naturae ( Periphyseon ) and in a commentary on Martianus Capella. He assigns the highest note to the “celestial sphere” (fixed star sphere) due to its extremely fast movement, and the lowest note to slow Saturn, whereupon the scale rises to the moon. In the commentary, the implementation of the spherical distances between Saturn (the outermost planet) and the sun and between the sun and the moon in musical intervals results in one octave each, i.e. a total of one double octave; Eriugena also assumes a double octave between Saturn and the sphere of fixed stars. In Periphyseon, on the other hand, with reference to Pythagoras, he places the sun in the middle between the earth and the outermost sphere and assumes an octave each from the sun to the earth and from the sun to the fixed stars.

The doctrine of heavenly harmony was also known in the Arabic and Persian-speaking world of the Middle Ages, for example among the Brothers of Purity and in Sufism from Rumi and the mysticism of Shihab ad-Din Yahya Suhrawardi . The famous philosopher and music theorist al-Farabi (10th century) rejected it.

The late medieval music theorist Jakobus von Lüttich tried to harmonize the contradicting traditions. He believed that Cicero's system relates to the daily orbit of the firmament, that of Nicomachus to the proper motions of the planets; According to the first model, the moon has the shortest distance, the lowest speed and thus the lowest tone, according to the other, the moon is the fastest with an orbital period of 27 days and therefore its tone is the highest, while Saturn takes 30 years to be the lowest Make sound. In the 13th century, however, there began to be doubts about the heavenly harmony after Aristotle's writing About Heaven in Latin translation became known. Scholastic university studies were increasingly oriented towards Aristotle. Under the influence of his arguments, with which he had rejected the idea, some late medieval scholars either left the question open or rejected “world music”. Thomas Aquinas shared Aristotle's view. Resolute opponents of the heavenly harmony were Roger Bacon and Johannes de Grocheo . Dante, on the other hand, used the motif extensively in the Divine Comedy . He separated the music of the seven planetary spheres from the song of the angels, which he only had in the area of ​​the fixed star sphere.

Early modern age

During the Renaissance , the humanist Coluccio Salutati († 1406) initially took sides with the opponents of heavenly sounds with physical arguments. Later, however, the enthusiasm for Plato of humanists like Marsilio Ficino led to the fact that in some circles inspired by the Pythagorean and Platonic world of thought the idea of ​​heavenly harmony was taken up again. Among the authors who described and accepted it were the music theorists Franchinus Gaffurius (Franchino Gafori) and Gioseffo Zarlino . The music theorist Glarean († 1563) also dealt with it, but expressed his skepticism in view of the controversial views of the ancient authors. Other music theorists rejected the acoustic existence of heavenly sound: Johannes Tinctoris († 1511) referred to Aristotle and Francisco de Salinas († 1590) said that God could not have thought up something as senseless as inaudible music. In 1585 the mathematician, physicist and astronomer Giovanni Battista Benedetti published an in-depth refutation of heavenly music with physical and musical arguments.

The enthusiasm that prevailed in some circles in the 16th century was expressed by William Shakespeare in his Merchant of Venice :

Sit, Jessica. Look how the floor of heaven
Is thick inlaid with patines of bright gold:
There's not the smallest orb which thou behold'st
But in his motion like an angel sings,
Still quiring to the young-eyed cherubins;
Such harmony is in immortal souls;
But whilst this muddy vesture of decay
Doth grossly close it in, we cannot hear it.

Come on, Jessica! See how the sky
is inlaid with discs of light gold!
Not even the smallest circle that you see, That does not
sing in swing like an angel,
To the choir of the bright-eyed cherubim.
Eternal spirits are so full of harmony:
only we, because this decrepit garment of dust
coarsely envelops us, we cannot hear them.

