(An et Quo ordine Musarum voces, & Chordarum sonos Caelestibus sphaeris accommodare oporteat)

[Margin: Sirens and Muses, presidents of the celestial orbs.]

[I.] I shall begin from Macrobius, who (bk. 2 on the Dream of Scipio, ch. 3) says: “Plato in his Republic (namely bk. 10), when he treated of the revolution of the celestial spheres, says that single Sirens sit upon the single orbs” — signifying that by the motion of the spheres a song is presented to the divine powers; for Siren, in the Greek understanding, means “one singing to God” (Deo canens). The Theologians too [posit] nine Muses, etc. And a little below: “That the Muses are the song of the World even the rustics know” (or, as others read, “the Etruscans know”) — who call them Camoenae, as if Canenae, from singing (canere); for these the meters were wont to be made with instruments.

[Margin: Strophe and Antistrophe, a symbol of the two heavenly motions.]

In the very hymns of the gods, too, by strophe and antistrophe the meters were applied to the tuneful verses — so that by the strophe the direct motion of the starry orb, and by the antistrophe the diverse retrograde [motion] of the wandering [planets], might be set forth; of which two motions, the first (by nature to be dedicated to God) took its beginning. Concerning the use of strophe and antistrophe and the motion in a circle, for representing the two motions of the heaven, this is held also by Didymus and Victorinus (in the scholia on Pindar), the ordinary gloss on Pindar, and Triclinius (on our Sophocles) — whose words Mazzoni reports (Defense of Dante, bk. 2, ch. 34); and he reconciles Didymus and Victorinus (who say the strophe was from right to left, to show motion from East to West) with the Gloss and Triclinius (who say it was left to right) — because the former spoke of the right and left of the World, the latter of the right and left of man.

[Margin: The number and names of the Muses.]

But returning to the Muses, there is no agreement among writers as to their number, names, order, or offices. Phurnutus related that there were once two, on account of Theory and Practice; three [say] Ephorus (in Arnobius), Varro, St. Augustine, and Tzetzes the Grammarian (on Hesiod) — namely Cephiso, Apollonis, and Borysthenis, daughters of Apollo — which Glareanus (Dodecachordon 2, ch. 14) says was a fiction on account of the threefold sound, made by voice, by breath, or by percussion. Yet four are posited by Aratus (bk. 5), daughters of Jupiter and the nymph Plusia — Arche, Melete, Thelxinoë, and Aoede; and likewise Cicero (On the Nature of the Gods 3) names four — Thelxiope, Mneme, Aoede, Melete. But Epicharmus, at the wedding of Hebe, reckons seven, daughters of Pierus and the nymph Pimpleïs — Nilus, Triton, Asopus, Heptapolis, Acheloïs, Tipoplus, and Rhodia. Yet the more common opinion, with Homer, Hesiod, and Orpheus, holds there were nine Muses, daughters of Jupiter and Mnemosyne; nor did Phurnutus dissent, saying that the ternary multiplied into itself (3 × 3) begets the novenary number of the Muses. Hesiod, in the Theogony, reckons their names in this order:

Clio, and Euterpe, and Thalia, and Melpomene, and Terpsichore, and Erato, and Polyhymnia, and Urania, and Calliope — who is she that excels all in order.

[Margin: The inventions and offices of the Muses.]

Their inventions and gifts, too, not all reckon alike. Our fellow-countryman Lilius Gregorius Gyraldus (Syntagma 7, On the gods of the nations, under Musa) reports these: Clio invented history; Thalia the art of planting; Euterpe the flutes; Melpomene the Ode (song); Terpsichore the Chorea (dance); Erato nuptial [songs] and dancing; Polyhymnia agriculture; Urania astrology; Calliope poetry. Yet below he interprets them allegorically: Urania = the sublimity of intelligence; Polyhymnia = the capacity of memory; Euterpe = the delight of the will; Erato = the love of like things; Melpomene = the profundity of thought; Terpsichore = the exercise of the arts; Calliope = the beauty of eloquence; Clio = the good fame and glory begotten of the foregoing; and Thalia = the germination of the virtues. The same Gyraldus sets forth this Greek epigram, rendered by him into Latin:

Calliope showed the hero the art of song; Clio brought forth the sweet-sounding measures of the lyre; Euterpe the resounding song of the tragic chorus; Melpomene moved the barbitons with sweet concord; and pleasing Terpsichore made ready to blow the reeds; but Erato found the gods’ delightful hymns; Polyhymnia joined harmony to numbers, and the dances; Urania [sang] the chorus of the stars and the heaven’s rotations; the comic life is thine, Thalia, and the manners found out.

[Margin: Apollo Musagetes.]

