Kepler and Kircher on the Harmony of the Spheres

Joscelyn Godwin

The Harmony of the Spheres, a transdisciplinary idea that unites cosmology, astronomy,mathematics, and music theory, has been a major vehicle of the Pythagorean current inthe intellectual history of the West. This article focuses on two figures who contributedlargely to it in the early phase of the Scientific Revolution. By learning and inclination,both had come under Neoplatonic and Hermetic influences; both were adherents of thatstream of Christian esotericism that sought a deeper understanding of the created world.But as we shall see, their attitudes to celestial harmonies were in stark contrast to oneanother.

Every book on Johannes Kepler (1571-1630), and most books on the history ofastronomy, make mention of the theory of celestial harmony that Kepler developed inHarmonices Mundi (1619).1 They often reproduce, as a curiosity, his notation of theplanetary songs:

Figure 1

The importance of this work for the history of science is undisputed. It completed whatwere later named the three Keplerian Laws of Planetary Motion: 1. Each planet moves inan ellipse with the sun at one focus. 2. The radius vector of each planet passes over equalareas in equal intervals of time. 3. The square of the period of revolution of a planet aboutthe sun is proportional to the cube of the mean distance of the planet from the sun.2Kepler himself was unable to provide a physical explanation for these laws, but theyformed the basis for Isaac Newton (1643-1727) to develop his theory of universalgravitation, which confirmed their validity and ensured their discoverers immortality.

It was the data of the new astronomy, as contained in the observations and tablesof his master Tycho Brahe (1546-1601), that had forced these conclusions on Kepler aftermany years of intense research and meditation. They necessitated two radical novelties inthe arrangement of the solar system: first, the acceptance of the Copernican orheliocentric system; and second, the elliptical orbits with their variable speeds of

planetary motion, which abolished the epicycles and equants that cluttered the Ptolemaicor geocentric system. While there were a few precedents for heliocentrism in the ancientworld, the second conclusion went against the entire astronomical tradition, andespecially against the principle enunciated by Aristotle and accepted by Ptolemy: thateverything in the heavens moves in perfect circles. Even Copernicus had not contravenedit.

Keplers laws saved the appearances more successfully than any previoustheory, but that was not enough for him, driven as he was by a lifelong passion todiscover the divine rationale behind the appearances. Having already justified theCopernican arrangement of the planets around the sun by means of a geometric argumentinvolving the five Platonic solids,3 he now addressed the irregularity of their orbits. Whyshould God have made these elliptical rather than circular, and so various in their degreesof ellipticality?

In seeking the answers to these questions, Keplers basic assumption was thePythagorean one: that the key to the cosmos lies in number. A secondary idea, equallyPythagorean in origin, was that harmony endows number with meaning, quantity withquality. It privileges certain numbers over others, namely the ones that, translated intomusical terms, produce the intervals that we perceive as consonant, pleasant, andmusically useful. Harmonices Mundi is a triumph of ingenuity in reading these principlesinto the data of the new astronomy, and thereby justifying the latter.

Historians of science are well aware of how Keplers argument works, and of theconnection between the planetary songs and the First Law, but to some readers it may behelpful to explain it here. In this exaggerated diagram of a planets elliptical orbit, itsmotion is seen to accelerate as it approaches perihelion (nearest to the sun) and todecelerate as it moves away towards aphelion (furthest from the sun).

Figure 2

Following Keplers Second Law, its acceleration depends on the degree of ellipticality ofits orbit. For example, Mercurys orbit is much more elliptical than Venuss, which is

almost circular. Therefore the difference between Mercurys extreme positions is muchgreater than that of Venus, and the musical interval expressing that difference muchwider.

The natural philosophers of antiquity believed that the planets are not silent intheir orbits. Setting aside the question of whether they move through air or through somefiner medium like ether, it seemed logical that these great bodies should make a sound,just as moving bodies do on earth; and the many theories of the Harmony of the Spheresremain as attempts to specify what that sound could be, translated into the language ofmusic.

There are two main schools of thought as to how this translation should be made.The first one assumes that the relative distances of the planets from the earth relateharmonically, as if they were different points on a string. This theory derives fromPythagorass school, in which the distance of the earth from the moons sphere wasreckoned to be 126,000 stades. Taking this distance as equivalent to a whole-tone, thedistances to the other planetary spheres were proportioned like the intervals of a diatonicscale.4 The second school holds that it is the motions of the planets that relateharmonically, their different rates of revolution corresponding to differences of pitch.These all presume a stationary and silent earth, though it was not certain whether therevolutions should be calculated relative to the earth, in which case Saturn, havingfurthest to travel, would move fastest, or relative to the zodiac, in which case Saturnwould be the slowest planet, taking 30 years to make one circuit, and the moon, with itscycle of 28 days, the fastest.5

There are other schemes, especially those of the Arab astronomers and the variousinterpreters of the scale of Platos Timaeus, but they need not concern us here. Whatresults from every scheme prior to Kepler is that the planetary tones are derived fromsome existing scale or interval-sequence that cannot possibly be valid in any scientific,quantitative way, because the known proportions of either distances or motions are vastlydifferent from the proportions of the tones used to represent them. This is where Keplersapproach differed from all his predecessors: his work of 1619 was the first time that atheory of celestial harmony was derived directly from astronomical observation.