Johannes Kepler firmly committed himself to the Pythagorean tradition and tried to renew it by transferring its basic idea to his heliocentric model. In doing so he dealt with Ptolemy's harmony ; he saw in the Greek astronomer a forerunner who had suspected the celestial harmony, but had not proven it in physical reality because of its false geocentric model. Kepler believed that he was the first to have a correct, detailed understanding of the harmonic structure of the cosmos. With regard to the musical side, he relied in particular on the results of the music theorist Vincenzo Galilei , who, however, had criticized the traditional Pythagorean interpretation of the relationship between mathematics and music for inadmissible simplification. In his work Harmonice mundi ("World Harmony"), Kepler presented his model of a harmoniously ordered cosmos in 1619 and tried to reformulate the idea of ​​spherical harmony within the framework of his knowledge of planetary movements at the time. According to his description, the movements of the heavenly bodies result in a perennis quidam concentus rationalis, non vocalis (a certain incessant, rational, non-acoustic harmony). So he did not return to the old idea that the planetary movements produce a harmony of physical tones, but only meant that they are determined by numerical relationships that correspond to those of musical harmony. He did not proceed from the distances between the planets and the sun, but from the ratio between their smallest and largest angular velocity. His concern was to show that the laws of astronomy are in principle the same as those of music, since both can be traced back to the same divine author.

In the 17th century, among others, the doctor and writer Robert Fludd and the polymath Athanasius Kircher advocated an all-encompassing world harmony, which they described in detail, using musical terms. They symbolized world harmony with a world monochord, Kircher also with a world organ. In line with the understanding of the celestial harmony at the time, the music theorist Andreas Werckmeister († 1706) wrote: It is true that the opinion is not that the stars should give their natural sonos [tones]; but it is certain that they are set in their harmonious proportions and order by God the Creator and in their course they should keep and respect the order of the musical proportions and harmonia. The topic of world harmony was also the subject of the controversy between the composers and music writers Johann Mattheson and Johann Heinrich Buttstedt in the early 18th century. They argued about whether an identity of heavenly and earthly music could be asserted on the grounds that both must be based on the same eternal harmony and that this is therefore realized everywhere in the same proportions; Mattheson considered this to be unprovable. From another point of view Isaac Newton dealt with the model of the solar system present in the ancient doctrine of the harmony of the spheres; he saw in this a preliminary stage of his knowledge of the relationship between the force of gravity and the distance between the masses.

The music of the planets continued to be a popular theme in poetry, with the Christian motif of angel choirs often interwoven, as was the case with Shakespeare; for example in John Milton's verse epic Paradise Lost and in Odes by Klopstock . Milton also described the harmony of the spheres in his lyrical poem Arcades .

For the wedding of the Grand Duke Ferdinando I de 'Medici (1589) Emilio de' Cavalieri and Cristofano Malvezzi composed an intermedium "L'armonia delle sfere". Sigmund Theophil Staden composed a piece ( elevator ) in 1645 "The seven virtues of planets, tones or voices". In Mozart's Azione teatrale (one-act play) “ Il sogno di Scipione ” (1772; KV 126; libretto by Pietro Metastasio ) Scipio is given the opportunity to hear the music of the spheres, which is normally imperceptible to human ears.

Modern

In the “ Prologue in Heaven”, which Goethe prefaces his Faust , the Archangel Raphael proclaims the harmony of the spheres:

The sun shines the old way
in fraternal spheres of contest,
and their prescribed journey
completes it with a thunderous walk.

In some places in his poems Rainer Maria Rilke alludes to the music of the spheres.

The Cologne judicial councilor and member of the Reichstag, Albert von Thimus (1806–1878), tried to reconstruct Pythagorean music theory in his two-volume work Die harmonikalische Symbolik des Alterthums (Cologne 1868 and 1876), compared it with non-European traditions and tried the idea of ​​the harmony of the spheres underlying, as well as to prove fruitful for the modern age. The partly very speculative and metaphysical " Kayser Harmonics" developed by Hans Kayser (1891–1964), which deals with the mathematical aspect of music in the sense of the Pythagorean tradition and shows a "harmony of the world", is based on his preliminary work and Kepler's ideas tries. Kayser's successor, Professor Rudolf Haase , who taught at the University of Music and Performing Arts Vienna , continued this work and gave it an empirical direction. At this university in 1967 he founded the “Hans Kayser Institute for Basic Harmonics Research” (since 2002 “International Harmonics Center”, headed by Prof. Werner Schulze).