Apollo himself, moreover, is called Μουσηγέτης (Musagetes), that is, the Leader and Choirmaster of the Muses — as Phurnutus, Macrobius (bk. 2 on the Dream of Scipio, ch. 3), and Proclus (on Plato) relate; whose words are: “Apollo is worshipped as Musagetes, because he is the unity [tending] to harmony in the universe; and he is the choirmaster of the Muses of the whole novenary number — by which two [the unity and the nine] the whole world is bound together with indissoluble bonds.”

[II.] As for what pertains to the order of the Muses with the celestial [spheres]…

[The catchword “caele-” points to p. 522 (PDF 557), which continues ¶II on the order of the Muses and the spheres, within Chapter VII.]

(printed p. 522 — Chapter VII continued. The order of the Muses with the spheres is expounded from Cicero’s Dream of Scipio and Macrobius, with Calliope as the ninth, the symphony of all the spheres; three differing assignments (Glareanus, Ficino and Zarlino, Gyraldus) are set out in a synopsis table. Riccioli then gives his verdict that these analogies were fixed “more elegantly than truly,” supported by four reasons against the scheme, the fourth beginning at the page’s end.)

[Margin: The order of the Muses in the heavens. — Cicero’s opinion. — And Macrobius’s.]

[II.] As for what pertains to the order of the Muses compared with the celestial [spheres], various [authors] think variously. Eudoxus indeed determined nothing of this; nor did Cicero in the Dream of Scipio — though he indicated his mind obscurely in these words: “Nine orbs, or rather globes, are all connected: of which one — the outermost and celestial, embracing all the rest — is the supreme God himself, restraining and containing the others, in which are fixed those everlasting courses of the turning stars. Beneath it are the seven, turned backward by a motion contrary to the heaven’s,” etc.; and a little below: “And in the lowest orb the Moon is kindled by the Sun’s rays” (the lowest of the moving bodies); for soon after he adds: “For that which is the middle and ninth, the Earth, neither moves and is the lowest, and toward it all things are borne by their own weight.” Wherefore, by Cicero’s mind, the lowest Muse is to be assigned to the Earth, the highest to the sphere of the Fixed stars (or to the whole heaven, as containing in itself all the others’ motions).

This passage of Cicero Macrobius illustrates (bk. 2 on the Dream of Scipio, ch. 3), teaching that the Muses are to be ascribed to the celestial spheres in exactly the order Hesiod enumerated — so that Clio [is given] to the lowest, Urania to the eighth sphere, and Calliope is the most beautiful voice, as rising from the concord of all the spheres. Macrobius’s words: “The Theologians too held there were nine Muses — the eight musical songs of the spheres, and one greatest [harmony] containing [them], which consists of all; whence Hesiod in the Theogony calls his eighth Muse Urania, because after the seven wandering [spheres] beneath, the eighth, the starry sphere placed above, is by its own name called heaven. And to show there is a ninth and greatest [Muse], which the concordant whole of sounds produces, he added: ‘Calliope, and she is the most excellent of them all’ — showing by the name that the very sweetness of voice is called the ninth Muse (for Καλλιόπη is the Greek for ‘best voice’); and to mark more closely that she is the one consisting of all, he assigned to her the word of the whole, namely ‘most excellent of all.’”

[Margin: Glareanus’s opinion.]

The same of Calliope held Glareanus (Dodecachordon 2, ch. 12): “that the ninth orb must be understood as the symphony conflated from these eight sounds, and on this account called Calliope, as Plato philosophizes of the Muses in the Republic” — not rashly, in the judgment of all the learned; the same is Cicero’s treatment in the Dream of Scipio. And (ch. 14) he affirms, from Plato (Republic 10), that the Sirens assigned to the single spheres are called the eight Muses on account of the eight sounds, and the Symphony conflated from these is called by him the ninth Muse, and by Hesiod Calliope, as the most excellent of all; and he praises Cristoforo Landino (above Servius) for interpreting, of this universality and excellence of voices comprehended in Calliope, that verse of Virgil (Aeneid 9): “You, O Calliope, I pray, breathe upon me as I sing” — where the best of Poets, using the plural, is addressing Calliope as her who comprehends all the others in or under herself.

In the System of the World, then, [Glareanus], together with Hesiod, assigns to the Moon Clio; to Mercury Euterpe; to Venus Thalia; to the Sun Melpomene; to Mars Terpsichore; to Jupiter Erato; to Saturn Polyhymnia; to the Fixed stars Urania; and to the last orb of all, Calliope.

[Margin: Marsilio Ficino’s opinion.]

But Marsilio Ficino (in [his commentary on] Plato’s dialogue On Poetic Fury), and subscribing to him Zarlino (Harmonic Institutions 2, ch. 19), apply: to the Moon Thalia; to Mercury Euterpe; to Venus Erato; to the Sun Melpomene; to Mars Clio; to Jupiter Terpsichore; to Saturn Polyhymnia; to the Fixed-stars sphere Urania; and over the single spheres and all together they set Calliope, to signify the concord arising from them all.

