The musica universalis (literally universal music), also called music of the spheres or harmony 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 music. This "music" is not thought to be audible, but rather a harmonic, mathematical or religious concept. The idea continued to appeal to scholars until the end of the Renaissance, influencing many kinds of scholars, including humanists. Further scientific exploration discovered orbital resonance in specific proportions in some orbital motion.
The discovery of the precise relation between the pitch of the musical note and the length of the string that produces it is attributed to Pythagoras. The Music of the Spheres incorporates the metaphysical principle that mathematical relationships express qualities or "tones" of energy which manifest in numbers, visual angles, shapes and sounds – all connected within a pattern of proportion. Pythagoras first identified that the pitch of a musical note is in inverse proportion to the length of the string that produces it, and that intervals between harmonious sound frequencies form simple numerical ratios. In a theory known as the Harmony of the Spheres, Pythagoras proposed that the Sun, Moon and planets all emit their own unique hum based on their orbital revolution, and that the quality of life on Earth reflects the tenor of celestial sounds which are physically imperceptible to the human ear. Subsequently, Plato described astronomy and music as "twinned" studies of sensual recognition: astronomy for the eyes, music for the ears, and both requiring knowledge of numerical proportions.
From all this it is clear that the theory that the movement of the stars produces a harmony, i.e. that the sounds they make are concordant, in spite of the grace and originality with which it has been stated, is nevertheless untrue. Some thinkers suppose that the motion of bodies of that size must produce a noise, since on our earth the motion of bodies far inferior in size and in speed of movement has that effect. Also, when the sun and the moon, they say, and all the stars, so great in number and in size, are moving with so rapid a motion, how should they not produce a sound immensely great? Starting from this argument and from the observation that their speeds, as measured by their distances, are in the same ratios as musical concordances, they assert that the sound given forth by the circular movement of the stars is a harmony. Since, however, it appears unaccountable that we should not hear this music, they explain this by saying that the sound is in our ears from the very moment of birth and is thus indistinguishable from its contrary silence, since sound and silence are discriminated by mutual contrast. What happens to men, then, is just what happens to coppersmiths, who are so accustomed to the noise of the smithy that it makes no difference to them. But, as we said before, melodious and poetical as the theory is, it cannot be a true account of the facts. There is not only the absurdity of our hearing nothing, the ground of which they try to remove, but also the fact that no effect other than sensitive is produced upon us. Excessive noises, we know, shatter the solid bodies even of inanimate things: the noise of thunder, for instance, splits rocks and the strongest of bodies. But if the moving bodies are so great, and the sound which penetrates to us is proportionate to their size, that sound must needs reach us in an intensity many times that of thunder, and the force of its action must be immense.
- musica mundana (sometimes referred to as musica universalis)
- musica humana (the internal music of the human body)
- musica quae in quibusdam constituta est instrumentis (sounds made by singers and instrumentalists)
Musica universalis, which had existed since the Greeks, as a metaphysical concept was often taught in quadrivium, and this intriguing connection between music and astronomy stimulated the imagination of Johannes Kepler as he devoted much of his time after publishing the Mysterium Cosmographicum (Mystery of the Cosmos) looking over tables and trying to fit the data to what he believed to be the true nature of the cosmos as it relates to musical sound. In 1619 Kepler published Harmonices Mundi (literally Harmony of the Worlds), expanding on the concepts he introduced in Mysterium and positing that musical intervals and harmonies describe the motions of the six known planets of the time. He believed that this harmony, while inaudible, could be heard by the soul, and that it gave a “very agreeable feeling of bliss, afforded him by this music in the imitation of God.” In Harmonices, Kepler who differed from Pythagorean observations, laid out an argument for a Christian-centric creator who had made an explicit connection between geometry, astronomy, and music, and that the planets were arranged intelligently.
Harmonices is split into five books, or chapters. The first and second books give a brief discussion on regular polyhedron and their congruences, reiterating the idea he introduced in Mysterium that the five regular solids known about since antiquity define the orbits of the planets and their distances from the sun. Book three focuses on defining musical harmonies, including consonance and dissonance, intervals (including the problems of just tuning), their relations to string length which was a discovery made by Pythagoras, and what makes music pleasurable to listen to in his opinion. In the fourth book Kepler presents a metaphysical basis for this system, along with arguments for why the harmony of the worlds appeals to the intellectual soul in the same manner as the harmony of music appeals to the human soul. Here he also uses the naturalness of this harmony as an argument for heliocentrism. In book five, Kepler describes in detail the orbital motion of the planets and how this motion nearly perfectly matches musical harmonies. Finally, after a discussion on astrology in book five, Kepler ends Harmonices by describing his third law, which states that for any planet the cube of the semi-major axis of its elliptical orbit is proportional to the square of its orbital period.
In the final book of Harmonices, Kepler explains how the ratio of the maximum and minimum angular speeds of each planet (its speeds at the perihelion and aphelion) is very nearly equivalent to a consonant musical interval. Furthermore, the ratios between these extreme speeds of the planets compared against each other create even more mathematical harmonies. These speeds explain the eccentricity of the orbits of the planets in a natural way that appealed to Kepler’s religious beliefs in a heavenly creator.
