To thee, the heaven and its stars make music,
“Hymn to Hathor,” a dual Egyptian god of love and music, Temple of Dandera
Sun and moon sing praises to thee,
The whole earth is making music for thee.
This ancient Egyptian hymn suggests that some form of the concept of “music of the spheres,” the notion that musical sounds are produced by the movements of the planets, was known in Egypt long before the beginning of European literature. If there were logic supporting this concept, for the ancients it would have proceeded something like this: [1] music tones are created by vibration, [2] vibration is caused by movement, hence [3] the movement of the planets must ipso facto create sound. But there was a problem because no one could hear these sounds. The ancients did not yet understand the role of air in carrying the sounds of music, nor did they understand there was no air in space. They only knew they could not hear the Music of the spheres and the efforts of those who felt obligated to explain this makes for interesting reading.
The basic concept of the Music of the spheres had much to recommend for itself to the ancient Greeks, who were always very interested in the relationship of man and nature. Surviving ancient Greek literature tends to associate this concept with Pythagoras, 570-490 BC, to whom history assigns the discovery of the numerical ratios of the lower part of the overtone series. Again, believing everything in nature must be related, they presumed that the ratios representing the separation of the lower tones of the overtone series must be the same ratios as those representing the distances separating the planets.
But there are problems with Pythagoras, beginning with the fact that there are no extant writings by him. All we have are the ideas attributed to Pythagoras by his followers and students.
Aristotle (384–322 BC) acknowledged that Pythagoreans were the first to take up mathematics, and that they “supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number.”1
Some think it necessary that noise should arise when so great bodies are in motion, since sound does arise from bodies among us which are not so large and do not move so swiftly; and from the sun and moon and from the stars in so great number, and of so great size, moving so swiftly, there must necessarily arise a sound inconceivable great. Assuming these things and that the swiftness has the principle of harmony by reason of the intervals, they say that the sound of the stars moving on in a circle becomes musical. And since it seems unreasonable that we also do not hear this sound, they say that the reason for this is that the noise exists in the very nature of things, so as not to be distinguishable from the opposite silence; for the distinction of sound and silence lies in their contrast with each other, so that as blacksmiths think there is no difference between them because they are accustomed to the sound, so the same things happen to men. What occasions the difficulty and makes the Pythagoreans say that there is a harmony of the bodies as they move, is a proof.2
In the end, Aristotle stated his belief without qualification: this concept is not true.
It is clear that the theory that the movement of the stars produces a harmony, ie., that the sounds they make are concordant, in spite of the grace and originality with which it has been stated, is nevertheless untrue.3
Plutarch (1st century, AD), one of the last of the ancient Greek philosophers, provides some additional information on the beliefs regarding the music of the spheres held among the followers of Pythagoras. It appears that many new claims had been superimposed on the original concept of Pythagoras during the four centuries after Aristotle.
Others there are, who fancy the earth to be in the lowest string of the harp, called proslambanomenos; and so proceeding, they place the moon in hypate, Mercury and Venus in the diatoni and lichani; the sun they likewise place in mese, as in the midst of the diapason, a fifth above the earth and a fourth from the sphere of the fixed stars.
But neither doth this pleasant conceit of the latter come near the truth, neither do the former attain perfect accuracy. However, they who will not allow the latter to depend upon Plato’s sentiments will yet grant the former to partake of musical proportions; so that there being five tetrachords, and in these five distances they place all the planets; making the first tetrachord from the Moon to the Sun and the planets which move with the Sun, that is, Mercury and Venus; the next from the Sun to the fiery planet of Mars; the third between this and Jupiter; the fourth from thence to Saturn; and the fifth from Saturn to the sphere of the fixed stars. So that the sounds and notes which bound the five tetrachords bear the same proportion with the intervals of the planets….