Hitherto, these theories had almost unanimously assigned a single, unvarying toneto each planet, as one would expect to result from a perfect circular orbit.6 However, withan inspired leap of the imagination Kepler saw that the planetary tones must now vary,their pitch rising and falling in proportion to their acceleration and retardation. Hecalculated the exact amount by comparing the daily motion of a planet at perihelion withits daily motion at aphelion, expressed as degrees of a circle. This gave a simpleproportion, which like all proportions could be translated into musical intervals byregarding the two terms as different string-lengths.

For example, Saturns angular motion at aphelion, following Keplers data, is 106minutes of arc. At perihelion, it is 135 minutes. The proportion of the two quantities,106:135, is approximately 4:5. Two strings of relative lengths 4 and 5 sound pitches amajor third apart. Therefore Saturns song is contained within the limit of a major third(see Figure 1).7

The corresponding figures for Jupiter are: motion at aphelion 270 minutes; motionat perihelion 330 minutes. The proportion 270:330 is approximately 5:6, thus its musicalinterval is a minor third.

In the case of Venus, which has an almost circular orbit, the pitch difference is24:25, an interval smaller than a semitone which Kepler notates as a unison. In the caseof Mercurys orbit, its musical representation covers an octave plus a minor third (thoughit is erroneous to assume, as the notation suggests, that its upward and downward coursesare different).

Kepler could now satisfy his need to find divine reason in the planetary motions:it was Gods desire that the cosmos should produce a variety of tones and harmonies.With somewhat forced arguments, he found in these both the major and the minor modes,but unfortunately the music of all the planets singing at once was horribly discordant byseventeenth-century standards. Since the six planets hardly ever coincide on the notes ofa perfect triad, Kepler tabulated all the cases in which five or even only four of them doso, filling many pages in a desperate attempt to adapt the data to traditional harmony. Infact, his planetary music, when transposed within our range of auditory perception,sounds much more like twentieth-century electronic music, as one can hear from therecording made in 1979 by two professors at Yale University, John Rodgers and WillieRuff.8

None of the believers in the Harmony of the Spheres contended that we can hearit on earth. Tycho Brahe himself, not contesting the existence of the heavenly music, hadused our deafness to it as sure evidence that the heavens cannot be filled with air.9 Keplercould not leave it at that. Having taken such pains to establish the existence of an entirelynew kind of planetary music, he had to integrate it with his search for meaning andpurpose in the cosmic ordering: someone, besides God, had to benefit from it. In the finalchapter of his book, he refers to Tychos surmise that the planets might be inhabited, andsuggests that the intellect best able to appreciate the planetary harmonies might reside inthe place from which they are measured, namely the Sun. What use is this furnishing, ifthe globe is empty? Do not the very senses themselves cry out that fiery bodies inhabit it,which have the capacity for simple minds, and that in truth the Sun is, if not the king, atleast the palace of the intellectual fire?10

By modern criteria, Kepler seems to have had a split personality, half scientist,half mystic. His obsession with cosmic harmony puts him in the same category as RobertFludd, author of Utriusque cosmi historia (1617) and other encyclopedic works ofChristian Hermetism; yet in the Appendix to Harmonices Mundi, Kepler attacks Fluddssystem on the grounds that what he endeavors to teach us as harmonies are meresymbolism...rather than philosophical or mathematical.11 The immense value of Keplersdiscoveries, to his own way of thinking, was anything but a split: it lay in the fact that hisNeoplatonic intuitions were backed up by hard, scientific data.

To his sorrow, they were received in profound silence by the scientific world, inwhich the Harmony of the Spheres was as irrelevant as the quest for the unicorn. Theheliocentrists, Copernicus and Galileo, had ignored the time-honored myth, and it playedno part in the rapid triumph of their cosmology. It would take Newton to sift HarmonicesMundi and extract the scientific wheat from the speculative chaff. However, afterKeplers death his work found one careful reader: Athanasius Kircher (1602-1680),whose combination of a scientific mentality with Christian piety and a Hermetic-Neoplatonic philosophy resembled Keplers own.

It is instructive to see these esoteric inclinations occurring across the sectariandivide that separated the heterodox Lutheran12 Kepler from the Jesuit Kircher, and to

compare the consequences of it for our subject. Take first the Copernican question. In hisstandard history of the Copernican Revolution, Thomas S. Kuhn writes that Protestantleaders like Luther, Calvin and Melanchthon led in citing Scripture against Copernicusand urging the repression of Copernicans. [...] For sixty years after Copernicus deaththere was little Catholic counterpart for the Protestant opposition to Copernicanism.13His system was known in the Catholic universities, and his calculations aided in thepreparation of the new Gregorian Calendar of 1582. For a while, the Church held noofficial position on the subject, and free debate prevailed among those able tocomprehend the mathematical arguments pro and con. In 1584 Giordano Bruno publishedhis cosmological ideas, including a defence of Copernicus, in his Cena de le Ceneri, andlived, for the time being, unmolested.