In a concrete way, the anthroposophists took up the Pythagorean concept. Rudolf Steiner († 1925), the founder of anthroposophy, asserted that behind the concept of the harmony of the spheres there was a real, but not sensual, but purely spiritual perception, which the Pythagoreans and Goethe reported and which in principle is also accessible to modern people . It happens with those who are capable or trained for it through the "spiritual ear".

Some modern musicians were fascinated by the idea of ​​the harmony of the spheres. Gustav Mahler wrote about his Eighth Symphony : “Imagine that the universe begins to sound and sound. It is no longer human voices, but planets and suns that revolve. ”The Danish composer Rued Langgaard wrote a music of the spheres ( Sfærernes Musik ) for soloists, choir and large orchestra from 1916–1918 . The famous conductor Bruno Walter, referring explicitly to Pythagoras, said that the spiritually understood harmony of the spheres is a reality that can be achieved by “richer natures”. Paul Hindemith interpreted the harmony of the spheres in the sense that the music was an expression of "forces" "placed in the human sphere of the palpable", "which are like those that keep the sky ... in motion." In 1957 he wrote the opera The Harmony of the World , which deals with the fate of Kepler, whose main work is reminiscent of its title; Hindemith also wrote the libretto. The worldview on which the idea of ​​spherical harmony is based plays a central role in this. The composer Josef Matthias Hauer described the twelve-tone music as a "revelation of the world order, the harmony of the spheres".

In March 2008 the British musician Mike Oldfield released his interpretation of the music of the spheres with the album Music of the Spheres .

Recently, the physicist Brian Greene , who is one of the best-known exponents of string theory , has resorted to musical metaphors in natural philosophy as part of a popular scientific presentation of this theory. He explicitly refers to the spherical sounds of the Pythagoreans and the traditional idea of ​​harmonies in nature: "With the discovery of the superstring theory, these musical metaphors gain an amazing reality." He compares the vibrating "strings" - this English word - assumed by the theory means “thread” or “string” - because of their vibration pattern with the strings of musical instruments and means that the cosmos is considered “nothing but music” from this point of view.

Source collections

  • Joscelyn Godwin (Ed.): The Harmony of the Spheres. A Sourcebook of the Pythagorean Tradition in Music. Inner Traditions International, Rochester VT 1993, ISBN 0-89281-265-6 .
  • Bartel Leendert van der Waerden : The astronomy of the Pythagoreans . Amsterdam 1951, pp. 29–37 (compilation and criticism of all sources on the harmony of the spheres)

literature

Overview display

Overall presentations and investigations

  • Klaus Podirsky: Foreign Body Earth - Golden Ratio and Fibonacci Sequence and Structure Formation in the Solar System. Info3-Verlag, Frankfurt 2004
  • Lukas Richter : "Tantus et tam dulcis sonus". The doctrine of the harmony of the spheres in Rome and its Greek sources. In: Thomas Ertelt , Heinz von Loesch , Frieder Zaminer (ed.): History of music theory. Volume 2: Konrad Volk (ed.): From myth to specialist discipline. Antiquity and Byzantium. Wissenschaftliche Buchgesellschaft, Darmstadt 2006, ISBN 3-534-01202-X , pp. 505-634.
  • Hans Schavernoch: The harmony of the spheres. The history of the idea of ​​harmonizing with the world and attuning the soul (= Orbis academicus . Problem stories of science in documents and representations. Special volume 6). Alber, Freiburg et al. 1981, ISBN 3-495-47459-5 .
  • Joachim Schulz: Rhythms of the Stars. Philosophical-anthroposophical publishing house, Dornach 1963
  • Irini-Fotini Viltanioti: L'harmonie des Sirènes du pythagorisme ancien à Plato (= Studia Praesocratica , vol. 7). De Gruyter, Boston / Berlin 2015, ISBN 978-1-5015-1086-1
  • Hartmut Warm: The signature of the spheres. About the order in the solar system. 3rd edition, Keplerstern, Hamburg 2011, ISBN 978-3-935958-05-9
  • Friedrich Zipp : From the original sound to world harmony. Becoming and working of the idea of ​​the music of the spheres. 2nd, improved and supplemented edition. Merseburger, Kassel 1998, ISBN 3-87537-216-6 .