So it is most probable that the bodies of the stars, the distances of spheres, and the swiftness of the motions and revolutions, have their sundry proportions, as well one to another as to the whole fabric, like instruments of music well set and tuned, though the measure of the quantity be unknown to us.4
Plutarch’s Roman contemporary of the first century, Pliny the Elder, also mentions the music of the spheres but he does not take it seriously since he cannot hear these sounds. Nevertheless, we are indebted to him for providing us with information not found in earlier literature on Pythagoras, the latter’s correspondence of the ratios of the tones of the scale with the order of the planets. Pliny cannot help observing that he found this more entertaining than believable.
But occasionally Pythagoras draws on the theory of music, and designates the distance between the earth and the moon as a whole tone, between Mercury and Venus the same, between her and the sun a tone and a half, between the sun and Mars a tone, between Mars and Jupiter half a tone, between Jupiter and Saturn half a tone, between Saturn and the zodiac a tone and a half; the seven tones thus producing the so-called diapason, i.e. a universal harmony; in this Saturn moves in the Dorian mode, Jupiter in the Phrygian, and similarly with the other planets — a refinement more entertaining than convincing.5
During the following years of the early Christiana Era discussion of the Music of the Spheres continued. The Roman Quintilian (30–96 AD) confessed he was “ready to accept the verdict of antiquity.”6 Porphyry, (d. 301 AD) wrote that only Pythagoras could hear this music, Harmony of the Universe, and understood the universal music of the spheres, and of the stars which move in concert with them, and which [the rest of us] cannot hear because of the limitations of our weak nature.7
On the other hand, St Ambrose of Milan (374-397 AD) described the music of the spheres not only as something real, but as something he could hear.
By the impact and motion of these spheres there is produced a tone full of sweetness, the fruit of consummate art and of the most delightful modulation, inasmuch as the air, torn apart by such artful motion, combines in even and melodious fashion high and low notes to such a degree that it surpasses in sweetness any other musical composition.8
An important book on music by a “pagan” philosopher of the 5th century is the allegorical description of The Marriage of Philology and Mercury, by Martianus Capella. This work is a defense of the importance of the seven liberal arts, which were by this time established in the Roman schools. These were the Trivium, consisting of Grammar, Dialectic, and Rhetoric, and the Quadrivium, consisting of Geometry, Arithmetic, Astronomy, and Music. The book was written at a time when Christianity had not yet won its final battle against the “pagans” and might well be thought of as an attempt to fight back against the efforts of the new Church to shut down traditional education and knowledge. Thus this book represents one of the efforts which helped keep the liberal arts alive during the “Dark Ages.” Music for its own sake had been rejected by the Church and it could only find its place in the Church schools as a branch of mathematics.
Capella makes reference to the music of the spheres after “Harmony” [Music] has sung at the allegorical wedding which his book describes. Some of the guests wondered at the “pains and labor involved in the production of the music and the effort and unabated concentration that must have gone into the mastery and attainment of harmonies so soft and caressing as to enthrall the innermost emotions of their hearts.” The answer provided by “Harmony” begins with reference to the disinterest by the Church and mentions the music of the spheres.
A loathsome and detestable creature to earthborn mortals, I have been striking against the star-studded heavenly spheres, where I am forbidden to discourse on the precepts of my art — this despite the fact that the swirling celestial mechanism, in the swiftness of its motion, produces a harmony which it recognizes as concordant with the gamut of all proportions.9
Cassiodorus (480–573 AD), one of the great philosophers of the 6th century, mentions the music of the spheres in a letter to the famous Boethius (475–524 AD). He recalls that earlier philosophers had found the lyre in the constellations and points out that while Nature has not prepared us to hear the music of the spheres, Reason assures us it must exist. In any case, he offers the consolation that we will finally hear this music in Heaven!
Yet, the harmony of heaven cannot be fittingly described by human speech, as nature has not revealed it to human ears, but the soul knows it through reason only. For they say that we should believe that the blessedness of heaven enjoys those pleasures which have no end, and are diminished by no interruption.10
His great contemporary, the famous mathematician Boethius, in De institutione musica, divided music into three kinds, in an apparent descending order of importance: Cosmic Music (which included the music of the spheres), Human music (meaning vocal music) and Instrumental Music. It was a definition which would be followed for centuries, as we can see, for example, in the Musica Disciplina by Aurelian of the 9th century who faithfully copies the three divisions of music by Boethius. While Aurelian admits that man cannot actually hear the music of the spheres, he finds evidence for it in a passage from the Old Testament book, Job 38:37, “… or who can make the harmony of heaven to sleep.” Modern translations have filtered out any reference to Music in this passage.