But Gyraldus (Syntagma 7, On the gods of the nations, under Musa) attributes Thalia to the Earth, as silent and having no concord; to the Moon Clio and the hypodorian mode; to Mercury Calliope and the hypophrygian; to Venus Terpsichore and the hypolydian; to the Sun Melpomene and the dorian; to Mars Erato and the phrygian; to Jupiter Euterpe and the lydian; to Saturn Polyhymnia and the myxolydian; to the Fixed stars Urania and the hypermyxolydian. To which opinion subscribes, in Mersenne (on Genesis 4, verse 21, p. 1704), an unnamed author in these verses:

Persephone [a — the Moon] and Clio breathe; therefore the hypodorian is born: whence the Proslambanomenos [b — the lowest string] generates its origin. And next [Calliope] gives the hypophrygian chord that follows, which Calliope herself brings forth — the interpreter [c — Mercury] himself brings it forth — of the gods. The third shows the hypolydian beginnings on the strings: Terpsichore meets it; kindly Paphis [d — Venus] sets it in order. Melpomene and Titan [e — the Sun], believe me, appoint the mode which is said to stand in the fourth place, the Dorian. Erato would prescribe the fifth string to the Phrygian — Mars too, ever loving battles, not peace. The Lydian thou shalt have of Euterpe and of Jupiter; she, sweetly holding [it], bade that to be the sixth string. Saturn drives Polyhymnia’s seventh string, the principle whence the myxolydian takes its rise. And while Urania searches out the eighth, her friend, the hypermyxolydian turns the pole by art.

[The margin keys the planets: a = Moon, b = Proslambanomenos (the lowest string), c = Mercury, d = Venus, e = Sun. The verses encode exactly Gyraldus’s assignment of Muse, planet, and mode. A few phrases are awkward in the original Latin mnemonic; “Prosmeledes” stands for the Proslambanomenos, “Paphis” = Venus, “Titan” = the Sun.]

It pleases me, therefore, to bring these opinions together into one synopsis, in the following table:

The Distribution and Place of the Muses in the System of the World

(Musarum Distributio et Locus in Systemate Mundi)

(The ”—” marks where the original sets a cross, i.e. no Muse assigned to that place.)

And so all agree in the distribution of three Muses — Urania, Polyhymnia, and Melpomene [= the Fixed stars, Saturn, and the Sun]; in the rest they do not all agree.

[Margin: Our opinion, and a censure from Aristotle and Pliny.]

[III.] You will now ask our opinion: to which indeed we reply that these analogies and harmonies have been determined by the aforesaid authors more elegantly than truly — to use Aristotle’s words (On the Heaven 2, text 52), or to say with Pliny (bk. 2, ch. 22): “Saturn is moved by the Dorian, Mercury by [its] phthongus, Jupiter by the Phrygian,” and the like in the rest, with a subtlety more pleasant than necessary; and Macrobius himself (bk. 2 on the Dream of Scipio, ch. 4) says that to pursue these things more subtly “belongs to one showing off, not to one teaching.” And of the same opinion are Glareanus (Dodecachordon 2, ch. 13, at the end), Zarlino (Harmonic Institutions 2, ch. 29, at the end), Mersenne (on Genesis 4, p. 1704), and Kircher (Musurgia 10, p. 381).

[Margin: Our reasons.]

But the reason that moves me is not a single one.

First — how inconstant the tradition has been concerning the number, names, and properties of the Muses, we have made plain enough at number 1 [in ¶I].

Second — the order of the celestial spheres itself was various among the older Astronomers, as is clear from the variety of world-systems already expounded by us (bk. 3, ch. 6, and bk. 9, sect. 3); wherefore you would not even satisfy Macrobius by assigning Thalia and Euterpe to Venus and Mercury, since he allows those planets to be carried above the Sun as well.

Third — if the Sun is the leader of the Muses (and so called Musagetes), how does one of the Muses preside over the Sun’s own sphere — or [is she there] as his vicar or helper? Again, if no ninth sphere is granted, distinct from the others as a Prime Mobile, but each planet is moved by a single spiral motion, there will be no sphere to which Calliope (or any other ninth Muse) can be assigned; and much less is a Muse to be given to the Earth, since it does not move.

Fourth — how, with the pla[nets]…

[The text breaks off mid-word at “Quartò quomodo cum Pla-”; the fourth reason continues on p. 523 (PDF 558), within Chapter VII.]

(printed p. 523 — Chapter VII continued. The case against the Muse-sphere scheme concludes — better to recognize the Peripatetic Intelligences as governesses of the heavens — and a sub-section opens on the analogy of the strings and the celestial spheres. The celestial Lyre’s disputed invention and string-number are surveyed; then the positive case for real celestial harmony from Cicero and Macrobius, the cause of the authors’ disagreement (the twofold motion and the orbs’ size), and the First opinion, which gives the higher pitch to the swifter superior spheres.)

