412:), and two altos (Venus and Earth). Mercury, with its large elliptical orbit, was determined to be able to produce the greatest number of notes, while Venus was found to be capable of only a single note because its orbit is nearly a circle. 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 reminds us that harmonic order is only mimicked by man, but has origin in the alignment of the heavenly bodies:
255:
36:
295:. He is primarily interested with how polygons, which he defines as either regular or semiregular, can come to be fixed together around a central point on a plane to form congruence. His primary objective was to be able to rank polygons based on a measure of sociability, or rather, their ability to form partial congruence when combined with other polyhedra. He returns to this concept later in
200:, and was often called the "music of the spheres." Kepler was intrigued by this idea while he sought explanation for a rational arrangement of the heavenly bodies. When Kepler uses the term "harmony" it is not strictly referring to the musical definition, but rather a broader definition encompassing congruence in
416:
Accordingly you won't wonder any more that a very excellent order of sounds or pitches in a musical system or scale has been set up by men, since you see that they are doing nothing else in this business except to play the apes of God the
Creator and to act out, as it were, a certain drama of the
182:
and the adoption of geometrically supported musical ratios; this would eventually be what allowed Kepler to relate musical consonance and the angular velocities of the planets. Thus, Kepler could reason that his relationships gave evidence for God acting as a grand geometer, rather than a
601:, including the use of a specific six-voice choir (recorded by the microtonal choir Ekmeles), the particular just intonation intervals, and the harmonies allowed in Kepler's diagrams. The text sets the Prayer to the Sun by
347:
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
431:
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 inharmonic ratio of 18:19.
247:
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
212:
bodies. He notes musical harmony as being a product of man, derived from angles, in contrast to a harmony that he refers to as being a phenomenon that interacts with the human
444:, which shows a constant proportionality between the cube of the semi-major axis of a planet's orbit and the square of the time of its orbital period. Kepler's previous book,
782:
Brackenridge, J. (1982). Kepler, elliptical orbits, and celestial circularity: A study in the persistence of metaphysical commitment part II. Annals of
Science, 39(3), 265.
470:
A small number of recent compositions either make reference to or are based on the concepts of
Harmonice Mundi or Harmony of the Spheres. The most notable of these are:
174:) allowed him to explore new theorems. Another important development that allowed Kepler to establish his celestial-harmonic relationships was the abandonment of the
562:
Symphony (originally entitled
Symphonie „Die Harmonie der Welt“ in German), IPH 50, is a symphony composed in 1951, and which served as the basis for the 1957 opera
541:
980:
889:
840:
Schoot, A. (2001). Kepler's search for form and proportion. Renaissance
Studies: Journal of the Society for Renaissance Studies, 15(1), 65–66.
584:
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in its orbit approximates a harmonic proportion. For instance, the maximum angular speed of the Earth as measured from the Sun varies by a
190:
The concept of musical harmonies intrinsically existing within the spacing of the planets existed in medieval philosophy prior to Kepler.
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detailing the mathematical data and proofs that he intended to use for his upcoming text, which he originally planned to name
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with relation to astronomical explanations. In the second chapter is the earliest mathematical understanding of two types of
1349:
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314:; they would later be called Kepler's solids or Kepler Polyhedra and, together with two regular polyhedra discovered by
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721:(1984). A Lutheran astrologer: Johannes Kepler. Archive for History of Exact Sciences, Vol. 31, No. 3, pp. 207–219.
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in geometrical forms and physical phenomena. The final section of the work relates his discovery of the so-called
879:
Walker, D. P. (1964). Kepler’s celestial music. Journal of the
Warburg and Courtauld Institutes, Vol. 30, pp. 249.
1379:
730:
Voelkel, J. R. (1995). The music of the heavens: Kepler's harmonic astronomy. 1994. Physics Today, 48(6), 59–60.