Web links

Wiktionary: Sphere harmony  - explanations of meanings, word origins, synonyms, translations
Wiktionary: music of the spheres  - explanations of meanings, word origins, synonyms, translations

Remarks

  1. ↑ Carl A. Huffman advocates this: Philolaus of Croton , Cambridge 1993, pp. 279–283; against it are Walter Burkert: Wisdom and Science. Studies on Pythagoras, Philolaos and Plato , Nuremberg 1962, p. 328 f. and Leonid Zhmud : Science, Philosophy and Religion in Early Pythagoreanism , Berlin 1997, p. 222.
  2. ^ Leonid Zhmud: Science, Philosophy and Religion in Early Pythagoreanism , Berlin 1997, p. 219.
  3. ^ Aristotle, De caelo 290b. For the Archytas fragment see Carl A. Huffman: Archytas of Tarentum. Pythagorean, Philosopher and Mathematician King , Cambridge 2005, pp. 136-138.
  4. ↑ James A. Philip: Pythagoras and Early Pythagoreanism , Toronto 1966, p. 125.
  5. ^ Carl A. Huffman: Archytas of Tarentum. Pythagorean, Philosopher and Mathematician King , Cambridge 2005, pp. 104 ff., 136-138; see. 481 f.
  6. ^ Walter Burkert: Wisdom and Science , Nuremberg 1962, p. 334.
  7. ^ William KC Guthrie : A History of Greek Philosophy , Vol. 1, Cambridge 1962, pp. 299 f .; Leonid Zhmud: Science, Philosophy and Religion in Early Pythagoreanism , Berlin 1997, p. 225.
  8. ^ Iamblichos, De vita Pythagorica 65.
  9. ↑ Plato, Politeia 616b – 617d (cf. 530d); Timaeus 35a – 36d, 38c – 39e (cf. 47b – e, 90c – d). See Lukas Richter: "Tantus et tam dulcis sonus" . In: Thomas Ertelt et al. (Hrsg.): Geschichte der Musiktheorie , Vol. 2: Konrad Volk (Hrsg.): From myth to specialist discipline. Antike und Byzanz , Darmstadt 2006, pp. 505–634, here: 513–518.
  10. ^ Walter Burkert: Wisdom and Science , Nuremberg 1962, p. 311.
  11. ↑ Aristotle, De caelo 290b-291a.
  12. ↑ See Luke Richter: "Tantus et tam dulcis sonus" . In: Thomas Ertelt et al. (Hrsg.): Geschichte der Musiktheorie , Vol. 2: Konrad Volk (Hrsg.): From myth to specialist discipline. Antike und Byzanz , Darmstadt 2006, pp. 505–634, here: 567–570.
  13. ↑ Cicero, De re publica 6.17 f .; see. also his dialogue De natura deorum 2,7,19; 2,46,119; 3.11.27. See Paul R. Coleman-Norton: Cicero and the Music of the Spheres . In: The Classical Journal 45, 1949-1950, pp. 237-241.
  14. ↑ Pliny, Naturalis historia 2,3,6.
  15. ↑ On Plutarch's considerations, see Luke Richter: "Tantus et tam dulcis sonus" . In: Thomas Ertelt et al. (Hrsg.): Geschichte der Musiktheorie , Vol. 2: Konrad Volk (Hrsg.): From myth to specialist discipline. Antike und Byzanz , Darmstadt 2006, pp. 505–634, here: 571–576.
  16. ↑ Lukas Richter: "Tantus et tam dulcis sonus" . In: Thomas Ertelt et al. (Hrsg.): Geschichte der Musiktheorie , Vol. 2: Konrad Volk (Hrsg.): From myth to specialist discipline. Antike und Byzanz , Darmstadt 2006, pp. 505–634, here: 577 ff.