…[Fourthly] — how, with the Platonic opinion, will the Muses and the Sirens stand together, if Greece has elsewhere fabled that the Sirens were conquered by the Muses in a contest of song? It is better, therefore, these fables being dismissed, to recognize in the place of the Muses the Peripatetic Intelligences — which the Theologians too acknowledge — as the governesses of the heavens.

On the Analogy of the Strings and the Celestial Spheres

(De Chordarum & Caelestium sphaerarum Analogia)

[Margin: The inventor of the Lyre — Mercury or Apollo?]

[IV.] Before we treat of the strings of the celestial Lyre, it must briefly be inquired who was the inventor of the Lyre, and of how many strings. For if we believe Diodorus Siculus, Mercury devised the three-stringed Lyre, but Orpheus made it four-stringed; while Terpander (by Plutarch’s testimony, in the opuscule On Music) added to it the laws and the names of the strings — though Suidas, Boethius (bk. 1, ch. 20), and Aristotle (sect. 19, problem 32) attribute the seven-stringed Lyre to him. But Macrobius (Saturnalia 1, ch. 19) relates that the tetrachord [four-stringed] was attributed to Mercury, to signify as many regions of the world or seasons of the year; and he adds that “by the seven-stringed Lyre of Apollo the motions of as many celestial spheres are given to be understood, over which Nature set the Sun as governor.” But in his poetic Astronomicon, Hyginus affirms that Mercury was the inventor of the seven-stringed Lyre, on account of the number of the seven Pleiades (or Atlantides); and that, when Mercury had driven off Apollo’s cattle, to satisfy Apollo (who pursued him) he complied and conceded that Apollo should name himself the inventor of the seven-stringed Lyre — which was moreover increased by Apollo with that wand by which, a little after, Mercury (reconciling two serpents) was wont to carry the caduceus in place of the lyre.

But even before Hyginus, Homer, in the hymn he dedicated to Mercury, acknowledges him the inventor of seven symphonies through as many strings made from birds’ entrails, in this verse:

Ἑπτὰ δὲ συμφώνους ὀΐων ἐτανύσατο χορδάς — that is, “And he stretched seven consonant strings from the entrails of sheep.”

With whom agrees Horace (Odes 3, Ode 11), addressing Mercury and his lyre (testudo):

“And thou, O lyre, skilled to resound with seven strings.”

In imitation of this — or to imitate the seven symphonies, whether celestial or human — Pan is believed to have first compacted seven reeds into one wind-instrument; such a pipe Ovid mentions (Metamorphoses 2) in this hemistich: “…the pipe unequal with seven reeds”; and Corydon in Virgil (Eclogue 2): “I have a pipe compacted of seven unequal hemlock-stalks.” Though that Menalcas in Theocritus boasts of a pipe of nine tones (or reeds) made by himself, in this verse:

Σύριγγ’ ἐποίησα καλὰν ἐγὼ ἐννεάφωνον — that is, “I myself made a beautiful syrinx of nine tones.”

[Margin: The 7 Species of the Diapason.]

But returning to the seven-stringed Lyre: Glareanus (Dodecachordon 2, ch. 12) judges that by its seven strings are signified the seven species of consonances into which the Diapason is divided, and which reign in the two octochord instruments; and to this he draws that verse of Virgil (Aeneid 6):

“And likewise the Thracian priest [Orpheus] in the long robe accompanies [them] with his numbers, the seven distinctions of tones.”

And those species of the Diapason are: Diapason-diapente; Disdiapason; Diapason-with-ditone; Diapason-with-semiditone; Diapason-with-greater-hexachord; and Diapason-with-lesser-hexachord — unless for these you understand the seven simple consonances which we enumerated in ch. 4, table 1.

[Margin: Cicero’s opinion on the high sound of the supreme sphere.]

[V.] But whatever may be the case about the inventor and purpose of the seven- (or even nine-) stringed Lyre or pipe, it is certain that not a few authors, and not to be despised, recognized in the celestial spheres the intervals and distinctions of grave and acute voices, and so adapted to them the strings of the Lyre or of the harmonic system. In which, from the Platonic source, Cicero led the way in the Dream of Scipio: when Scipio asks, “What is this, I say — what so great and so sweet a sound that fills my ears?”, he brings in his father Paulus answering in these words: “This is that [sound] which, joined by intervals unequal yet distinguished in due proportion, is produced by the impulse and motion of the orbs themselves; which, tempering high with low, makes equable concords. For the motions cannot be set going in silence; and nature brings it about that the extremes sound, on the one side gravely, on the other acutely. For which cause that highest course of the starry heaven, whose revolution is swifter, is moved with a high, excited sound; but the lowest, the Moon’s, with the gravest. For the Earth, ninth, remaining immobile, always clings in the lowest seat, embracing the middle place of the world. But those eight courses — in which the same force is [shared by] two — produce seven sounds distinct by intervals, which number is the knot of nearly all things; which learned men, imitating with strings and songs, have opened for themselves a return to this place.”

