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1619 __ « Harmonices Mundi »
Johannes Kepler (1571-1630)
Comment : Musica universalis (lit. universal music, or music of the spheres) is an ancient philosophical concept that regards proportions in the movements of celestial bodies.the Sun, Moon, and planets.as a form of musica (the Medieval Latin name for music). This 'music' is not literally audible, but a harmonic and/or mathematical and/or religious concept. « Harmonices Mundi » (The Harmony of the Worlds, 1619) is a book by Johannes Kepler. In the work Kepler discusses harmony and congruence in geometrical forms and physical phenomena. The final section of the work relates his discovery of the so-called "Third Law" of planetary motion. Kepler divides « The Harmony of the World » into five long chapters: the first is on regular polygons; the second is on the congruence of figures; the third is on the origin of harmonic proportions in music; the fourth is on harmonic configurations in astrology; and the fifth on the harmony of the motions of the planets. While medieval philosophers spoke metaphorically of the "music of the spheres," Kepler discovered physical harmonies in planetary motion. He found that the difference between the maximum and minimum angular speeds of a planet in its orbit approximates a harmonic proportion. For instance, the maximum angular speed of the Earth as measured from the Sun varies by a semitone (a ratio of 16:15), from mi to fa, between aphelion and perihelion. Venus only varies by a tiny 25:24 interval (called a diesis in musical terms). Kepler explains the reason for the Earth's small harmonic range: “The Earth sings Mi, Fa, Mi: you may infer even from the syllables that in this our home misery and famine hold sway.” At very rare intervals all of the planets would sing together in 'perfect concord': Kepler proposed that this may have happened only once in history, perhaps at the time of creation. Kepler also discovers that all but one of the ratios of the maximum and minimum speeds of planets on neighboring orbits approximate musical harmonies within a margin of error of less than a diesis (a 25:24 interval). The orbits of Mars and Jupiter produce the one exception to this rule, creating the unharmonic ratio of 18:19. In fact, the cause of Kepler's dissonance might be explained by the fact that the asteroid belt separates those two planetary orbits, as discovered in 1801, 150 years after Kepler's death. (Compiled from various sources)
French comment : A côté du discours symbolique des alchimistes convaincus, la théorie fédératrice de la musique des sphères perdure et connaît un développement sous différentes formes. L’application la plus connue et la plus développée de la musique des sphères due à l’astrologue et astronome Johannes Kepler (1571-1630). Celui-ci a établi dans la première moitié du 17e siècle une corrélation unique entre les observations astronomiques et la musique, bien que cela ait été très controversé et vivement critiqué. Le travail de Johannes Kepler montre bien la diversité et le développement de la science aux 16e et 17e siècles. D’un côté astrologue et auteur de la théorie de l’hérédité planétaire, de l’autre astronome et fervent défenseur du système de Nicolas Copernic (1473-1543) mis en place plus de 70 ans auparavant, il réunit à lui seul toute la complexité du passage entre les sciences occultes et la connaissance nouvelle. Dans son œuvre, Kepler met sous une lumière critique les idées anciennes pour obtenir une connaissance nouvelle. Ainsi en 1619, Kepler, âgé alors de 48 ans, dans son ouvrage Harmonices Mundi (Kepler 1979) ne se réfère plus uniquement aux suppositions pythagoriciennes et à des constructions imaginaires. Il crée des relations que l’on pourrait qualifier aujourd’hui de sonification des données. En partant de calculs mathématiques plus ou moins complexes il cherche, et finalement trouve, les sons correspondant aux mouvements des planètes du système solaire. Pour Kepler, de la même façon que pour les Pythagoriciens, il ne s’agit pas de la création d’une composition musicale, mais d’une recherche purement « scientifique ». Le travail de Kepler consiste en une simple explication de faits qui sont déjà acceptés. Ainsi, la production du son et des harmonies des sphères « ...sont d’abord une conception mathématique et non pas une conception musicale » (Knobloch, 1992, p.128). En effet, sur la base de la géométrie des polygones et des polyèdres, Kepler cherche à trouver l’harmonie, mais il s’agit ici de l’harmonie géométrique. Une fois cette harmonie trouvée, il « confronte la suite de toutes les vitesses angulaires périhéliques et aphéliques des planètes avec l’échelle des intervalles musicaux » (Knobloch, 1992, p.129). Ensuite, il sera possible de construire des lignes mélodiques définies par les vitesses respectives des planètes. Les termes que l’on considère comme musicaux - harmonie ou intervalle - sont pris par Kepler dans leur sens géométrique. Ainsi, les distances des planètes deviennent les intervalles et les vitesses angulaires des harmonies musicales. Ce mélange de vocabulaire est tout à fait logique puisque, même si le résultat n’est pas directement audible, il ne s’agit pas d’une théorie artistique ou esthétique de la musique, mais uniquement d’un lien entre des données physiques. Pour trouver les rapports des nombres consonants, Kepler