Meanwhile, the Lutheran astronomer Tycho had become increasingly dissatisfiedwith the Aristotelian model of the heavens. His observation of comets had persuaded himthat the heavens did not consist of solid, crystalline spheres, but that comets, planets, andthe earth all floated in a rarefied ether. This conclusion freed him from dependence oneither the Aristotelian-Ptolemaic system or on the Copernican, while his aristocratic andindependent nature induced him to invent his own solution. By 1587 he was writing to hiscorrespondent Christoph Rothmann about a certain theory concerning the arrangementof the heavenly revolutions other than the Ptolemaic or Copernican, far more agreeablethan these, and recently ascertained by me, informed by experience itself.14

While Tychos system was indeed based on his observations, and these of aprecision hitherto unequalled, he too subscribed to Neoplatonic notions of a living andharmonious cosmos. He wrote: As that divine philosophy of the Platonists seems to haveappropriately realised, heaven is animated, and the heavenly bodies are themselvesanimated, endowed with the living spirit of a particular heaven.15 He rejectedCopernicus system, but mainly on aesthetic grounds because he found it ill-proportionedwhen compared with the ratios, symmetries, and harmonies found in the microcosm.Referring to the heliocentric hypothesis, he says that That ungeometric, and asymmetric,and disordered way of philosophising would produce something very foreign to divinewisdom and providence.16 His own solution, known as the Tychonian system, has theplanets revolving around the sun, while the sun, together with the moon and the fixedstars, revolves around an unmoving earth.

It was this cosmology that was eventually adopted by the Society of Jesus, andthus of necessity by Kircher. Originally, the Jesuits had no official position on the matter,except that the Societys rules required that In matters of any importance professors ofphilosophy should not deviate from the views of Aristotle, unless his view happens to becontrary to a teaching that is accepted everywhere in the schools; or especially if hisopinion is contrary to the orthodox faith.17 Nonetheless, by the early years of theseventeenth century the Society had become one of the Copernican systems mainpromoters, albeit unintentionally, because of the excellent astronomical teaching of theircolleges in which all systems were studied from a mathematical point of view, even ifonly to refute them.18 Jesuit scientists shared in the excitement about the discoveries thatGalileo was making through his telescope, such as the four satellites of Jupiter and thephases of Venus, and when in 1611 Cardinal Bellarmine (himself a Jesuit) asked them toevaluate the discoveries, they confirmed them, despite their deviation from Aristotelianorthodoxy.19

Kepler had long been convinced by Copernicus, and in his Astronomia Nova(1609) could shrug off the objections of his fellow Protestants in the following boldwords:

In theology the influence of authority should be present, but in philosophy it is theinfluence of reason that should be present. St. Lactantius denied that the earth isround; St. Augustine conceded its roundness but denied the antipodes; today theHoly Office concedes the smallness of the earth but denies its motion. But for methe holy truth has been demonstrated by philosophy, with due respect to theDoctors of the Church, that the earth is round, that its antipodes are inhabited, thatit is quite despicably small, and finally that it moves through the stars.20

This was exactly the kind of attitude that led, under the Catholic hegemony, to theprohibition placed upon Galileo in 1616, not to hold or teach the Copernican system.As is generally acknowledged by scholars today, it was not because the geocentric systemwas official dogma, but because Galileo, as a layman, had presumed to interpret the Bibleand the Church Fathers as suited his scientific program. Rivka Feldhay, in her usefulsummary of the Trials of Galileo, writes that from the point of view of the churchauthorities, an attempt to prove the motion of the earth might result in an encroachmenton the domain of scholastic phlosophers and theologians, who, in fact, had beenunchallenged by the traditional form of astronomy. It could also be perceived as a threatto the monopoly of priests in the interpretation of the Scriptures which the decrees of theCouncil of Trent for the first time had anchored in canon law.21

The prohibition had the immediate effect of placing Copernicanism itself under aban in Catholic lands. The General of the Jesuits, Claudio Aquaviva (1543-1615) hadalready been tightening the screws on the Orders members to enforce Aristotelian andThomist orthodoxy.22 After the prohibition of 1616, the Jesuit scientists had to find somenon-Copernican system within which to work, and the Tychonian, which had room forrecent discoveries but did not require a re-interpretation of the Scriptures, was the bestthey could find.

This was not a happy situation for the scientists, and its consequences are starklysummed up in the words of Robert Blackwell: Jesuit science thus died on the vine, justas the first blossoms appeared.23 Blackwell writes of the typical predicament of OrazioGrassi (1583-1654), who held the Chair of Mathematics at the Collegio Romano (theJesuit college in Rome), and who had had a long controversy with Galileo:

As an informed astronomer he knows that the Aristotelian-Ptolemaic hypothesis isbeset with serious difficulties; as a Jesuit he knows that the Churchscondemnation of Copernicanism obliges him under religious obedience to acceptthe qualification that the Copernican hypothesis is erroneous. So just three yearsafter the condemnation, Grassi turned to the Tychonic model as a compromise areaction which he shared with many other Jesuit astronomers at the time.24