[Margin: Macrobius’s opinion.]

Explaining these words, Macrobius (bk. 2, ch. 4) teaches that from a great and swift collision of the air an acuter [higher] sound is made, but from a slow and more sluggish one a graver [lower] — which he confirms by the example of a rod [swung] through the air, and of strings (which, stretched by a tighter pull, sound higher; by a looser, lower), and of flutes and pipes (whose narrower holes, or those more remote from the blower’s mouth, give a graver sound than the wider or nearer). Whence he concludes that to the supreme starry orb — both for its magnitude, by which it extends immensely, and for the greatest velocity of its diurnal motion to the West — the acutest [highest] sound is due; but to the Moon, for the narrowness of its orb and the slowness of its motion, the gravest [lowest]; and, of the other spheres described by Tully, that the Earth is immobile, the other eight mobile — yet that there are only seven sounds, because Mercury and Venus move with the same motion as the Sun, and therefore Cicero said the force of the two is the same.

[Margin: Glareanus’s exposition of Cicero and the text.]

But Glareanus (Dodecachordon 2, ch. 12) thinks the passage of Cicero is corrupt and not sufficiently understood by Macrobius, and that the word “seven” should be referred not to the sounds but to the intervals — so that the eight courses produce [eight] sounds, but distant from one another by seven intervals; or rather it should be read: “But those courses, in which the force of the extremes is the same, produce sounds distinguished by seven intervals.” For from Music it is read that eight phthongi (or principal voices) produce seven intervals, that is, the seven species of the Diapason.

[Margin: The cause of the diversity of opinions in this matter.]

[VI.] Now from the sources of Plato and Cicero three different opinions have flowed: of which the First assigns to the supreme sphere the highest [acutest] of the strings — that is, either the Mese (the highest of the prior nine strings of the harmonic system) or the Nete hyperbolaeon (the highest in the ancient 15-string system). The Second assigns to the supreme sphere the gravest [lowest] string — namely the Proslambanomenos, or at least the Hypate hypaton. The Third, finally, either adheres to both under differing considerations, or strives to reconcile them, though leaning more to one than the other.

The cause of the diversity of these opinions is, on the one hand, the twofold motion apparent in the heaven, and on the other, the diverse distance and magnitude of the orbs. For if the common motion (called the Prime Mobile’s, toward the West) be regarded, the Fixed stars move faster than Saturn, and Saturn than the lower planets; and by that reckoning the highest sound is due to [the Fixed sphere]. But if the proper apparent motion toward the East be regarded, slowest is the course of the Fixed stars, then Saturn, etc.; wherefore, for this [smallness] of motion, the gravest sound seems assignable to them. And by distance — since the length of a string and the magnitude of bodies give a graver sound than shortness and smallness (as Aristotle teaches, sect. 19, problem 8) — it seems that to the spheres and orbs more remote from the Earth a graver [lower] sound should be attributed.

It is moreover disputed whether the string giving the gravest sound ought to be placed in the innermost place of the musical System and of the tetrachords (the highest in the supreme place), or rather the gravest in the supreme and the highest in the lowest — on which Glareanus disputes acutely (Dodecachordon 1, ch. 5, and bk. 2, ch. 8).

[Margin: The 1st Opinion — of Cicero, Macrobius, and Guido of Arezzo.]

[VII.] The First opinion is that of Guido of Arezzo, whom many have followed; who (as is clear from the systems set forth in ch. 5, after number 3) placed in the innermost place the gravest string [Gamma], to which succeeds the Proslambanomenos, and in the supreme degrees of the Scale the higher sounds — which agrees with Cicero (Republic 6, the Dream of Scipio) and Macrobius: namely, that the superior bodies, as swifter in the diurnal motion, give a higher but lesser sound, but the inferior, as slower, a greater but graver [lower] sound…

[The text breaks off at “graviorem so-” (sonum); ¶VII continues on p. 524 (PDF 559), within Chapter VII.]

(printed p. 524 — Chapter VII continued. The First opinion (highest pitch to the supreme sphere) is completed with its followers and supporting analogies from the cithara, organ, and human voice, plus Mersenne’s cabalistic ten-stringed Cithara of David set out in a table. Then the Second opinion is given: the superior spheres, being slower and bigger, sound the graver note — held by Nicomachus, Servius, Poliziano, and Boethius, and judged “much more probable” by Glareanus, who offers two diagrams.)