  17. ↑ Jean Pépin: Harmony of the Spheres . In: Reallexikon für Antike und Christianentum , Vol. 13, Stuttgart 1986, Sp. 593–618, here: 610 f .; Lukas Richter: "Tantus et tam dulcis sonus" . In: Thomas Ertelt et al. (Hrsg.): Geschichte der Musiktheorie , Vol. 2: Konrad Volk (Hrsg.): From myth to specialist discipline. Antike und Byzanz , Darmstadt 2006, pp. 505–634, here: 592–595.
  18. ↑ On Nicomachus see Flora R. Levin: The Harmonics of Nicomachus and the Pythagorean Tradition , University Park 1975.
  19. ↑ For the representation of Macrobius see Günther Wille : Musica Romana , Amsterdam 1967, pp. 623–630 and Lukas Richter: "Tantus et tam dulcis sonus" . In: Thomas Ertelt et al. (Hrsg.): Geschichte der Musiktheorie , Vol. 2: Konrad Volk (Hrsg.): From myth to specialist discipline. Antike und Byzanz , Darmstadt 2006, pp. 505–634, here: 531–538.
  20. ↑ Jean Pépin: Harmony of the Spheres . In: Reallexikon für Antike und Christianentum , Vol. 13, Stuttgart 1986, Sp. 593–618, here: 607.
  21. ↑ Martianus Capella, De nuptiis Philologiae et Mercurii 1, 11-13; 1.27 f .; 2.169-202; 9,899 ff. See also Günther Wille: Musica Romana , Amsterdam 1967, p. 635 ff.
  22. ↑ Dominic O'Meara: Hearing the harmony of the spheres in Late Antiquity . In: Mauro Bonazzi u. a. (Ed.): A Platonic Pythagoras , Turnhout 2007, pp. 147–161, here: 152–157.
  23. ↑ Ambrosius, De Abraham 2,8,54, ed. by Karl Schenkl : Sancti Ambrosii opera , part 1 (= CSEL vol. 32/1), Prague / Vienna / Leipzig 1896, pp. 499–638, here: p. 608, lines 7-14 and Exameron 2,2,6 f., ed. by Karl Schenkl : Sancti Ambrosii opera , part 1 (= CSEL vol. 32/1), Prague / Vienna / Leipzig 1896, pp. 1–261, here: p. 45 line 6 - p. 46 line 17. Ambrosius has, however, expressed itself in a more positive sense elsewhere, see Jean Pépin: Harmony of the Spheres . In: Reallexikon für Antike und Christianentum , Vol. 13, Stuttgart 1986, Sp. 593–618, here: 616 f.
  24. ↑ Basilius the Great, Homilies to the Hexaemeron 3,3, ed. by Stanislas Giet: Basile de Césarée, Homélies sur l'Hexaéméron , 2nd, revised edition, Paris 1968, pp. 200–202.
  25. ↑ Jean Pépin: Harmony of the Spheres . In: Reallexikon für Antike und Christianentum , Vol. 13, Stuttgart 1986, Sp. 593–618, here: 615; Henri-Irénée Marrou: Une théologie de la musique chez Grégoire de Nysse? In: Jacques Fontaine, Charles Kannengiesser (ed.): Epektasis , Paris 1972, pp. 501–508, here: 504–506.
  26. ↑ See Roger Bragard: L'harmonie des sphères selon Boèce . In: Speculum 4, 1929, pp. 206-213.
  27. ↑ On the medieval reception of Martianus Capella see Mariken Teeuwen: Harmony and the Music of the Spheres , Leiden 2002, pp. 20–59.
  28. ↑ In addition to Weish 11, 20 also Job 38, 7, where the morning stars praise God, and Job 38, 37 (in the medieval Latin Vulgate version: “et concentum caeli quis dormire faciet?”, “And who becomes the unison of heaven calm down?"); on the latter, see Mary L. Lord: Virgil's Eclogues, Nicholas Trevet, and the Harmony of the Spheres . In: Mediaeval Studies 54, 1992, pp. 186-273, here: 210-213.