This, then, was the system that Athanasius Kircher was obliged to adopt in hispublished works, whatever he thought in private:25 a constriction that would naturallyaffect any theory he might have on the Harmony of the Spheres. In his early work on

optics, Ars Magna Lucis et Umbrae (1646), Kircher outlines philosophical principleshardly different from Keplers. Celestial bodies (he writes) are placed by the Creator tocomplement discord with concord, consonance with dissonance, and sometimes to giveabsolute harmony. (This is exactly what Kepler found in combining the planetary songs.)As we see, the sun encourages growth and procreation, then in the autumn when it retires,things decay. But God has put the moon there to perform twelve circuits to each one ofthe sun, and to supplement the want of sunlight. The combination of influences isresponsible for all the generation in our world.26 For the same reason, the rest of theplanets have various courses, aspects, and anomalous movements relative to the earth andthe sun, so that by their approach and departure from the sun, moon, and earth, and by thevarious mixtures of light and qualities, they cause various effects here below.27

Towards the end of Ars Magna Lucis, Kircher draws up a chart, based on datafrom Tycho Brahes observations and conjectures about the distances of the planets fromthe sun and from the earth, and his estimates of the diameters of the planets and the sun.28This was bound to give different figures from Keplers elliptical orbits and heliocentricsystem, but the most notable thing about the chart is its emphasis on proportion. Kirchertabulates the proportions of the earths radius to the radii of the sun, moon, and planets;the proportions of the earths volume to the volumes of the same; and the proportions ofthe suns diameter to the radii29 of the planets.

In the sciences of the classic Quadrivium (Arithmetic, Geometry, Music, andAstronomy), proportion is studied in the context of musical intervals, and consequently,proportional tables immediately put one in mind of intervallic studies. What leaps out ofthis chart is that the great majority of the proportions give non-harmonic intervals, notused in the musical system.30 There is no possibility of deriving a theory of the Harmonyof the Spheres from them, and Kircher perhaps intended to show the absurdity of anysuch attempt.

Keplers harmonies receive specific attention in Kirchers encyclopedic work onmusic, Musica Universalis (1650), whose tenth and last book, Decachordon Naturae,promises to demonstrate that the nature of things in all respects observes musical andharmonic proportions, and that even the nature of the universe is nothing other than themost perfect music.31 Introducing the theme of the Harmony of the Spheres, Kircherwrites that many have tried to specify the celestial harmonies, but that all their efforts areflawed.32 Yet according to Pythagoras, Seneca, Saint Augustine, Cicero, Plato, Philo,Boethius, and many others, the world must be harmonious; or (to draw on Kirchersfavored metaphor), if the universe is the Temple of God and the Church of the Blessed,then it cannot lack for singers and organs.33

Modern astronomy, Kircher continues, has exploded the ancient belief that thecelestial bodies make audible harmony, since the heavens have no solidity, nor is theorder of the spheres the same as the ancients thought. Having thus dismissed the ancients,he turns to Kepler, who replaced Ptolemys theories with a new structure of the heavens,yet wrapped it in almost unintelligible, mystical terms. Kircher summarizes Keplerstheory of the Platonic solids as dictating the planetary orbits, with a diagram, andconcludes I truly do not see how the intended harmony of the heavens can be provenfrom these [speculations] by Philosophers and Mathematicians, since one could rather saythat the heavens are forced into his violently distorted five solid bodies, than that thebodies are applied to the heavens.34

It was the inaccuracies in Keplers scheme that displeased Kircher, as indeed ithad displeased Kepler, who, finding that the orbits did not fit perfectly between the fivesolids, was set on the path that led to the solutions of Harmonices Mundi. Turning to thelatter, Kircher reproduces Keplers astronomical data and the songs derived from them,but refuses to grant that the proportions between perihelion and aphelion motion deserveto be called harmonic. They are simply not accurate enough. Saturns proportion of135:106 is not a major third, says Kircher; that would require the latter figure to be 108.For Jupiters interval to be a minor third, its proportion should be not 270:330 but270:324. In short, there are no perfect consonances in Keplers data.

Kircher passes from Keplers theories to those of the Bohemian astronomer AntonMaria Schyrleus de Reita, which need not concern us here.35 He then tells his readerswhat the heavenly harmony really consists of. (Because of Kirchers verbose writing, Igive a prcis36 rather than a complete translation.) The heavenly harmony (he says)cannot be shown in numbers of motions or the sensible collision of heavenly bodies, butonly in their admirable disposition, and their ineffable proportion one to another, so thatto take one away would cause the whole to perish. It is also in the exact quantity andmagnitude of each body for achieving the desired effect. Thus the sun, moon, and earthhave the requisite distances and magnitudes for perfect mutual influence, aid, andpreservation. (Kircher gives no figures for any of these.) An example is the temperatureon the earth, ideal for human life which would be impossible if the sun were closer orfurther away.

The distances between the sun, earth, and planets are such as to balance the sunsheat with the moons coldness. For example, in summer the sun is strong, the moonweak, causing a variety and mixture of consonance and dissonance. The influence of thesun and moon is like a perfect octave. However, God has added Venus to give supportwith virtues such as vary the lunar influences; meanwhile, Mercury modifies that whichis noxious in the sun. The changing distances from the earth bring about different effects.