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proportio qua est inter binorum quorumcunque
Planetarum tempora periodica, sit præcise sesquialtera proportionis
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Kepler discovers that all but one of the ratios of the maximum and minimum speeds of planets on neighboring
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proportion between the periodic times of any two planets is precisely the sesquialternate proportion
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548:(2016–2017), premiered at St John's College, Cambridge (2016); revised version performed at the
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Chapter 5 includes a long digression on astrology. This is immediately followed by Kepler's
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also composed the score according to this theory. This opening sequence can be seen here:
791:
Cromwell, P. R. (1995). Kepler's work on polyhedra. Mathematical
Intelligencer, 17(3), 23.
19:"Harmony of the Worlds" redirects here. For the episode of Cosmos: A Personal Voyage, see
8:
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1313:
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The Earth sings Mi, Fa, Mi: you may infer even from the syllables that in this our home
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700:(Philadelphia, Pennsylvania: American Philosophical Society, 1997); see especially
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in musical terms). Kepler explains the reason for the Earth's small harmonic range:
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981:"At the V&A: Tim Watts' Musically and Dramatically Compelling Kepler's Trial"
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890:"Books stolen from the National Library of Sweden between the years 1995–2004"
517:(cycle in five movements for mixed choir and string orchestra), composed 2001.
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in terms of basic triangles. The book features illustrations of solids and
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The Golden Ratio: The Story of Phi, The World's Most
Astonishing Number
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is available as: Johannes Kepler with E. J. Aiton, A. M. Duncan, and
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The Edge of Objectivity: An Essay in the History of Scientific Ideas
1059:. Tr. Charles Glenn Wallis. Chicago: Encyclopædia Britannica, 1952.
353:
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1066:. Ed. Stanley Sadie. 20 vol. London, Macmillan Publishers, 1980.
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Historical dictionary of modern and contemporary classical music
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was a traditional philosophical metaphor that was taught in the
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The Five Books of Johannes Kepler's The Harmony of the World
118:. In the work, written entirely in Latin, Kepler discusses
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from the original on 12 December 2021 – via YouTube.
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The celestial choir Kepler formed was made up of a tenor (
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in ancient Greek, a poet heavily quoted in Kepler's text.
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around 1599, which was the year Kepler sent a letter to
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Miriam Monaghan (British recorder player and composer)
583:
In Tune (October 2019) with full concert premiere at
702:
music is deadly ?id=rEkLAAAAIAAJ&pg=PA411 p. 411
1028:"BBC Radio 3 - In Tune, Rachel Podger, Palisander"
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291:contain most of Kepler's contributions concerning
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678:(But it is absolutely certain and exact that the
154:closely resembled that of the subject matter for
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983:. Seen and Heard International. 11 November 2017
682:of their mean distances, that is, of the actual
481:(1977). An excerpt of the piece was selected by
1064:The New Grove Dictionary of Music and Musicians
960:
458:A copy of the 1619 edition was stolen from the
376:only varies by a tiny 25:24 interval (called a
258:Page with geometric illustrations, including a
166:Kepler would use (most notably the adoption of
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499:, (English musician and composer, born 1953),
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227:While writing the book, Kepler had to defend
216:. In turn, this allowed Kepler to claim the
892:. National Library of Sweden. Archived from
585:London International Festival of Early Music
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340:patterns, some of which are related to the
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103:Harmonice Mundi (Harmonices mundi libri V)
34:
963:"Joep Franssens – Harmony of the Spheres"
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662:(Linz, (Austria): Johann Planck, 1619),
643:Ioannis Keppleri Harmonices mundi libri V
133:
21:Cosmos: A Personal Voyage § Episodes
253:
150:. Kepler was aware that the content of
749:. Princeton University Press. pp.
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231:in court after she had been accused of
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417:ordination of the celestial movements.
220:has a soul because it is subjected to
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961:Dutch Composers (21 November 2012).