…[the superior bodies, as swifter, give a higher but lesser sound, the inferior a greater but graver] — which opinion was followed by Guglielmo Philander (on Vitruvius bk. 5, ch. 4, attributing it to the ancients), Gyraldus (Syntagma 7, under Musa), Valla (on Pliny bk. 2, ch. 22), Fr. Athanasius Kircher (Musurgia 10, p. 393), and the unknown Author in Mersenne (on Genesis 4, verse 21, p. 1704). For they give the gravest string to the Moon or Earth, and the acutest to Saturn or the sphere of the Fixed stars.

To this favors, first, the order of the strings in the Cithara, which is contrary to the order in the Lyra: for in the Lyra the gravest and thickest string is in the supreme place (whether three-, four-, or six-stringed), but in the Cithara the gravest and thickest is in the lowest seat, and the acutest in the supreme — the order our organs still keep, in which the thicker pipes are set in the lower, the thinner in the upper row. And the human voice, too, more often begins not from the highest but from the lowest [note] and a graver sound, and gradually by a natural transition ascends to the higher; for the graver voice is, as it were, the foundation, without which the higher and acuter voices seem to degenerate into chattering, unless sustained by the strength of a graver voice. For though the highest voice may seem to soothe the hearing more sweetly, yet (as Glareanus noted above) no song is more pleasant than when the lowest, firm voice sounds; and the higher voices accomplish almost nothing without the Bass of the lower (so Julius Pollux names the graver voices); nor today is the Diatessaron admitted unless propped from below by a Diapente (the fifth), or even a third.

Mersenne too — although (on Genesis 4, p. 1704) he repudiates such fictions — yet (p. 1705), from the arcana of the Cabalists, describes the ten-stringed Cithara of David by the following analogy, in which he assigns the acuter [higher] sound to the supreme spheres and spirits. Behold it in the table:

The strings of the Davidic Cithara, according to the Cabalists

(Davidicae citharae nervi iuxta Cabalistas) — ascending from the lowest string (1) to the highest (10)

(The “Body” column stands in the original as planet-symbols, here given by name; it runs in the ascending Ptolemaic order — Elements, then Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn, the Fixed stars, and the Prime Mobile. So the higher strings answer to the higher spheres and higher angelic orders — the First opinion’s arrangement.)

[Margin: The 2nd Opinion.]

[VIII.] The Second opinion assigns to the superior spheres the graver [lower] sound — either because it thinks them slower (regarding their proper motion), or because, even if the greater velocity of the common [diurnal] motion lends them acuteness, yet the length of the interval and the magnitude of the bodies make a graver and greater sound — just as in the strings of many-stringed instruments, where the thicker and greater string begets a graver but more sonorous voice.

[Margin: Nicomachus’s, and Servius the Grammarian’s.]

Of this opinion was Nicomachus (in the Enchiridion of Harmonics, as Boethius and Philander report), who accordingly ascribed the Hypate to Saturn and the Nete to the Moon; and Servius Honoratus, who explains Virgil’s “through the friendly silences of the silent Moon” thus: “‘Silent,’ he says, [means] the Moon — either it signifies night, in the poetic manner; or he spoke by a physical reason. For there are seven circles — of Saturn, Jupiter, Mars, the Sun, Venus, Mercury, the Moon; and the first, that is Saturn, sounds vehemently, the rest less according to their order, as we have heard in the Cithara, whose last string sounds less.” — where he calls the last string in the cithara that which is nearer to our ears, and in that respect compares it with the Moon; not according to the order of high and low position (for the Moon is down, Saturn up), but contrariwise: in the cithara the acutest, thinnest, least-sounding string is up, the gravest down.

Wherefore Angelo Poliziano (Miscellanea, last chapter) neither understood Servius nor justly reproved him, when he says: “This will hold if you take the ‘last’ not as the lowest but as the highest — which in Greek is called Hypate — whence a graver sound is roused; just as from the other extreme, the thinnest string (which I would rather call the last), an acute voice is uttered, because it is stretched fully.” But Poliziano is more justly reproved by Glareanus (Dodecachordon 2, ch. 8), who teaches that Servius spoke truly and according to nature and the series of the celestial orbs (if there were sound there), and indeed according to the Cithara’s strings — for in it the Hypate, the gravest, holds the lowest place, the acutest the highest, which, even if stretched the most, is not for that reason heard the most. “For granted,” says Glareanus, “that in one and the same string the acuteness strikes the hearing more when it is stretched tight than the gravity when stretched looser; yet among different strings, the greater and thicker is heard more and makes a greater sound than the thinner, even if the latter be stretched more and sound higher — just as the voice of a well-voiced man is heard more than the wailing or clamor of a little boy. Hence too the higher voices accomplish almost nothing without the Bass and firmness of the graver.”

[Margin: Poliziano’s [agreement]; and Boethius’s.]