While Kepler did believe that the harmony of the worlds was inaudible, he related the motions of the planets to musical concepts in book four of Harmonices. He makes an analogy between comparing the extreme speeds of one planet and the extreme speeds of multiple planets with the difference between monophonic and polyphonic music. Because planets with larger eccentricities have a greater variation in speed they produce more “notes.” Earth’s maximum and minimum speeds, for example, are in a ratio of roughly 16 to 15, or that of a semitone, whereas Venus’ orbit is nearly circular, and therefore only produces a singular note. Mercury, which has the largest eccentricity, has the largest interval, a minor tenth, or a ratio of 12 to 5. This range, as well as the relative speeds between the planets, led Kepler to conclude that the Solar System was composed of two basses (Saturn and Jupiter), a tenor (Mars), two altos (Venus and Earth), and a soprano (Mercury), which had sung in “perfect concord,” at the beginning of time, and could potentially arrange themselves to do so again. He was certain of the link between musical harmonies and the harmonies of the heavens and believed that “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.”
Kepler was so convinced of a creator that he was convinced of the existence of this harmony despite a number of inaccuracies present in Harmonices. Many of the ratios differed by an error greater than simple measurement error from the true value for the interval, and the ratio between Mars’ and Jupiter’s angular velocities does not create a consonant interval, though every other combination of planets does. Kepler brushed aside this problem by making the argument, with the math to support it, that because these elliptical paths had to fit into the regular solids described in Mysterium the values for both the dimensions of the solids and the angular speeds would have to differ from the ideal values to compensate. This change also had the benefit of helping Kepler retroactively explain why the regular solids encompassing each planet were slightly imperfect. Kepler was convinced "that the geometrical things have provided the Creator with the model for decorating the whole world" and wanted to further explore the aspects of the natural world specifically being involved with astronomical and astrological concepts of music. When Kepler published Harmonices Mundi, Kepler was held liable in a dispute with Robert Fludd, who also published his own harmonic theory at the time. To Kepler, the celestial physics of the spheres were seen as geometrically spatial regions that consisted of each planetary orbit rather than its physical form.
Kepler's books are well-represented in the Library of Sir Thomas Browne who expressed a belief in the music of the spheres thus-
- For there is a musicke where-ever there is a harmony, order or proportion; and thus farre we may maintain the musick of the spheres; for those well ordered motions, and regular paces, though they give no sound unto the eare, yet to the understanding they strike a note most full of harmony. Whatsoever is harmonically composed, delights in harmony. 
Use in recent musicEdit
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The connection between music, mathematics, and astronomy had a profound impact on history. It resulted in music's inclusion in the Quadrivium, the medieval curriculum that included arithmetic, geometry, music, and astronomy, and along with the Trivium (grammar, logic, and rhetoric) made up the seven liberal arts, which are still the basis for higher education today. A small number of recent compositions either make reference to or are based on the concepts of Musica Universalis or Harmony of the Spheres. Among these are Music of the Spheres by Mike Oldfield, Om by the Moody Blues, The Earth Sings Mi Fa Mi album by The Receiving End of Sirens, Music of the Spheres by Ian Brown, and Björk's single Cosmogony, included in her 2011 album Biophilia. Earlier, in the 1910s, Danish composer Rued Langgaard composed a pioneering orchestral work titled Music of the Spheres. Music of the Spheres was also the title chosen for the musical foundation of the video-game Destiny, and was composed by Martin O'Donnell, Michael Salvatori, and Paul McCartney. Paul Hindemith wrote an Opera (1957), and a Symphony using the same music, called 'Die Harmonie der Welt' based upon the life of the Astronomer Johannes Kepler (1571–1630). On November 22, 2019, Coldplay released their eighth studio album, Everyday Life. In one of the pages of the CD liner notes is an image of a billboard with the phrase “Music of the Spheres” written in large text and the words “Coldplay coming soon” in smaller text. In addition, next to the billboard is a Rover car with the license plate “FFTF2024”. When asked about the image in an interview with Virgin Radio France, lead singer Chris Martin responded by saying that the phrase “definitely means something”. In 2018, Coldplay trademarked the phrase “Music of the Spheres” in connection with their Global Citizen-curated EP under the pseudonym “Los Unidades”.
- Weiss and Taruskin (2008) p. 3.
- Pliny the Elder (77) pp. 277–8, (II.xviii.xx): "…occasionally Pythagoras draws on the theory of music, and designates the distance between the Earth and the Moon as a whole tone, that between the Moon and Mercury as a semitone, .... the seven tones thus producing the so-called diapason, i.e.. a universal harmony".
- Houlding (2000) p. 28: According to the article written by Pythagoras was also presumed to have been able to hear music of spheres which he claims to have helped him encounter these musical intervals that could be demonstrated in ratios of small integers. He analyzed the tones and believed that they correlated with the celestial movements of the day in cohesion. His concepts were observed and criticized by Plato as well. According to this article, Pythagoras told Egyptian priests that he was given the ability to hear the music of these spheres and He believed that only Egyptians of the proper bloodline,or familyline could have these connections. For Philolaus, mathematician and Pythagorean astronomer, working around 400 BC, the world was 'harmony and numbers'; everything is ordered according to proportions that correspond to three basic musical intervals: 2:1 (harmony), 3:2 (fifth), 4:3 (fourth). Nicomachus of Gerasa (also a Pythagorean, towards the year 200 BC) assigns the notes of the octave to the celestial bodies, so that they generate a music. "The doctrine of the Pythagoreans was a combination of science and mysticism… Like Anaximenes they viewed the Universe as one integrated, living organism, surrounded by Divine Air (or more literally 'Breath'), which permeates and animates the whole cosmos and filters through to individual creatures … By partaking of the core essence of the Universe, the individual is said to act as a microcosm in which all the laws in the macrocosm of the Universe are at work".
- Davis (1901) p. 252. Plato's Republic VII.XII reads: "As the eyes, said I, seem formed for studying astronomy, so do the ears seem formed for harmonious motions: and these seem to be twin sciences to one another, as also the Pythagoreans say".
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