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249:harmonic configurations in astrology
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688:An English translation of Kepler's
13:
1114:translated by Charles Glenn Wallis
1049:
579:. Extracts were premiered live on
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162:, but was not concerned. The new
14:
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1168:Kepler's laws of planetary motion
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544:, (English composer, born 1979),
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1239:Epitome Astronomiae Copernicanae
921:. Lanham, Md.: Scarecrow Press.
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672:mediarum distantiarum, id est
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479:Kepler's Harmony of the Worlds
1:
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538:, where the astronomer lived.
513:(Dutch composer, born 1955),
442:third law of planetary motion
332:to describe the formation of
262:, the stellated dodecahedra (
260:truncated trihexagonal tiling
204:and the workings of both the
128:third law of planetary motion
1400:Dynamics of the Solar System
666:From the bottom of p. 189:
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312:great stellated dodecahedron
7:
1350:17th-century books in Latin
741:Gillispie, Charles Coulston
609:
595:Motet: Harmony of the World
593:, American composer, wrote
577:Palisander Recorder Quartet
503:(album released in 2008 by
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869:https://vimeo.com/66697472
550:Victoria and Albert Museum
460:National Library of Sweden
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915:Gagné, Nicole V. (2012).
356:(a ratio of 16:15), from
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1410:Works by Johannes Kepler
1215:Mysterium Cosmographicum
1057:The Harmony of the World
849:The opening of the film
698:The Harmony of the World
622:Mysterium Cosmographicum
320:Kepler–Poinsot polyhedra
289:The Harmony of the World
245:The Harmony of the World
185:Pythagorean numerologist
138:Kepler began working on
112:The Harmony of the World
16:Book by Johannes Kepler
1380:Pythagorean philosophy
1309:Kepler space telescope
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1104:Harmonies of the World
1062:"Johannes Kepler," in
515:Harmony of the Spheres
489:, launched aboard the
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134:Background and history
1282:Die Harmonie der Welt
801:Livio, Mario (2002).
565:Die Harmonie der Welt
560:Die Harmonie der Welt
523:, American composer,
487:Voyager Golden Record
485:for inclusion on the
414:
382:
257:
114:, 1619) is a book by
1385:Astrological aspects
1323:Astronomers Monument
950:Music of the Spheres
575:(2019), written for
501:Music of the Spheres
287:Chapters 1 and 2 of
1198:Keplerian telescope
1007:palisanderrecorders
558:, German composer,
466:Use in recent music
30:
1370:Astrological texts
1193:Kepler's Supernova
896:on 5 November 2018
676:ipsorum; ..."
641:The full title is
530:(2009), homage to
491:Voyager spacecraft
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193:Musica universalis
180:musical consonance
176:Pythagorean tuning
40:1619 first edition
28:
1395:Mathematics books
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1329:List of namesakes
1255:Rudolphine Tables
1183:Kepler's equation
1163:Kepler conjecture
1156:Scientific career
1055:Johannes Kepler,
928:978-0-8108-6765-9
857:Martin Villeneuve
658:Johannes Kepler,
552:, 9 November 2017
178:as the basis for
172:Copernican system
148:De harmonia mundi
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1247:Harmonices Mundi
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587:(November 2019).
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91:Publication date
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694:J. V. Field
686:, ..."
581:BBC Radio 3
210:terrestrial
1355:1619 books
1344:Categories
696:, trans.,
629:References
483:Carl Sagan
370:perihelion
364:, between
270:) and the
233:witchcraft
229:his mother
198:quadrivium
124:congruence
937:729863298
900:19 August
542:Tim Watts
436:Chapter 5
388:sery and
318:, as the
293:polyhedra
224:harmony.
206:celestial
164:astronomy
160:Harmonica
80:Publisher
70:Astronomy
1291:(mother)
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967:Archived
743:(1960).
610:See also
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354:semitone
276:elements
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1263:Somnium
815:154–156
684:spheres
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603:Proclus
410:Mercury
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855:, by
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374:Venus
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308:small
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108:Latin
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1068:ISBN
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