Johannes de Grecheo, in his De Musica (c. 1300 AD) proves himself to be a man far ahead of his time. He was the earliest philosopher, in our view, whose descriptions regarding the nature of music seem to ring true with readers of our own time. Taking up the traditional classification of music into Music of the Spheres, Human Music and Instrumental Music, a classification which theorists had accepted without comment for half a millennium, Grocheo now blasts Boethius into oblivion. He courageously attacks the faulty logic, the pseudo-science, the beliefs of the Church and the nonsense which Boethius had put forth.
Those who make this kind of division either invent their opinion or they wish to obey the Pythagoreans or others more than the truth, or they are ignorant of nature and logic. First of all, they say universally that music is a science concerning numbered sound. Nevertheless, celestial bodies in movement do not make a sound, although our ancestors believed this.11
A 15th century Italian, Franchino Gaffurio, in his De Harmonia, finds the soul organized in correspondence with the ratios of sound and the planets.
The intellective part corresponds to the octave, the sensitive to the fifth, and the habitual to the fourth. The species of fourth are analogous to the motions of the habitual soul — increase, stasis, and decrease; the species of fifth, to the powers of the sensitive soul — sight, hearing, smell, and taste; the species of octave, to the function of the intellective soul — imagination, intellect, thought, reflection, opinion, reason and knowledge.12
Marsilio Ficino, 15th century, founder of the famous Florentine Academy, contributed a new definition of the purpose of music. Music, he believed, served man’s “spirit” in the same way medicine serves the body and theology the soul. The music one hears provokes a memory in the soul of the divine music found in the mind of God and in the music of the spheres. He also found correlations between the music of the spheres and the signs of the zodiac and with the tones of the scale.
The great 15th century theorist, Tinctoris, followed the lead of Aristotle and declared that the heavenly spheres do not make sound. Music, he says, is of the earth, not the heavens.
But although, as Boethius says, some assert that Saturn is moved with the deepest sound and, taking the remaining planets in proper order, the moon with the highest, while others, however, conversely attribute the deepest sound to the moon and the highest to the stars in their movement, I adhere to neither position. On the contrary, I unshakably agree with Aristotle…together with our more recent philosophers, who most clearly prove that there is neither real nor potential sound in the heavens. For this reason I can never be persuaded that musical consonances, which cannot be produced without sound, are made by the motion of heavenly bodies.13
The best-known English writer of the early Renaissance, Chaucer (14th century), finds the music of the spheres to be the original source for melody and harmony in the world.14
And after shewede he hym the nyne speres,
And after that the melodye herde he
That cometh of thilke speres thryes thre,
That welle is of musik and melodye
In this world here, and cause of armonye.
During 16th century Italy we also find writers who are still willing to believe in the music of the spheres. The great theorist, Gioseffo Zarlino, in his Le Istitutioni Harmoniche, takes the position that we may not hear the music of the spheres but we can understand it on the basis of Reason.