utilise la division du cercle par un polygone inscrit à l’intérieur. Ainsi les côtés du polygone divisent la circonférence en plusieurs parties. Les rapports entre ces parties indiquent l’intervalle et la constructibilité du polygone détermine si l’intervalle est consonant ou non. Kepler a ainsi déduit sept intervalles consonants pour l’octave. [...] Pour Kepler, ces rapports sont ensuite appliqués à la musique, l’astrologie et l’astronomie. Les harmonies sont donc une réalité tout à fait objective et non une spéculation philosophique. Le scientifique et l’artiste sont mis à égalité puisque à la base leur travail est le même. La première loi de Kepler stipule, que les planètes se déplacent autour du Soleil sur un trajet écliptique où le Soleil est dans un des foyers. La deuxième loi indique que la vitesse de la planète n’est pas uniforme, mais change en fonction de la position de la planète par rapport au Soleil : plus la planète se trouve près du Soleil, plus grande est sa vitesse et plus elle en est éloignée, plus elle se déplace lentement. C’est donc la vitesse de la planète qui change dans le temps et c’est justement cette vitesse qui sera prise comme paramètre pour la transformation des paramètres acoustiques. [...] Les données astronomiques de Kepler sont en fait bien connues sous le nom de « lois de Kepler », publiées en 1609 dans Astronomia nova et, dans l’Epitome astronomiae copernicanae, en 1618. Une fois les mouvements des planètes calculés, il suffit de trouver des liens cohérents avec les paramètres acoustiques pour obtenir des proportions harmoniques. Kepler a donc le choix entre plusieurs données astronomiques pour chercher les proportions harmoniques : il est possible de prendre les rayons des orbites, les vitesses orbitales, les révolutions, etc. Son choix se porte sur les rapports de vitesse puisque la vitesse comme les intervalles musicaux concerne le temps. Pour ses calculs, Kepler décide qu’il faudrait se placer dans le soleil, pour pouvoir percevoir le son produit par des vitesses aphéliques et périphéliques vues du soleil. Les résultats de ces calculs sont des ensembles de hauteurs (des sortes de gammes), que produisent les planètes en tournant autour du soleil et le son est ainsi produit en boucle. D’après ces données, la Terre fait davantage entendre un vibrato - un demi-ton - et Vénus une sorte de mouvement microtonal - l’intervalle est de 25:24- (James, 1997, p.175). En plus des correspondances physiques, le système de Kepler comporte des correspondances entre les planètes et les voix humaines. De la même façon que les voix se divisent suivant leurs hauteurs, les planètes qui produisent aussi des hauteurs peuvent obtenir des noms de voix : soprano, ténor, basse etc. (Proust, 1990, p.42). Kepler ne calcule pas les hauteurs d’un son pour produire de la musique dans le sens d’une composition musicale. Il le fait de la même façon que pour des calculs acoustiques. Lorsqu’il obtient une hauteur, c’est en fait le résultat de relations géométriques d’après lesquelles les relations entre les intervalles mélodiques sont ensuite calculées. Astronomie et musique sont alors intimement liées à l’aide de l’harmonie de la géométrie. (Alexander Mihalic, "Le Calcul de la musique”)
Original excerpt : « Book III of The Harmony of the World by Johannes Kepler.On the origin of the harmonic proportions, and on the nature and differences of those things which are concerned with melody.[...] In what follows it will not be right to depart at all from the natural method, so that the learning of the human mind, which quite often uses a different route, may be given all the more assistance. For what the nature of the subject requires is that we should now thirdly expound in the abstract those proportions which occur between a circle and a part cut off on any side, and the other kinds of cases which arise from the combination and separation of such proportions ; then fourthly that we should pass to the operations of the world, which either God himself the Creator has adjusted to proportions of that kind, or Sublunary Nature applies daily according to the rule of those proportions in the angles between the stellar rays ; and finally we should add human music, showing how the human mind, shaping our judgement of what we hear, by its natural instinct imitates the Creator by showing delight and approval for the same proportions in notes which have pleased God in the adjustment of the celestial motions. For it is indeed difficult to abstract mentally the distinctions, types, and modes of the harmonic proportions from musical notes and sounds, since the only vocabulary which comes to our aid, as is necessary to expound matters, is the musical one. [...] Certainly, just as it is ordained in all human affairs that in those things which are bestowed on us by nature, use precedes understanding of causes, similarly as far as melody is concerned it happened to the human race that from its very beginning it used without speculating or knowing about their causes the same rhythms and intervals between notes as we commonly use today, in the chanting of melodies, not only in churches and in choirs of musicians, but everywhere without applying any art, even at crossroads and in the fields. [...] Throughout we shall indeed speak of melody, that is harmonious intervals which are not abstract but realized in sound ; yet to