Moreover, God has placed two dissonant bodies, Mars and Saturn, from whosepestiferous evaporations all the earths ills come. Yet between them is the benign star ofJupiter. The malefic planets act like caustic medicines which attract sick matter andliberate it, so that there is no ill in nature that does not turn to good.

In musical terms, Mars and Saturn are dissonances, tied in perfect syncopation toJupiter, while Mercury sounds a dissonance between the concords of Venus and themoon. The seven planets together give a perfect tetraphony or four-part harmony thatKircher now illustrates with a short musical example:

Figure 3

This trivial phrase may compare poorly with Keplers spectacle of ever-changingharmonies, but perhaps it was deliberately poor, just as the tables of proportions in ArsMagna Lucis were conspicuously un-harmonic: they showed, as Kircher undoubtedlybelieved, that the heavenly harmonies could not possibly be reproduced in earthly music.

The solar system of Kirchers day had become much more complex than theseven traditional planets. Although Uranus, Neptune, and Pluto still lay undiscovered, theprimitive telescope had revealed four moons around Jupiter, and twin bulges or adjacentsatellites (actually, the rings) of Saturn. Wanting to find a rationale for these phenomena,Kircher hit on the idea that the heavenly bodies were grouped in choirs. The outermostone was the Choir of Saturn, in which the planet was given two moons to supplementthe light of the distant sun. Next came the Choir of Jupiter, the only instance in whichKircher offers a harmony based on astronomically determined numbers. According toReitas figures, Jupiters moons were distant by 3, 4, 6, and 10 diameters of their planet.Whatever is requisite for music certainly lies concealed in these numbers: for thedistances of each body correspond precisely to a harmonic quantity: 3:4:6:10.37 But thereal purpose of the Jovian Choir was to cast an ever-changing variety of light and shadeand thus to moderate the influences that Jupiter sends down to our world. Then there isthe The Solar or Apolline Choir, which contains in itself Venus, Mercury, the moon,the earth, and is parallel, as it were, to the Jovian Choir; of which enough has been said atthe beginning, so we will not repeat it here.38 The one planet left out of any choir isMars, whose eccentric orbit carries it now close to Jupiter, now to the sun, bringing toeach its syncopations and baleful influences.

To deter those who might suspect other purposes in such a complicatedarrangement, Kircher draws a corollary that seems directly aimed at Keplers boldspeculations about other inhabited spheres:

Some say that in places where men are unable to dwell because of the excessiveintensity of the light, or because of temperatures incompatible with human nautre,there are creatures endowed with a different nature. Since nothing of the kind is

known to us, nor can be known, it seems to be fundamentally dangerous to theFaith. Who could regard it otherwise than as a blind and baseless imagination, anovelty and fiction of sectaries?39

Kirchers vision of a harmonious cosmos was second to none in its elaborationand imaginative power, of which I have given only a slight sampling here; but whereasKepler had presented his planetary songs as factual, Kirchers choirs were mere figures ofspeech, his Decachord of Nature a metaphor for the Hermetic principle ofcorrespondences that he believed to underlie all of creation.

In conclusion, I will mention some of the later developments of Keplers andKirchers ideas. Keplers faith in an astronomical rationale for the Harmony of theSpheres lay latent for nearly three centuries, until with the dawn of the twentieth centurya few isolated researchers began reconsidering it. The first of these was Emile AbelChizat (1855-after 1917), a French composer and impresario.40 His approach consisted ina revision of the first type of planetary music, as described above, which compares theplanetary distances to intervals on a hypothetical string. Unlike the Greek and medievaltheorists, whose musical system was limited to two or three octaves, Chizat found that ittook over seven octaves to notate the intervals of the planets from Mercury to Neptune,including the asteroids Hungaria, Vesta, Ceres, Psyche, and Ismene, and to discover thatthey fell into place in a gigantic major chord.

I will only mention briefly the theories of some other twentieth-centuryresearchers: W. Kaiser, who found harmonies not in the distances between the planets, asChizat did, but in their mean distances from the sun;41 Alexandre Dnraz, whoconstructed a scale based on taking the Golden Section of the planetary distances;42Rodney Collin, who used as his data the conjunctions of the planets;43 Thomas MichaelSchmidt, who derived significant (musical) harmonies by comparing the time-periods ofthe planets rotation around the sun.44 More relevant to this study are those who addressedthemselves specifically to Keplers harmonies.

In 1909 Ludwig Gnther revisited Harmonices Mundi, corrected Keplers valuesaccording to modern astronomy, and applied their principle to Uranus and the asteroidsCeres, Vesta, Pallas, and Juno.45 This exercise was completed by Francis Warrain in hisbook on Kepler, published in 1942, which included the perihelion and aphelion values forNeptune (discovered 1843) and Pluto (1930).46 Finally, Warrains data were analyzed byRudolf Haase following the methods of Hans Kayser, the re-founder of the science ofHarmonics in modern times.47 Haase took the aphelion value of Saturn as thefundamental of a theoretical harmonic series, and related all the other values to it in termsof the tones to which they corresponded, irrespective of octave displacements. He foundthat the great majority of them fell on the tones C, D, E, and G, thus validating the beliefthat the planetary orbits accord with the laws we know as harmonic. Haases approach tothe data, and the conclusions he draws from it, are quite different from Keplers,expressed as they are in secular and scientific terms and free from the anachronisticinfluences of musical practice, but they show the continuing vigor of Keplers example.