Every reason persuades us to believe at least that the world is composed with harmony, both because its soul is a harmony (as Plato believed), and because the heavens are turned around their intelligences with harmony, as may be gathered from their revolutions, which are proportionate to each other in velocity. This harmony is known also from the distances of the celestial spheres, for these distances (as some believe) are related in harmonic proportion, which, although not measured by the sense [of hearing], is measured by the reason.15
This relationship between the music of the spheres and the soul, mentioned by Zarlino, is found again in Castiglione’s famous book, The Courtier. Here Signor Gaspare questions whether music is something appropriate to “real” men and the Count answers,
The wisest of philosophers held the opinion that the universe was made up of music, that the heavens make harmony as they move, and that as our own souls are formed on the same principle they are awakened and have their faculties, as it were, brought to life thorough music.16
Among the 16th century French writers we find two more explanations why we cannot hear the music of the spheres. First, the important theorist, Pontus de Tyard, in his book, Solitaire second, a character named “le Curieux,” speaks of the ancient Greek notion of the universe being a kind of harmony, in which all of its parts have some comparable relationship with the harmony found in music. He mentions the Music of the spheres, offering the explanation for man’s inability to hear it that, taken together, its effect is that of silence. Then he contends that the basic elements of the earth are related as the tones of the tetrachord, earth being as the lowest pitch, then water, air and fire.
For Montaigne, it is the constant, never ending quality of the Music of the spheres which makes them unnoticeable to us, as for example in the case of the blacksmith who is able to tolerate the noise of his shop.17
One of the most curious philosophical books of 16th century Germany which is worthy of some attention is Henry Agrippa’s three-volume De occulta philosophia, written in 1509–1510 before the appearance of Luther on the German scene. In spite of the title, “Occult Philosophy,” Agrippa was at this time a philosopher in the old mold of Catholic Scholasticism. In a chapter, “Concerning the Agreement of them with the Celestial Bodies, and what Harmony and Sound is Correspondent of every Star,” he goes far beyond any earlier philosopher by adding emotional qualities to the celestial sounds. This can only be understood as being the result of Humanism thought.
But understand now, that of the seven planets, Saturn, Mars, and the Moon have more of the voice than of the harmony. Saturn hath sad, hoarse, heavy and slow words, and sounds, as it were pressed to the center; but Mars, rough, sharp, threatening, great and wrathful words; the Moon observeth a mean between these two.
Agrippa makes no attempt to explain why we cannot hear any of this music of the spheres, but in Book III, he offered a unique explanation for the source of music’s ability to soothe. He begins with a discussion of “divine frenzy,” which is so often mentioned by the ancient poets. This comes from the Muses, he says, and the Muses, in turn, are the souls of the separate planets. Of these only the Sun is given a musical soul.18
Andreas Ornithoparchus, in Musice active micrologus, of 1517, begins by dividing music into Mundane, Human and Instrumental Music. Mundane music, he finds in the “harmony caused by the motion of the stars and the violence of the spheres,” which he also relates to elements and climate. Here he quotes a nice phrase, from a lost work by the philosopher, Dorilaus, “The world is God’s organ.” Even, as he admits, if we cannot hear the music of the spheres, one has to admit that God has created in all things number, weight, and measure. Since these are also the principal properties of music, therefore it is reasonable to believe that the Music of the spheres exists.
Shakespeare also seems to have been well read with respect to earlier theories on music, as we can see in his several references to the ancient Greek notion of the “Music of the Spheres.” The most extended of these is found in The Merchant of Venice,19 where Lorenzo reflects,
How sweet the moonlight sleeps upon this bank!
Here will we sit, and let the sounds of music
Creep in our ears; soft stillness and the night
Become the touches of sweet harmony.
Additional references to the Music of the Spheres in the plays of Shakespeare can be found in As You Like It,20 Henry VIII,21 and Twelfth Night or What You Will.22
One of the most important studies on music of the 17th century was the monumental Harmonie universelle (1636), in five treatises, by Marin Mersenne. Mersenne begins his discussion of this subject by stating that he will not attempt to prove the existence of the Music of the spheres, and then devotes many pages to doing precisely that. [Book II, V] First he offers some possibilities why we cannot hear this music,
Of course, we shall not be able to show whether the planets and stars make any sound. If the air extends as far as the firmament or infinity, as some people believe, having no doubt that God created it infinite…
It is probable that the stars and planets make some sound, inasmuch as they do move in the air. We do not hear the sound, for we are accustomed to it from the wombs of our mothers. Sometimes the sound is too far from us, too low, too high, or too great to be heard, as happens with certain other phenomena. We are, for example, unable to hear the sound or noise which ants and other little animals make when they walk, run, crawl, or fly, inasmuch as the sound is too little and too feeble.