  29. ^ Regino von Prüm, Epistola de harmonica institutione , chapter 5.
  30. ↑ Johannes Scottus Eriugena, Periphyseon 715B-723C, ed. by Edouard Jeauneau: Iohannis Scotti seu Eriugenae periphyseon. Liber tertius , Turnhout 1999, pp. 137-149. On Eriugena see Barbara Münxelhaus: Pythagoras musicus. On the reception of Pythagorean music theory as a quadrivial science in the Latin Middle Ages , Bonn 1976, pp. 199–204; Lukas Richter: "Tantus et tam dulcis sonus" . In: Thomas Ertelt et al. (Hrsg.): Geschichte der Musiktheorie , Vol. 2: Konrad Volk (Hrsg.): From myth to specialist discipline. Antike und Byzanz , Darmstadt 2006, pp. 505–634, here: 623 f.
  31. ↑ Amnon Shiloah: L'Epitre sur la Musique des Ikhwān al-Safā. In: Revue des Etudes Islamiques. Born 1965–1967, pp. 125–162 and 159–193, especially pp. 157 and 175.
  32. ↑ Jean During, Zia Mirabdolbaghi, Dariush Safvat: The Art of Persian Music , Washington (DC) 1991, pp. 170, 179-181.
  33. ↑ Barbara Münxelhaus: Pythagoras Musicus. On the reception of Pythagorean music theory as a quadrivial science in the Latin Middle Ages , Bonn 1976, p. 208, note 2.
  34. ↑ Barbara Münxelhaus: Pythagoras Musicus. On the reception of Pythagorean music theory as a quadrivial science in the Latin Middle Ages , Bonn 1976, p. 198 f .; Lukas Richter: "Tantus et tam dulcis sonus" . In: Thomas Ertelt et al. (Hrsg.): Geschichte der Musiktheorie , Vol. 2: Konrad Volk (Hrsg.): From myth to specialist discipline. Antike und Byzanz , Darmstadt 2006, pp. 505–634, here: 616 f.
  35. ↑ Reinhold Hammerstein : The music of the angels. Studies on the perception of music in the Middle Ages , Bern 1962, p. 176 f .; Hans Schavernoch: The Harmony of the Spheres , Freiburg 1981, pp. 113–119.
  36. ^ Claude V. Palisca: Humanism in Italian Renaissance Musical Thought , New Haven 1985, pp. 184 f.
  37. ↑ Simeon K. Heninger, Jr .: Touches of Sweet Harmony. Pythagorean Cosmology and Renaissance Poetics , San Marino (California) 1974, p. 182 f.
  38. ↑ Lukas Richter: "Tantus et tam dulcis sonus" . In: Thomas Ertelt et al. (Hrsg.): Geschichte der Musiktheorie , Vol. 2: Konrad Volk (Hrsg.): From myth to specialist discipline. Antike und Byzanz , Darmstadt 2006, pp. 505–634, here: 618–622; Claude V. Palisca: Humanism in Italian Renaissance Musical Thought , New Haven 1985, pp. 166-181.
  39. ↑ Lukas Richter: "Tantus et tam dulcis sonus" . In: Thomas Ertelt et al. (Hrsg.): Geschichte der Musiktheorie , Vol. 2: Konrad Volk (Hrsg.): From myth to specialist discipline. Antike und Byzanz , Darmstadt 2006, pp. 505–634, here: 631–633; Claude V. Palisca: Humanism in Italian Renaissance Musical Thought , New Haven 1985, pp. 181-186.
  40. ^ Claude V. Palisca: Humanism in Italian Renaissance Musical Thought , New Haven 1985, pp. 186 f.