Yet it appears that Poliziano felt rightly in this, in conceding the graver sound to the Hypate, and by placing it in the highest place subscribed to Servius, who assigns this to Saturn. Of the same opinion, finally, was Severinus Boethius: for he not only acknowledged the Hypate as the gravest of the strings, but ascribed it to the superior spheres; for (bk. 1 of his Music, ch. 20) he says of the strings: “And among these, the one that was gravest was called Hypate, as if greater and more venerable — whence they call Jupiter also Hypatos, and name the Consul by the same name for the excellence of his dignity; and it [the Hypate] is attributed to Saturn, for the slowness of his motion and the gravity of his sound.” So (bk. 4, ch. 10) he places the Proslambanomenos in the supreme place and the Nete in the lowest.

[Margin: Glareanus’s opinion.]

But even Glareanus, Boethius’s follower — though he absolutely denies that there is any sound in the heavens, or any true principle of Symphony (Dodecachordon 2, ch. 14, from the paragraph “Moreover” to the end) — nevertheless, on the supposition that there were some sound in heaven, or that one should philosophize of the celestial bodies as of terrestrial sounding ones, leans to Boethius’s view. For (Dodecachordon 1, ch. 5) he says: “I am not unaware that to many this order of the strings posited by Guido seems inverted and altogether against the natural course of the heaven (whence this scheme was taken) — inasmuch as the superior bodies of the celestial orbs give a graver sound, being the greater; and this the divine Boethius too seems everywhere to have observed in his demonstrations.” And a little after: “Whether, then, [we take them] inverted, so that the superior be the graver — namely that we place the hypaton tetrachord in the supreme place, with the Proslambanomenos — which Severinus several times did, either for the name Hypatos (which sounds ‘principal’), or because the first teachers of this art so judged. For many old instruments — three-, four-, and six-stringed — still have it so, etc.” And (bk. 2, ch. 8) he says that Servius spoke truly and according to nature and the series of the celestial orbs (if there be sound there); and it is clear from what was said that Servius gave Saturn the gravest and most vehement sound. And (ch. 13), having recalled Cicero’s opinion, withdrawing from it he adds: “Others, on the contrary, ascribe the acuter sounds to the inferior bodies, and the graver (or greater) to the superior — because greater bodies give a greater sound, smaller a smaller; which opinion seems to me much more probable, since the heaven, like this sensible world, has bodies [proportioned so].” And he subjoins a twofold diagram: one Ciceronian, in which he assigns the shorter and acuter strings to the superior spheres; the other Boethian, in which …

[The text breaks off at “alterum Boëtianum, in quo” (the other, Boethian [diagram], in which…); the two diagrams and the rest follow on p. 525 (PDF 560), within Chapter VII.]

(printed p. 525 — Chapter VII concludes, then Chapter VIII opens. The Second opinion is finished and the Third (Zarlino’s indifferent position, giving both a Ciceronian and a Boethian system) is stated, with a wide comparison table of the celestial strings assigned by each authority. Riccioli’s own opinion follows: the analogies are pursued “more wittily than truly,” there being no real sound in the heavens, supported by five reasons against fixing strings to spheres. Chapter VIII then opens, on fitting the harmonic intervals to the distances of the stars, beginning with the ancient authorities.)

(conclusion — Bettini, Zarlino’s third opinion, the comparison table, and the Author’s verdict)

[Margin: And Bettini’s.]

…[the other, Boethian, diagram], in which he assigns the longer and graver strings to the superior [spheres] — which diagrams we shall set out below in a table with the rest; but in ch. 14 he chose only the Boethian. Likewise Mario Bettini (Apiarium 10, Progymnasma 1, Proposition 1), inasmuch as he applies the Hypate to the Fixed stars, the Parhypate to Saturn, and the Nete to the Moon. And the order of the Lyra favors this opinion, in which the thicker, graver-sounding string holds the supreme place, and the acuter-sounding string the lowest — which is also kept in most instruments.

[Margin: The 3rd Opinion.]

[IX.] The Third opinion shows itself indifferent — in which is Zarlino (Harmonic Institutions, part 2, ch. 29), who posits two systems: one according to Cicero (but assigning the Mese to the Fixed stars, and the Proslambanomenos to the Moon); the other according to Boethius. Yet in the aforesaid three opinions there remains some variety as to the whole order of the strings, as will appear more clearly from the following tables.