These scattered instances pale in comparison with the recent publishing campaignof John Martineau (born 1967). His books, illustrated with finely-drawn geometricaldiagrams, present a mass of evidence that the solar system is in fact designed inaccordance with the principles sensed by Pythagoras, the Platonists, and especially

Kepler.48 For instance, in The Harmony of the Spheres Martineau shows that Kepler wasright in principle, both in his interpretation of the planetary orbits as governed by simplegeometrical figures and in his conviction that simple musical proportions control theirorbits; only these principles need to be tested against contemporary astronomical data,whereupon they prove far more fruitful and accurate than they ever were in the past. ABook of Coincidence collects an astounding number of instances of the geometrical andharmonic placement and interrelation of the planets, any one of which might be dismissedas coincidence, but which, taken as a whole, confirm that, in Platos words, God alwaysgeometrizes.49

Kircher would have been delighted by these discoveries. While renouncing theattempt to transcribe the heavenly music in earthly terms, he readily embraced it as ametaphor for the intelligent design of creation. Whereas Keplers God had taken delightin assembling a cosmos out of geometric solids and making music out of its motions,Kirchers God was more a scientist than an artist or musician, calibrating the planetarymotions and distances in exactly the right proportions to facilitate life on earth. Concordand discord were merely the musical equivalent of benefic and malefic planetaryinfluences; harmony, of the indescribable complexity and ultimate benevolence of Godsdesign. These principles, as Kircher believed, could survive any revision of the figures,and even stand aloof from the debate over the Copernican system, of which he himselfwas a dutiful opponent.

Such an attitude to the Harmony of the Spheres, even if excluded from scientificdiscourse, served as a fruitful metaphor for three centuries of poets.50 And this was notthe end of it. In the 1990s, Kirchers notion of the finely-calibrated earth resurfacedamong a few influential biologists, already leaning towards the Anthropic Principle(that the only universe we can know is one that happens to contain humans), and to GaiaTheory (that the earth is best studied as if it were itself a living organism).51 Theyobserved that the presence and variety of the biosphere depends on a delicate equilibriumof earths characteristics, such as its distance from the sun, gravity, atmosphere, oxygen,water, ocean salinity, axial inclination, presence of the moon, etc. If any of these wereeven slightly different, life could not have evolved as it has done: a situation playfullychristened The Goldilocks Effect.52 For Kircher, this could only be the work of aconcerned, personal God, and its sole purpose was to serve man, whose purpose in turnwas to serve and love God. Todays scientists prefer non-theistic explanations, but thephenomenon of earths fine-tuning remains as a challenge to cosmologists, who may findthemselves unwittingly continuing where Kepler and Kircher left off.

1This article was first published in Italian translation by Paolo Magagnin in Forme e correnti dellesoterismo occidentale, ed. Alessandro Grossato (Milan: Edizioni Medusa, 2008), pp. 145-164. It is an expanded version of a paperdelivered at a conference on the history of Western Esotericism at the Giorgio Cini Foundation in Venice, on October 29-30, 2007.

Johannes Kepler, Harmonices Mundi Libri V, Linz: J. Planck, 1619. I refer to the definitive English edition: The Harmony of the World, translated with an Introduction and Notes by E.J. Aiton, A.M. Duncan, and J.V. Field, Philadephia: American Philosophical Society, 1997 (Memoirs of the American Philosophical Society, vol. 209). For clarifications of Keplers often obscure text, I am indebted to Bruce Stephenson, The Music of the Heavens: Keplers Harmonic Astronomy, Princeton: Princeton University Press, 1994.2 Definitions from Van Nostrands Scientific Encyclopedia, 3rd ed., Princeton: D. Van Nostrand Co., 1958, p. 930, s.v.

Keplerian Laws of Planetary Motion. The first two laws were enunciated in Keplers Astronomia nova, Prague, 1609.3 In Keplers Mysterium Cosmographicum, Tbingen, 1596.

4 Examples of this approach include the systems of Pliny, Martianus Capella, Censorinus, Theon of Smyrna, and

Achilles Tatios.5 This is the approach of Boethius, Nicomachus of Gerasa, and probably Cicero (in The Dream of Scipio).