Mersenne quotes at length another contemporary who believed in the music of the spheres, the German astronomer Johann Kepler (1571–1630), from whom he borrows the notion that,
… if the planets produce harmony, it would be necessary to make Saturn and Jupiter the bass, Mars the tenor, the Earth and Venus the alto, and Mercury the soprano, because Mercury has a greater range and is livelier than the others.
In another place, Mersenne cites Gosselin and Guy Aretin relative to their theories that the musical intervals and the voice can be related to the planets, concluding that Jupiter is the root, Saturn is the second, the Moon is the third, Mercury is the fourth, Venus is the fifth, the Sun is the sixth, Mars is the seventh and Jupiter again the octave. Mersenne, however, finds this knowledge not necessary for practical musicianship, although he observes that if there really is music of the spheres, the musical instruments should be tuned to these pitches.
One of the greatest continental scientists of the 17th century, Christian Huygens, left a treatise entitled, The Celestial Worlds Discovered where he speculates on the nature of the music to be heard on the other planets and concludes it would be about the same as on Earth.
The English poet, John Donne, one of a number of 17th century English poet who mention the Music of the spheres, suggests it cannot be heard but can be felt,
Make all this All, three Choirs, heaven, earth, and spheres,
The first, Heaven, hath a song, but no man hears,
The Spheres have Musick, but they have no tongue,
Their harmony is rather danced than sung.23
The greatest English poet of the 17th century, Milton, devoted much attention to the Music of the Spheres. He mentions this frequently in his poetry, in Paradise Lost,24 where God listens to the music of the spheres, in The Hymn,25 and in Ardcades.26 I,74.
Eventually, Milton left a lengthy discussion, On the Music of the Spheres, which appears to have been intended as his contribution to a debate on this subject. In this work he summarizes the history of comments by various philosophers and concludes with this thought,
But if we possessed hearts so pure, so spotless, so snowy, as once upon a time Pythagoras had, then indeed would our ears be made to resound and to be completely filled with that most delicious music of the revolving stars.27
Among the Restoration poets, Dryden mentions the Music of the Spheres, but cautions that “upon the sounding of the trumpet on the Day of Judgment this music will end, “Musick shall untune the sky.”28
Alexander Pope, in his poem, An Essay on Man, argues that God was wise in not making man’s senses more sensitive than they are, as he would likely be miserable. Of music, he says,
If nature thundered in his opening ears,
And stunned him with the music of the spheres,
How would he wish that heaven had left him still
The whispering zephyr, and the purling rill?29
There are a number of references to the Music of the spheres among the Jacobean playwrights, among them Marston’s The Insatiate Countess,30 “Let sphere-like music breathe delicious tones” and Dekker’s Old Fortunatus,31 “With tunes more sweet than moving of the Spheres.”32
Among the Restoration playwrights we find in George Villiers, The Rehearsal,33 a person who can hear the Music of the Spheres. A stage direction reads, “Soft Music.” And in George Farquhar’s Comedy, Love and a Bottle,34 when the character, Rigadoon, comments,
From a prodigious great bass-viol with seven strings, that played a Jig called the Musick of the Spheres: The seven Planets were nothing but fiddle-strings.35
Finally, we come to Johannes Kepler (1571–1630), the last astronomer to take seriously the Music of the Spheres. His conclusions comprise a sizable volume, which one may find as one of the volumes of the famous “Great Books” library. This book requires an advanced understanding of mathematics to make any sense and here we will simply provide representative examples of his writing.
One day, when teaching a geometry class in 1595, he was drawing on the blackboard a triangle inscribed within a circle, in the center of which there was yet another circle, whereupon he experienced a sudden insight — it seemed to him that the ratio between these two circles was the same as that between the orbits of Saturn and Jupiter. This led to a long period of study in which he attempted to prove that the organization of the planets followed basic geometric figures.