The Order of the Celestial Strings

(Chordarum Caelestium Ordo) — each celestial sphere (read downward, Fixed stars to Earth) set against the string assigned to it by each authority

A. According to Cicero & Macrobius (Ad mentem Ciceronis & Macrobij) — the higher the sphere, the higher the string

B. According to Nicomachus & Boethius (Ad mentem Nicomachi & Boëtij) — the higher the sphere, the lower (graver) the string

(Transcribed as printed. In the Boethian half the original does not re-print the planet-symbols beside each row, but the alignment is fixed by the text just above — Bettini “applies the Hypate to the Fixed stars, the Parhypate to Saturn, the Nete to the Moon” — and the Glareanus–Zarlino column runs in exact parallel, its gamut ascending A-a as the sphere descends Fixed-Moon. The Greek string-names in Glareanus’s Boethian diagram are his own labeling and do not match the usual letter-assignments. Below the table the original adds: “Add to these the [Cithara of David] which I delivered from the Cabalists at the end of number 7” — i.e. the table on p. 524.)

[Margin: The Author’s opinion. — Macrobius’s excellent judgment. — Glareanus’s definitive judgment. — Our 1st reason… 2nd reason.]

[X.] Now what our own opinion is in this matter can already be clear from what was said from the beginning of number 3 — namely, that these things are inquired into more wittily than truly, with a subtlety more pleasant than necessary, as we said there with Aristotle and Pliny. And Macrobius (bk. 2 on the Dream of Scipio, ch. 4), having this controversy in hand, prudently concluded thus: “To illuminate, as I think, the obscurity of Cicero’s words, this brief treatise on Music will suffice, with what brevity was allowed. For to hunt out the Netes and Hypates and the names of the other strings, and the minute subtleties of tones and limmas — and what in the sounds is taken for a letter, what for a syllable, what for a whole name — belongs to one showing off, not teaching. For not because Cicero here made mention of music must one therefore run through all the treatises that can be made on Music, which (so far as my opinion bears) I judge to have no end.” In imitation of whom, I believe, Glareanus (Dodecachordon 2, near the end of ch. 13) concluded: “Not without reason did this notion seem to Aristotle more pleasant to say than likely to be true”; and a little after: “But this indulgence is granted to antiquity, which judged these things in some way fit to raise human minds to the contemplation of celestial things.” Zarlino too (part 2, end of ch. 29) concludes with Pliny that these are investigated with a charm more subtle than necessary; and Marin Mersenne (on Genesis 4, verse 21, p. 1704) repudiates them all as fictions put forth without sufficient proof. But long before, St. Ambrose (in the book On Isaac and the Soul, ch. 7) denied that such fancies of a concord of the heavens find credence — though, for the pleasantness of the discourse, they are heard with favor and sweetness, as we showed (ch. 2) from his own words.

Nor indeed does that reason move me alone — that there is no real sound in the heavens (for what I think of this I said in the same ch. 2) — but:

First, that even if there were some sound, yet the truer order of the Planets is not the one those authors suppose. And indeed it seems strange that Fathers Mersenne and Kircher, more recent Astronomers, should place Mercury nearer the Moon than Venus — unless you say they spoke from the opinion of the ancients. But since these two planets [Mercury and Venus] are carried now below, now above the Sun, do they not measure out by their own motions their whole portion of that system, which runs from their Apogee to their Perigee? Likewise Mars, who sometimes comes nearer the Earth than the Sun, himself by his own ascent and descent occupies a great part of that interval through which the Sun, Venus, and Mercury rise and fall, and so mingles himself with them — so that you cannot assign him a distinct string or interval.

Secondly: Since it is more probable that the planetary heavens are fluid, and that the planets move by themselves in them, and not by the motion of [solid] orbs (as said in sect. 1, ch. 2, qu. 2)… a greater sound could indeed be granted to the sphere of the Fixed stars (as solid, and as to a greater body); but a greater [sound] cannot be granted to Saturn, Jupiter, and Mars than to the Sun, since the Sun is greater than those three planets.

[Margin: 3rd reason. — 4th reason. — 5th reason.]

Thirdly: Since there are eight different species of harmonic Systems — as I taught from Martianus Capella (ch. 5, at the end of the Chromatic and Enharmonic system) — it is very uncertain which of those three [genera — Diatonic, Chromatic, Enharmonic] belongs to the celestial system.

Fourthly: If it were free to play in these matters, one would have to take account both of the Satellites of Saturn and Jupiter, and of the diverse position the planets hold at the Apogee and Perigee of the Eccentric and Epicycle, and of the different [reckoning] which the Fixed stars hold.

Fifthly: As for the velocity and slowness of motion — since [the planets] really move by another real motion than toward the West, and by [their] slowness the lower [bodies] seem to fall back toward the East — the higher [planets] ought to be given the acuter [higher] sound, as absolutely swifter in this [diurnal] motion (except when they are Retrograde); but on the other hand, the three superior Planets, by the greater bulk of their body, would give a graver [lower] sound than the three inferior. Therefore one reason destroys the other; and so this analogy — sung with a certain oratorical and academic charm — loses its concord in the very discord — to say nothing of the disagreement of the authors in distributing the strings to the heaven.