the educated ears of the mind the underlying reference throughout will be to the intervals abstracted from the sounds. For it is not only in sounds and in human melody that they yield their charm, but also in other things which are soundless, as we shall hear in the fourth and fifth Books.Book IV of the Harmony of the World by Johannes Kepler.On the harmonic configurations of the stellar rays on the earth, and their effects on events in the sky and other natural phenomena.On the use of mathematics in Natural Philosophy and Politics which most of all concern the Harmonic part of it on radiations. It furnishes everything that is important for the contemplation of natur, declaring the most splendid order of the ratios, according to which the whole of this universe has been constructed, and the analogy of the proportions, which connects together everything in the world, as Timaeus says somewhere, and which restores friendship between things which are in conflict, and relations and mutual affection between those which are widely separated. [...] It remains for us to apply the harmonies, which we have hitherto described, to the cosmos, in three other books, of which the first would attribute the harmonies to God the Creator of the heavens, the second to Nature the director of different motions, and the third to Man the controller of his voice, which originates from motion. However, the requirements of stating the arguments have persuaded us not only to reverse the order, starting from human song, passing from that to the works of Nature, and thus finally to the work of Creation, which was the first and most perfect of all, but also to combine the end of abstract speculation with the beginning of actual harmonies in melody, in the same third book. Therefore, after starting this application to the cosmos in the preceding book, and transferring the harmonies to human melody, which others usually embrace in the general term Art, there now follows the fourth book, which in this reverse order attributes to Nature the second part in actual harmony. [...]Book V of the Harmony of the World by Johannes Kepler.[...] Chapter VI - That in the Extremes of the Planetary Motions Have Been Expressed, in a Fashion, the Musical Modes or Tones.This follows from what has already ben said, and does not require many words ; for the individual planets represent in a fashion individual positions in the system by their motion at perihelion, insofar as it is granted to each to traverse some particular interval in the musical scale, encompassed by certain notes in it, or positions in the system. [...] They do not indeed form the intermediate positions, which you here see filled in with notes, specifically, as they do the extremes ; for they advance from one extreme to the opposite one not by leaps and intervals, but with a continually changing note, pervading all between (potentially infinite) in reality. I could not express that un any other way but by a continuous series of intermediate notes. Venus remains almost on unison, not amounting in the breadth of its tuning even to the smallest of the melodic intervals. Yet by the designation of two notes in a common system, and the shaping of the skeleton of the octave, by spanning a definite melodic interval, there is a certain first step towards distinguishing tones or modes : therefore the musical modes have been distributed among the planets. To be sure I know that for the shaping and defining of distinct modes many things are needed , which are proper to human melody, that is to say when it has intervals ; and so I have used the voice in a fashion. Now it will be open to a musician to draw his own conclusion as to which mode each planet more nearly expresses, now that the extremes have here been assigned for him. [...]Chapter X - Conjectural Epilogue on the Sun.From the heavenly music to the hearer ; from the Muses to Apollo the choirmaster ; from the six planets which go around and make the harmonies, to the Sun at the center of all the orbits, motionless in his place, but revolvong on his own axis. For whereas there is the most complete harmony between the extreme motions of the planets, not in the sense of the true speeds through the ethereal air, but in the sense of the angles which are formed by the ends of the daily arcs of the planets' orbits, joined to the center of the Sun, yet the harmony does not ornament the ends, that is, the individual motions, in themselves, but insofar as they are linked and compared with each other and are made the object of some mind ; and since no object is arranged vainly, and without something which is moved by it, those angles seem in fact to presuppose some agency, like our sight, or certainly the sensation of it [...]. » (Transl. by E.J. Aiton, A.M. Duncan, J.V. Field)
Source : Kepler, Johannes (1619), “The Harmony of the World”. Tr.: E.J. Aiton, A.M. Duncan, J.V. Field. Pub. by The American Philosophical Society (Eds), 1997.
Source : Kepler, Johannes (1619), “The Harmony of the World”. Tr. Charles Glenn Wallis. Chicago: Great Books of the Western World. Pub. by Encyclopedia Britannica, Inc., 1952.
Urls : http://musinf.free.fr/texte/Alex24-II.pdf (last visited ) http://www.skyscript.co.uk/kepler.html (last visited ) http://posner.library.cmu.edu/Posner/books/book.cgi?call=520_K38PI (last visited )

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