Music, Kepler contends, reveals to us an order which is the principle also of our own being. The task of the astronomer is to correlate the harmony within with the harmony without. In the same way, he believed mathematical insights are only discovered, not invented. It follows that God, when making man, implanted in him consciousness of the fundamental harmonies which served as a pattern in the creation of the world.
It is in Book Five, of the Harmony of the Universe, that Kepler summarizes his theories of the “Music of the Spheres” and the relationship of this music to planetary mechanics. He begins by reflecting on the many years of study which have brought him to this understanding, not failing to pay due tribute to those past and present who deserved recognition. It is important to remember that Kepler was about to set forth in considerable mathematical detail theories which were most unorthodox, and at a time when the idea that the Earth moved, and was not the center of the universe, was as yet by no means commonly believed. It was for this reason that Kepler concludes his introductory remarks by saying that he had decided to get up his courage and publish the book anyway. It’s OK, he says, if it goes neglected for another hundred years — after all, God waited six thousand years for someone [Kepler] to come along to discover the musical relationships of the cosmos.
He reminds the reader of his study of the relationship of the five basic geometric figures and the planetary system and admits that he could not quite make them fit. Since Kepler admits the concept of geometric figures is not sufficient to explain the planetary organization, it follows there must be other principles at work. This, of course, will turn out to be music. In Chapter Four he provides some preliminary relationships with music.
If you compare the extreme intervals of different planets with one another, some harmonic light begins to shine. For the extreme diverging intervals of Saturn and Jupiter make slightly more than the octave; and the converging, a mean between the major and minor sixths. So the diverging extremes of Jupiter and Mars embrace approximately the double octave; and the converging, approximately the fifth and the octave. But the diverging extremes of the Earth and Mars embrace somewhat more than the major sixth; the converging, an augmented fourth. In the next couple, the Earth and Venus, there is again the same augmented fourth between the converging extremes; but we lack any harmonic ratio between the diverging extremes: for it is less than the semi-octave (so to speak), ie., less than the square root of the ratio 2:1. Finally, between the diverging extremes of Venus and Mercury there is a ratio slightly less than the octave compounded with the minor third; between the converging there is a slightly augmented fifth.
Now satisfied that he had discovered a natural correspondence between planetary movement and the relationship of pitches in the overtone series, in Chapter Five Kepler turns his attention to the search for a natural cosmic scale.
Now the aphelial movement of Saturn at its slowest, ie., the slowest movement, marks G, the lowest pitch in the system with the number 1’46”. Therefore the aphelial movement of the Earth will make the same pitch, but five octaves higher, because its number is 1’47”, and who wants to quarrel about one second in the aphelial movement of Saturn? But let us take it into account, nevertheless; the difference will not be greater than 106:107, which is less than a comma. If you add 27”, one quarter of this 1’47”, the sum will be 2’14”, although the perihelial movement of Saturn has 2’15”; similarly the aphelial movement of Jupiter, but one octave higher….
Accordingly all the notes of the major scale…are marked by all the extreme movements of the planets, except the perihelial movements of Venus and the Earth and the aphelial movement of Mercury, whose number, 2’23”, approaches the note c sharp. For subtract from the 2’41” of d one sixteenth or 10”, and 2’30” remains for the note c sharp. Thus only the perihelial movement of Venus and the Earth are missing from this scale.
Following a third attempt at scale construction, Kepler constructs scale fragments for each planet, based on the eccentricity of the orbit. He finds Saturn produces G, A, B, A, G; Jupiter, G, A, Bb, A, G; Mars, F, G, A, Bb, C, Bb, A, G, F; Earth, G, Ab, G; Mercury, a C major scale; the Moon, G, A, B, C, B, A, G; and Venus, which produces only Es. From this it was evident to Kepler that the Church modes must have had their origin in the heavens.
Eventually Kepler provides a step by step summary of his logic and his contentions, expressed in a series of very complicated axioms. One example:
XXXVIII. Proposition. The increment 243:250 to 2:3, the compound of the private ratios of Saturn and Jupiter, which was up to now being established by the prior reasons, was to be distributed among the planets in such fashion that of it the comma 80:81 should accede to Saturn and the remainder, 19,683:20,000 or approximately 62:63, to Jupiter.
