Of Mundane Music

The Two Kinds of Animastic Music

Dividing then Animastic Music, we shall say that it is of two sorts — Mundane and Human. The Mundane is that harmony which is known to exist not only among those things that are seen and understood in the heavens, but is comprehended also in the binding of the Elements and in the variety of the seasons. I say that it is seen and understood in the heavens from the revolution, the distances, and the positions of the celestial spheres; and from the aspects, the nature, and the situation of the seven planets, which are the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and Saturn.

The Harmony of the Celestial Spheres

For it has been the opinion of many ancient philosophers — and above all of Pythagoras — that the revolution of so great a machine with so swift a movement does not pass without sending forth some sound. This opinion, although it is refuted by Aristotle, is nonetheless favored by Cicero in Book 6 of the Republic, where the elder Scipio Africanus, answering the younger who had asked him: “What is this sound so great and so sweet that fills my ears?” — says: “This is that which, joined by unequal intervals, nonetheless made distinct by divided proportion, is produced by the impulse and movement of the circles themselves; which, tempering the high with the low, makes equally diverse concords. For so great movements cannot be made in silence, and Nature ordains that the extremes sound gravely on one side, acutely on the other.” Wherefore that supreme course of the starred heaven, whose revolution is swiftest, moves with a high and stronger sound; and this lowest lunar one with the gravest.

This Cicero says following the opinion of Plato, who, to show that from such revolution harmony is born, feigns that over each sphere there presides a Siren — for Siren means nothing other than Singer to God. And likewise Hesiod in his Theogony, alluding to this same thing, called the eighth Muse Ourania, which is appropriate to the eighth sphere, from ouranos, the name by which the Greeks call Heaven. And to show that the ninth sphere was the one that produced the great and concordant unity of sounds, he named it Kalliopê — which comes to signify Of Most Excellent Voice — wishing to show thereby the harmony that results from all those other spheres. As is alluded to by the Poet when he said:

Vos o Calliope precor aspirate canenti;

invoking Calliope alone in the singular number, as the principal, and as the one at whose sole will all the others move and revolve. And the ancients held this opinion so firmly for truth, that in their sacrifices they used musical instruments, and sang certain Hymns composed of sonorous verses, which contained two parts — one of which they named strophê and the other antistrophê — to show the diverse turnings made by the celestial spheres: for by the one they understood the movement made by the sphere of the fixed stars from East to West; and by the other, the diverse movements made by the other spheres of the planets proceeding contrariwise from West to East.

And with such instruments they also accompanied the bodies of their dead to burial: for they were of the opinion that after death the souls returned to the origin of the sweetness of Music — that is, to heaven. This custom was observed also by the ancient Hebrews at the death of their kin, of which we have most clear testimony in the Gospel, where is described the resurrection of the daughter of the ruler of the synagogue, at which there were musical instruments — the players of which our Lord commanded to play no more. And they did this (as Ambrose says) to observe the custom of their ancients, who in this manner invited those standing by to weep with them.

Many furthermore were of opinion that in this life every soul was overcome by Music, and that even though enclosed in the corporeal prison, remembering and being conscious of the Music of heaven, it would forget every hardship and tedium. But if this seems to us strange, we have testimony of the harmony of heaven in the Sacred Letters, where the Lord speaks to Job saying: “Who shall declare the reasons or voices of the Heavens? And who shall make their harmony sleep?” And if I were asked whence it proceeds that so great and sweet a sound is not heard by us, I would know how to answer nothing other than what Cicero says in the passage cited above — that our ears, filled with so much harmony, are deaf; just as for example happens to the inhabitants of those places where the Nile precipitates from the highest mountains, called Catadupa, who through the greatness of the roar lack the sense of hearing. Or just as our eye cannot fix its gaze on the light of the Sun, being overcome by its rays; so our ears cannot contain the sweetness of celestial harmony on account of its excellence and greatness. But every reason persuades us to believe at least that the world is composed with harmony.