6 A rare exception is Giorgio Anselmi Parmensis (before 1386-between 1440 and 1443), De Musica, ed. Giuseppe

Massera, Florence: Olschki, 1961, who anticipated Kepler in describing the planetary music as polyphonic and continually changing.7 The planetary songs should be imagined as glissandi moving up and down between the given limits, not as scales with

distinct tones, as Keplers notation suggests.8 See John Rodgers and Willie Ruff, "Kepler's Harmony of the World: A Realization for the Ear," American Scientist,

67 (1979). The recording was released on a long-playing record, and has been reissued as a compact disc. It includes theharmonies of the outer planets.9 Tycho Brahe, letter to Johannes Rothmann, August 17, 1588, cited in Adam Mosley, Bearing the Heavens: Tycho

Brahe and the Astronomical Community of the Late Sixteenth Century, Cambridge: Cambridge University Press, 2007, p. 89.10

The Harmony of the World, p, 496.11

The Harmony of the World, p. 505. The Fludd-Kepler debates are well known from their treatment in Wolfgang Pauli,The Influence of Archetypal Ideas on the Scientific Theories of Kepler, in C.G. Jung and W. Pauli, The Interpretationof Nature and the Psyche, New York: Pantheon Books for the Bollingen Foundation, 1955, pp. 149-240, and Frances A.Yates, Giordano Bruno and the Hermetic Tradition, London: Routledge & Kegan Paul, 1964, pp. 440-444. 12

Although a Lutheran by faith, Keplers personal beliefs kept him from being a regular communicating member of his church. Max Caspar writes: ...he had arrived at a conception of the doctrines concernings ubiquity [of the body of Christ] and the Eucharist, which deviated from the Augsburg Confession in which he had been reared; regarding ubiquity, he leaned toward the Catholic doctrine, but regarding the sacrament, toward the Calvinist. Max Caspar, Kepler, trans. C. Doris Hellman, London: Abelard-Schuman, 1959, pp. 82-83.13

Thomas A. Kuhn, The Copernican Revolution: Planetary Astronomy in the Development of Western Thought, New York: Vintage Books, 1959, p. 196. 14

Letter in Tychonis Brahe Dani Opera Omnia, ed. J. Dreyer et al., Copenhagen: Nielsen & Lydiche, 1913-1929, VI, 88.15-25, cited in Mosley, Bearing the Heavens, p. 79.15

Tychonis Brahe Opera Omnia, VI, 221.45-49, cited in Bearing the Heavens, p. 144.16

Tychonis Brahe Opera Omnia, VI, 222.27-31, cited in Bearing the Heavens, p. 145.17

Decree 41 of the Fifth General Congregation of the Society of Jesus (1593-94), as cited in Richard J. Blackwell, Behind the Scenes at Galileos Trial, Notre Dame: University of Notre Dame Press, 2006, pp. 208-209.18

See John Gascoigne, The Role of the Universities, in Reappraisals of the Scientific Revolution, ed. David C. Lindberg and Robert S. Westman, Cambridge: Cambridge University Press, 1990, pp. 207-260; here cited, p. 214.19

See Rivka Feldhay Galileo and the Church. Political Inquisition or Critical Dialogue? Cambridge: Cambridge University Press, 1995, p. 249.20

Kepler, Astronomia Nova, in Gesammelte Werke, Munich: C.H. Beck, 1937, III, 34, cited in Richard J. Blackwell, Galileo, Bellarmine, and the Bible, Notre Dame: University of Notre Dame Press, 1991, p. 56. 21

Galileo and the Church, p. 36.22

See Galileo, Bellarmine, and the Bible, pp. 138-139.23

Galileo, Bellarmine, and the Bible, p. 142.24

Galileo, Bellarmine, and the Bible, p. 156.25

On Kirchers leanings toward Copernicanism, see Galileo and the Church, p. 203; Galileo, Bellarmine, and the Bible,pp. 158, 163-164. On Kirchers astronomy in general, see Davide Arecco, Il sogno di Minerva: La scienza fantastica di Athanasius Kircher (1602-1680), Padova: CLEUP Editrice, 2002, pp. 93-100; Giuseppe Monaco, Tra Tolomeo e Copernico, in Athanasius Kircher. Il Museo del Mondo, ed. Eugenio Lo Sardo, Rome: Edizioni de Luca, 2001, pp. 142-158.26

Summarized from Ars Magna Lucis et Umbrae, Rome, 1646, pp. 47-48.27

Eandem ob causam reliqui Planetae varios ad terram, Solemque habitus, repectusque, variamque motum anomalian sortiti sunt; ut accessu, recessuque ad Solem, Lunam et terram ex varia liminis, qualitatumque mistura, varios quoque in

inferioribus effectus causentur. Ars Magna Lucis, p. 48.28

Ars Magna Lucis, p. 764.29

Sic, though a comparison of diameters or of radii is intended, the proportions being the same in both cases.30

For example: the proportions of radii are 17:5, 8:3, 11:6, 5:26, 11:6, 5:12, 11:31, and 3:13. 31

Naturam rerum in omnibus ad Musicas & harmonicas proportiones respexisse, atque ade Naturam universi nil aliudnisi Musicam perfectissimam esse ostenditur. A. Kircher, Musurgia Universalis, Rome, 1650, II, p. 364. 32

Musurgia Universalis, II, p. 373.33

Musurgia Universalis, II, p. 376. See the well-known engraving of the Organ of the Worlds Creation (Musurgia Universalis, II, opposite p. 366) in which the creations of the six days are symbolized as registers of an organ. A reproduction is in Athanasius Kircher: Il Museo del Mondo, p. 266.34

Verm quomodo ex his Philosophis & Mathematicis intenta coelorum harmonia demonstrari possit non video, cumipse in hoc potius coelos ad sua 5 corpora solida violenter detorta attraxisse, quam corpora coelis applicasse dici possit.Musurgia Universalis, II, p. 377.35