Finally, Kepler’s concept of the Music of the Spheres was based on a mathematical presumption of an observer based on the Sun. Because contemporary telescopes had not ruled out life even on the moon, much less the rest of the galaxy, he could not categorically rule out the possibility that some form of life existed there capable of hearing this cosmic music. And if not, then there is still the possibility that God has merely prepared the “seats” for future listeners, for even the Earth was created and existed before it was inhabited and thus for a time its “seats were empty.” And as if proof were needed, he quotes from Psalm 19:4,
The heavens are telling the glory o God…
Their voice goes out through all the earth,
And their words to the end of the world.
In them he has set a tent for the sun…
The great philosopher, Benedict Spinoza (1632–1677), wrote very little about music. He does mention the music of the spheres, perhaps because someone of the stature of Kepler was still writing about the subject. Spinoza makes it quite evident that he will have nothing to do with this belief.
Whatsoever affects our ears is said to give rise to noise, sound, or harmony. In this last case, there are men lunatic enough to believe that even God himself takes pleasure in harmony; and philosophers are not lacking who have persuaded themselves, that the motion of the heavenly bodies gives rise to harmony.36
And this is pretty much where 2,000 years of discussion ends. After the 17th century, both philosophy and science generally abandoned the concept of the “Music of the Spheres,” relegating it to the shelf reserved for those whom Spinoza identifies as those “men lunatic enough” to be interested. One might say that the Age of Reason closed the door on this subject.
Oh, oh …
In 2002, NASA’s Chandra X-ray Observatory found that a black hole in the Perseus cluster produces a B-flat, 57 octaves below middle C!
This essay first appeared in my book, Ancient Views on the Natural World (2013).
Notes
- in Metaphysis ↩︎
- De Caelo, II ↩︎
- De Caelo, 2980b.13 ↩︎
- Of the Procreation of the Soul. He adds that he finds the logic of all this to be the additional proof that the husband should rule the family! ↩︎
- Natural History, II, iii ↩︎
- The Education of an Orator, I, x, 12 ↩︎
- Life of Pythagoras ↩︎
- Six Days of Creation: Two, in Hexameron, trans. Savage, 50 ↩︎
- Quoted in Martianus Capella and the Seven Liberal Arts, trans. Stahl, 349 ↩︎
- in Variae, trans., Hodgkin, II, xl ↩︎
- De Musica, trans. Seay, 10. Grecheo also substitutes a new division of music into Civic, Regular and Church. ↩︎
- Quoted in Palisca, Humanism in Italian Renaissance Musical Thought, 177 ↩︎
- The Art of Counterpoint, trans. Seay, 14 ↩︎
- The Parliament of the Birds, 59ff ↩︎
- Quoted in Palisca, Humanism, op. cit., 179 ↩︎
- The Courtier, trans., Bull, I, 94ff ↩︎
- Essays, trans., Screech, I, xxiii, 123 ↩︎
- III, xxxii ↩︎
- V, I, 61ff ↩︎
- II, vii, 6 ↩︎
- IV, ii, 85ff ↩︎
- III, i, 109 ↩︎
- Complete Poetry, 260 ↩︎
- in VII, 557; in V, 625ff; and in II, 166 ↩︎
- I, 6 ↩︎
- I,74. The Works of John Milton, ed. Paterson ↩︎
- Ibid., XII, 149ff ↩︎
- Works of John Dryden, ed. Hooker, II, 109, 111 ↩︎
- Works of Alexander Pope, Gordian Press, II, 363 ↩︎
- III, iv ↩︎
- I, i ↩︎
- Additional references in two more Dekker plays, also in plays by Webster, Chapman, Fletcher and Marston. ↩︎
- V, i ↩︎
- II, ii ↩︎
- also see his The Inconstant, IV, iii ↩︎
- “The Ethics,” Concerning God, Appendix ↩︎