The Pythagorean Calculation of Planetary Intervals

First because (as Plato will have it) the soul of the world is harmony; and also because the heavens are revolved by their intelligences with harmony, as is understood from their revolutions, which are proportionately slower or swifter one than another. Such harmony is also known from the distances of the celestial spheres: for they are distant from one another (as pleases many) in harmonic proportion — which, although it is not measured by the sense, is nonetheless measured by reason. For the Pythagoreans (as Pliny demonstrates), measuring the distance of the heavens and their intervals, placed from the Earth to the first Lunar Sphere the space of 126,000 stadia, and said this to be the interval of the Tone — although this (in my opinion) is beyond all reason, since it cannot be that those things which by their nature are immobile, as the Earth is, should be apt to generate harmony, sounds having (as Boethius holds) their beginning from movement.

Then they went on to place from the sphere of the Moon to that of Mercury the interval of a major Semitone; and from Mercury to Venus that of the minor; and from Venus to the Sun the Tone and the minor semitone — and this they said to be distant from the Earth by three tones and one semitone, which space is named the Diapente. And from the Moon to the Sun they placed the distance of two tones and two semitones, which constitute the space of the Diatessaron. Returning then to the order begun, they said the Sun to be distant from Mars by the same distance as the Moon from the Earth; and from Mars to Jupiter to be the interval of the minor semitone; and from this to Saturn the space of the major semitone: from which to the last heaven, where the celestial signs are, they placed the space of the minor semitone. Wherefore from the last heaven to the sphere of the Sun the space and interval of the Diatessaron is understood to be; and from the Earth to the last heaven the space of five tones and two minor semitones, that is, the Diapason.

Whoever shall then wish to examine the heavens in their parts, according to what Ptolemy has done with great diligence, will find (comparing together the twelve parts of the Zodiac, in which the twelve celestial signs are) the musical consonances — that is, the Diatessaron, the Diapente, the Diapason, and the others in order; and in those movements made toward the East and the West he will be able to know that the gravest sounds are placed, and in those made in the middle of heaven the most acute. In the altitudes then he will find the Diatonic, the Chromatic, and the Enharmonic genus. Similarly in the latitudes the Tropes, or Modes as we wish to call them; and in the phases of the Moon, according to its various aspects with the Sun, the conjunctions of the Tetrachords.

But such harmony can be known not only from the aforesaid things, but also from the various aspects of the seven Planets — from their nature and from their position or situation. From the aspects, as from the Trine, the Square, the Sextile, the conjunctions, and the oppositions; which produce in lower things according to their influences good and bad effects, a such and so great diversity of harmony of things that it is impossible to explain. From the nature, since some (as the Astrologers will have it) being of sad and malign nature, are by those which are good and benign so tempered that there results such a harmony as brings great benefit and usefulness to mortals. And this is also understood from their Site or Position, since they are placed among themselves in such a way as are the virtues placed among the vices — so that just as the vices, which are extremes, are reduced to a virtuous habit by way of a fitting mean, so those planets which are of malign nature are reduced to temperance by way of another planet placed between them which is of benign nature.

Thus it is seen that, Saturn and Mars being placed in the high position of malign nature, such malignity is tempered by Jupiter placed between the one and the other, and by the Sun placed below Mars, with a certain harmony — so that they do not allow their bad influences to work in lower things that malign effect which they could work were there no such interposition. And their influences have such great power over lower bodies that while the first two named planets are found to have the dominion of the year, then the harmony of the four Elements is dissolved: for the air is so corrupted that it generates universal pestilence in the world.

They also hold that the two greater luminaries, which are the Sun and the Moon, make corresponding harmony of goodwill among men when at the birth of the one, that is in Sagittarius, and at the birth of the other the Sun is in Aries and the Moon in Sagittarius. Similar harmony they say is also made when at their birth they have had the same sign, or of similar nature, or the same planet of similar nature in the ascendant; or when two benign planets with the same aspect have beheld the angle of the East. This same thing they say occurs when Venus is found in the same house of their nativity, in the same degree.