  41. ↑ Act five, first scene.
  42. ^ Bruce Stephenson: The Music of the Heavens. Kepler's Harmonic Astronomy , Princeton 1994, p. 5.
  43. ^ Bruce Stephenson: The Music of the Heavens. Kepler's Harmonic Astronomy , Princeton 1994, p. 45.
  44. ↑ Kepler: Harmonice mundi 5.7.
  45. ^ Daniel P. Walker: Kepler's Himmelsmusik . In: Frieder Zaminer (Ed.): Hearing, measuring and calculating in the early modern times , Darmstadt 1987, pp. 81–108; Hans Schavernoch: The Harmony of the Spheres , Freiburg 1981, pp. 132–147.
  46. ↑ On Fludd see Kathi Meyer-Baer: Music of the Spheres and the Dance of Death , Princeton 1970, pp. 191–199; Hans Schavernoch: The Harmony of the Spheres , Freiburg 1981, p. 149 f .; Simeon K. Heninger, Jr .: Touches of Sweet Harmony. Pythagorean Cosmology and Renaissance Poetics , San Marino (California) 1974, pp. 184-189. On Kircher see Felicia Englmann: Sphärenharmonie und Mikrokosmos , Vienna 2006, p. 327 ff .; Friedrich Zipp: From the original sound to world harmony. Becoming and working of the idea of ​​music of the spheres , 2nd, improved and supplemented edition, Kassel 1998, p. 69.
  47. ↑ Quoted from Fritz Stege: Musik, Magie, Mystik , Remagen 1961, p. 148.
  48. ^ Jamie James, The Music of the Spheres , New York 1993, pp. 163-167.
  49. ↑ Friedrich Zipp: From the primordial sound of universal harmony. Becoming and working of the idea of ​​music of the spheres , 2nd, improved and supplemented edition, Kassel 1998, pp. 75 f., 81 f .; Hans Schavernoch: The Harmony of the Spheres , Freiburg 1981, pp. 167–169.
  50. ^ John Milton: Arcades ( online ).
  51. ^ L'armonia delle sfere ( online ). On this and on the reception of Plato in this work, see Kathi Meyer-Baer: Music of the Spheres and the Dance of Death , Princeton 1970, pp. 204–207.
  52. ↑ Il sogno di Scipione, libretto .
  53. ↑ Friedrich Zipp: From the primordial sound of universal harmony. Becoming and working of the idea of ​​music of the spheres , 2nd, improved and supplemented edition, Kassel 1998, p. 111 f.
  54. ↑ Rudolf Haase: History of the harmonic Pythagoreism , Vienna 1969, pp. 131–135.
  55. ↑ Rudolf Steiner: Theosophie , 32nd edition, Dornach 2005, p. 103 f. and human development and the knowledge of Christ , 3rd edition, Dornach 2006, p. 42 f.
  56. ^ Hermann Unger: Music history in self-testimonials , Munich 1928, p. 407.
  57. ↑ Friedrich Zipp: From the primordial sound of universal harmony. Becoming and working of the idea of ​​music of the spheres , 2nd, improved and supplemented edition, Kassel 1998, p. 121 f.
  58. ↑ Friedrich Zipp: From the primordial sound of universal harmony. Becoming and working of the idea of ​​music of the spheres , 2nd, improved and supplemented edition, Kassel 1998, pp. 126-130.
  59. ↑ Article by Herbert Henck on Hauer's view.
  60. ↑ Brian Greene: The elegant universe , Munich 2006, p. 163.