Reita or Rheita was the author of Oculus Enoch et Eliae, sive, Radius sidereomysticus, Antwerp, 1645, which proposed an algebraic solution to the (geocentric) planetary distances. Kircher explains it with apparent approval.36

Musurgia Universalis, II, pp. 381-382.37

Cert sub hisce numeris quicquid in musica desiderari potest abditum est, cm & distantiae vniuscuiusque corporis quantitate harmonic prorsus correspondeant. Musurgia Universalis, II, p. 386.38

Chorus Solaris siue Apollineus sub se continet Venerem, Mercurium, Lunam, Terram, estque Iouiali choro quasi parallelus; de cuius harmonia cm in principio sat dictum sit, hic eadem repetere noluimus. Musurgia Universalis, II, p. 388. To make the earth merely one of four choristers to the sun steers perilously close to heliocentricity.39

Sequitur etiam, ibi homines ob excessiuam luminis intensionem, & ob temperamentum loci humanae naturae incongruum habitare minim possit, qui ver ibi diuersae naturae creaturas conditas esse volunt; cum de ijs nihil nobis constet, sed nec constare possit, imo in Fide periculosum videatur, quis non videt id non nisi id temere & absque vllo fundamento nouitatum sectatoribus confictum excogitatumque? Musurgia Universalis, II, p, 387.40

See Azbel [Chizats pseudonym], Harmonie des mondes, Paris: Hughes Robert, 1903. English translation in Godwin, Harmony of the Spheres (see note 47 below), pp. 400-401.41

Kaisers theories are discussed in Hans Kayser, Lehrbuch der Harmonik, Zurich: Occident Verlag, 1950, pp. 214-216.42

Alexandre Dnraz, La Gamme, ce problme cosmique, Zurich, Hug, n.d.43

Rodney Collin, The Theory of Celestial Influence, London: Watkins, 1980, pp. 78-87.44

Thomas Michael Schmidt, Musik und Kosmos als Schpfungswunder, Frankfurt, Verlag Thomas Schmidt, 1974, pp. 174-185.45

Ludwig Gnther, Die Mechanik des Weltalls, Leipzig, 1909, pp. 142-143.46

Francis Warrain, Essai sur lHarmonices Mundi ou la Musique du Monde de Johannes Kepler, 2 vols., Paris, 1942.47

Rudolf Haase, Aufstze zur harmonikale Naturphilosophie, Graz: Akademische Druck- und Verlangsanstalt, 1974. The relevant articles are translated in Cosmic Music: Musical Keys to the Interpretation of Reality, ed. Joscelyn Godwin, Rochester, Vt.: Inner Traditions International, 1989. For further documentation and discussion of the present subject, with English translations of Keplers and Kirchers texts, see also my books Music, Mysticism and Magic: A Sourcebook, London: Routledge, 1985; Harmonies of Heaven and Earth: The Spiritual Dimension of Music from Antiquity to the Avant-Garde, London Thames & Hudson, 1987; The Harmony of the Spheres, A Sourcebook of the Pythagorean Tradition in Music, Rochester, Vt.: Inner Traditions International, 1993; Lsotrisme musical en France, 1750-1950, Paris: Albin Michel, 1991 (translated as Music and the Occult: French Musical Philosophies 1750-1950, Rochester, NY: University of Rochester Press, 1995); The Mystery of the Seven Vowels in Theory and Practice, Grand Rapids: Phanes Press, 1991 (Italian translation by Francesca Maltagliati: L e l: Il mistero delle sette vocali del nome di Dio, Casaletto Lodigiano: Mamma Editori, 1998); Athanasius Kirchers Theatre of the World, London: Thames & Hudson, forthcoming (2008). 48

John Martineau, A Book of Coincidence. New Perspectives on an Old Chestnut, Presteigne: Wooden Books, 1995; A Little Book of Coincidence, Presteigne: Wooden Books, 2001; Ofmil C. Haynes [pseudonym?], The Harmony of the Spheres, Presteigne: Wooden Books, 1997. 49

Platos dictum is reported by Plutarch, Convivialium disputationum, 8,2. Among recent attempts to reconcile ancient cosmological traditions with the findings of modern science, with an emphasis on harmony, Italian readers will appreciate the work of the erudite musician Roberto Caravella, Sphaerae: trattato sulliperrealt, Casaletto Lodigiano: Mamma Editori, 2001.50

For insights into this historical process, see Fernand Hallyn, La Structure potique du monde: Copernic, Kepler, Paris: Editions du Seuil, 1987; English translation: The Poetic Structure of the World: Copernicus and Kepler, New York: Zone Books, 1990, especially pp. 250-251 which treat Kircher. 51

A.J. Watson, Co-evolution of the Earth's Environment and Life; Goldilocks, Gaia and the Anthropic Principle, in James Hutton - present and future, ed. G.Y. Craig and J.H. Hull, London: Geological Society, 1999 (Special Publications, no. 150), pp. 75-88.52

Referring to the fairytale Goldilocks and the Three Bears, in which Goldilocks finds the Bears porridge to her satisfaction when it is not too hot, not too cold, but just right.