Harmonice Mundi
Encyclopedia
Harmonices Mundi 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:
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 orbit
s 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.
Kepler's previous book Astronomia nova
related the discovery of the first two of the principles that we know today as Kepler's laws
. The third law, 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, is set out in Chapter 5 of this book, immediately after a long digression on astrology
.
Johannes Kepler
Johannes Kepler was a German mathematician, astronomer and astrologer. A key figure in the 17th century scientific revolution, he is best known for his eponymous laws of planetary motion, codified by later astronomers, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican...
. In the work Kepler discusses harmony
Harmony
In music, harmony is the use of simultaneous pitches , or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...
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
Planet
A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...
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
Semitone
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically....
(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
Diesis
In classical music from Western culture, a diesis is either an accidental , or a comma type of musical interval, usually defined as the difference between an octave and three justly tuned major thirds , equal to 128:125 or about 41.06 cents...
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 orbit
Orbit
In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...
s 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
Asteroid belt
The asteroid belt is the region of the Solar System located roughly between the orbits of the planets Mars and Jupiter. It is occupied by numerous irregularly shaped bodies called asteroids or minor planets...
separates those two planetary orbits, as discovered in 1801, 150 years after Kepler's death.
Kepler's previous book Astronomia nova
Astronomia nova
The Astronomia nova is a book, published in 1609, that contains the results of the astronomer Johannes Kepler's ten-year long investigation of the motion of Mars...
related the discovery of the first two of the principles that we know today as Kepler's laws
Kepler's laws of planetary motion
In astronomy, Kepler's laws give a description of the motion of planets around the Sun.Kepler's laws are:#The orbit of every planet is an ellipse with the Sun at one of the two foci....
. The third law, 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, is set out in Chapter 5 of this book, immediately after a long digression on astrology
Astrology
Astrology consists of a number of belief systems which hold that there is a relationship between astronomical phenomena and events in the human world...
.
External links
- Harmonices mundi ("The Harmony of the Worlds") in fulltext facsimile; Carnegie-Mellon University
- Harmonies of the World excerpt from translated by Charles Glenn Wallis