The Harmony of the Elements

Having therefore had regard to all the above-mentioned opinions, and the World being (as some have affirmed) created by God — in declaring Mundane Music I have said that it is harmony which arises among those things seen and understood in heaven. And I added that it is also comprehended in the binding of the Elements: for they having been created by the great Architect God (as He created all other things) in Number, in Weight, and in Measure, from each of these three things such harmony can be understood.

First from Number, by means of the passive qualities, which are four and no more — that is, Dryness, Coldness, Humidity, and Heat, which are found in them: for to each of them one of these qualities is principally assigned, as Dryness to Earth, Coldness to Water, Humidity to Air, and Heat to Fire. Although Dryness is secondarily attributed to Fire, Heat to Air, Humidity to Water, and Coldness to Earth. By means of which, notwithstanding that among themselves these elements are contrary, they nonetheless remain in one middle element, according to one quality concordant and united: each of them (as we have seen) having two qualities assigned to it, by means of which they are marvelously joined together — and in such a way that, just as two square numbers agree in one proportionate mean number, so two of these elements are joined in one mean. For just as the Quaternary and the Novenaire, square numbers, agree in the Senary — which surpasses the Quaternary by the same quantity by which it is surpassed by the Novenaire — so Fire and Water, which are contrary in two qualities, are joined in one middle element. For Fire being by its nature hot and dry, and Water cold and humid, in Air, which is hot and humid, they are accompanied with great proportion — Air being separated from Water by the hot, yet joining itself to it by the humid. And if the humid of Water repels the dry of Earth, the cold does not fail to unite them together. So that they are joined together with such marvelous order that among them there is found no more disparity than is found between two proportionate mean numbers placed in the middle of two cubic numbers, as can be clearly seen in the following example.

[Site Editorial Note: Here Zarlino’s original text contains a numerical example showing two cubic numbers with two proportionate mean numbers placed between them. The example demonstrates that just as the numbers 8 and 27 (cubes of 2 and 3) are mediated by 12 and 18 (their proportionate means), so the four elements are harmonically bound together in continuous proportion — each pair sharing a quality with its neighbour.]

This binding made with harmony Boethius also explained, saying:

Tu numeris elementa ligas, ut frigora flammis Arida conveniant liquidis, ne purior ignis Evolet, aut mersa deducant pondera terras. Tu triplicem mediis [naturae cuncta moventem] Connectens animam per consona membra resolvit.

And in another place:

Haec concordia temperat aequis Elementa modis, ut pugnantia Vicibus cedant humida siccis Iungantque fidem frigora flammis, Pendulus ignis surgat in altum, Terrae graves pondere sidant.

The Harmony of Weight and Measure

But whoever will wish from their Weight also to understand the Mundane harmony will be able to know it: for each being heavier or lighter than the other, they are so linked and bound together that with a certain harmony the circumference of each is proportionately distant from the center of the World. We see that those which are by their nature heavy are drawn upward by those which are by their nature light; and the heavy draw downward the light in such a manner that none of them goes outside its proper place. And they stand together always so overcome and locked that among them there is found at no time, however brief, in any part the Vacuum — which Nature greatly abhors.

And they are so placed that the Earth, which by its nature is simply heavy, and Fire, which is simply light, are those which possess the extreme positions. The Earth holds the lowest place: for every heavy thing tends downward; and Fire is in the highest: for every light thing tends to such a place. But because the middle elements retain the nature of their extremes, the Creator has well ordained that Water and Air, being in a certain respect both heavy and light, should hold the middle place — Water accompanying itself to Earth as more heavy; and Air to Fire as more light; so that each should accompany itself to that which was of nature most similar to it.

Which order and binding Ovid elegantly expressed, saying:

Ignea convexi vis, et sine pondere coeli Emicuit, summaque locum sibi legit in arce. Proximus est aer illi levitate locoque; Densior his tellus elementaque grandia traxit, Et pressa est gravitate sui. circumfluus humor Ultima possedit, solidumque coercuit orbem.

The Harmony of the Mutual Transformation of Elements

But if we wish more subtly yet to examine the Constitution, we shall find the Mundane harmony in their measure and quantity, by means of the mutual transformation of parts that one makes into the other, as the Philosopher shows. For just as one part of Earth is transformed into Water, and of Water into Air, so is one part of Air transformed into Fire. And just as one part of Fire is transformed into Air, and one part of Air into Water, so is one part of Water transformed into Earth: for the transformation of Earth into Water comes about in the Decuple proportion. So that when one handful of Earth is transformed into Water, there are generated (as the philosophers say) ten handfuls of Water; and when such Water is transformed into Air, it comes to make a hundred handfuls of Air; wherefore, all this being transformed into Fire, it comes to multiply into a thousand handfuls of Fire. Contrariwise, a thousand handfuls of Fire are converted into a hundred of Air, and these into ten of Water, and ten of Water into one of Earth. And this happens from the rarity and density which is found more in one than in another element: for the closer they are to heaven and the farther from the center of the world, the more rare they are; and the closer they are to the center and the farther from heaven, the more dense.

Whence, judging their measure from this, one could say that the quantity of Fire is in Decuple proportion to that of Air; and that of Air to that of Water is likewise in decuple proportion; and so the quantity of Water to all the quantity of Earth in the same proportion. And one could also say (since the Elements are bodies of one and the same genus, and the whole agrees with the parts in one and the same nature and in one and the same reason) that the proportion found between the quantity of the sphere of Fire and all the mass of the Earth is that found between the number one thousand and unity.

The Harmony of the Seasons

In this way, then, from the movement, the distances, and the positions of the heavens; and similarly from the aspects, the nature, and the situation of the seven planets; and from the number, the weight, and the measure of the four elements, we have come to the recognition of the Mundane harmony. For their concordance and harmony produces the harmony of the seasons, which is known first in the Years, from the change of Spring into Summer and of Summer into Autumn; similarly of Autumn into Winter and of Winter into Spring. And then in the Months, from the regular waxing and waning that the Moon makes; and finally in the Days from the changing appearance of light and darkness. From which harmony is born the diversity of flowers and fruits: for as Plato affirms, when heat with cold and dry with humid are joined proportionately, from the harmony of these qualities there results each year most useful to every living thing, full of various kinds of fragrant flowers and most excellent fruits; nor does any other sort of plants or animals come to suffer harm. Just as on the contrary it comes about that from their discordance and distemper are generated pestilence, sterility, infirmity, and every thing noxious to men, beasts, and plants.

And truly Nature has followed a beautiful and most excellent order, causing that which Winter constrains and closes in, Spring opens and sends forth; and that which Summer dries, Autumn finally ripens. In such a way that one season is seen to offer help to another; and from four seasons harmonically disposed there is made one single body.

Mercury, Terpander, and the Strings of the Lyre

This harmony was well known to Mercury and to Terpander: for the one having invented the Lyre, or rather the Cithara, placed in it four strings in imitation of Mundane Music (as Boethius and Macrobius say) — which arises among the four Elements, or in the variety of the four seasons of the year — and the other ordered it with seven strings in the likeness of the seven Planets. The number of the four strings was then named Quadrichord, or Tetrachord, which means as much as of four strings. And that of seven Heptachord, which means of seven strings. But the first was received and embraced by musicians in such a way that the fifteen strings comprised in the greatest System were increased according to the number of the strings of the aforesaid Tetrachord — although they are found to be distant from one another in diverse proportions. And this may suffice as regards the declaration of Mundane Music.