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Library / Almagestum Novum, Book IX: On the System of the World

Section V — On the Harmonic System of the World

Chapter V, On Music, and the various Divisions and Genera of Melodies and Songs

(De Musica ac Melodiarum Cantuumque Divisionibus varijs, ac Generibus)

[Margin: The 1st and 2nd Division of Music.]

[I.] Music is twofold: one Theoretical, the other Practical. The Theoretical, on the authority of Boethius (bk. 1, ch. 2), is threefold: namely Mundane (of the World), which considers the harmony of the whole world and its parts — such as the symphonism and symmetry of the elements and of the heavens; Human, which treats of the proportions of body and soul among themselves and with their parts — that is, of the harmony of the Microcosm; and Organic (Instrumental), which contemplates the harmony resulting from sounds and voices, whether in a natural or an artificial manner. Zarlino, however (part 1, ch. 5), first divides Music in two — into Animastic and Organic — and afterward subdivides the Animastic into Mundane and Human, and the Organic into Natural and Artificial.

[Margin: The 3rd Division. — Natural and Artificial; what Music is.]

The Third Division, then, is of Organic Music into the Natural — which considers the sounds naturally produced by the instruments of the throat or larynx, the lungs, the palate, the tongue, the teeth, and the lips (for these are the natural instruments of the sound and voice of animals) — and into the Artificial, which considers a sound made (or makeable) by various instruments fashioned by art.

[Margin: Division of the Musical Instruments.]

Of these, the First Genus contains the Pneumatic (Greek ἐμπνεόμενα), that is, [instruments] resounding by the force of breath and animated by spirit — whether it be the breath of living things or the wind and air — of which kind are: reeds, hemlock-pipes, panpipes (syringes), shepherds’ or military pipes (Ital. Subioli or Cifoli); three-holed or six-holed pipes (Ital. Flauti); clarions or horns; bagpipes (Ital. Corni, Cornetti, Cornamuse); serpentine horns (Ital. Bischoni); tibiae (Ital. Pive or Pifferi); droning bagpipes (Ital. Pive sordine); trumpets, buccinas, war-trumpets (Ital. Trombe), and slide-trumpets (Ital. Tromboni); zooglossal pipes, with which we imitate the various voices of animals; and anthropoglossal pipes, with which we imitate human speech and laughter; but chiefly those which are properly called Organs (or, by Vitruvius, Musical Canons), compacted of many pipes or tubes of lead or cypress-wood and inflated by bellows.

The Second Genus comprises the stringed instruments (Greek ἔγχορδα / ἔντατα), that is, those of gut or sinew — consisting of one or more strings, which sound when struck by the fingers, nails, plectra, etc. — of which kind are: psalteries, harps, lutes (Testudines), lyres, barbitons, Cheles, sambucas, pandoras, mandoras, nablas, citharas, pectides, harpsichords (Clavicymbala), and the Turkish three-stringed [lute], commonly il Colachon or Colascione. For the Testudines, Pandorae, and Mandorae are called in Italian Leuti (lutes); the citharas, Cetre; the Spanish citharas, Chitariglie; the theorbos, Chitaroni; the small four-stringed Chelis, il Violino; the six-stringed Chelis, la Viola; the larger four-stringed Chelys, il Violone; the smallest Chelys or Lynterculus, il Lirino; the twelve-stringed Chelis or Lyra, Lira or Lirone; the Clavichordium (or Clavicymbalum, or Manichordium), called Clavicembalo, Manacordo, Spinetta.

Lastly, the Third Genus comprises the percussion instruments (Greek κρουστά), such as cymbals, sistra, drums (Tympana), bells, crotala, and xylophones (Zylorgana) — that is, those which, in place of pipes, have wooden cylinders. But concerning Musical instruments there have written excellently: Mersenne (on Genesis, ch. 4, verse 21, question 56, or from p. 1515); Othmar Luscinius (bk. 1 of the Musurgia); and our Kircher (bk. 2, chs. 3 and 6, and bk. 6 of the Musurgia) — where also, from his own and Mersenne’s experiments, he sets out the proportions of strings, pipes, etc., and what voices the strings of various metals, sinews, and wires give forth, or what sounds, and in what proportion, various woods struck [give forth].

[Margin: The 4th Division, from Isidore.]

Fourthly, Music is divided by Isidore (bk. 3 of the Origins) into Harmonic, which consists of the songs of voices; Organic, which rises from breath; and Rhythmic, which receives its numbers by the impulse of the fingers. But some include under Rhythmic both the metric art of syllables (for constructing verse) and the dance; others separate Metric from Rhythmic, as may be seen in Zarlino (part 1, ch. 5).

[Margin: The 5th Division, from Martianus Capella.]

Fifthly, Music is divided, according to Martianus Capella (bk. 9, On the Marriage of Philology), into three genera, of which the First is called εἰδικόν, which consonates from sound by like and persevering numbers and words (but the part of these pertaining to melody is called harmonic, that pertaining to numbers rhythmic, that pertaining to words metric); the Second is ἐργαστικόν, that is, operative; and the Third ὑπερεργαστικόν, that is, super-operative, or ἑρμηνευτικόν, that is, enunciative — concerning which consult that author himself, for this division is very obscure and accepted by almost no one.

[Margin: The 6th Division, into the Modes — Dorian, Phrygian, Lydian, etc. / The 12 Musical Modes.]

[II.] Sixthly, [Music] is divided into various Modes, but chiefly into the Dorian, Phrygian, Lydian, Aeolian, Ionian, Iastian, and into mixtures of these — according as these modes were invented by the Dorians, Phrygians, etc., or were more in use in those regions; although Alypius, in his Isagoge, says the Dorian was invented by Thamyras, the Phrygian by Marsyas, the Lydian by Amphion, the Hypodorian by Philoxenus, the Hypolydian by Polymnastus, and the Mixolydian by Sappho. But in assigning their distinctions there is a wonderful and almost inextricable confusion; see, if you please, the interpreters of Aristoxenus and Ptolemy — Glareanus (Dodecachordon 1, chs. 2 and 7), Mersenne (on Genesis 4, verse 24, from p. 1664), and Kircher (Musurgia 3, ch. 15, and bk. 7, p. 554) — who collect the opinions of others.

Here let it suffice to know that the Dorian was a grave and severe mode, in which Re–Sol reigned; the Phrygian religious and hard, in which Mi–La; the Lydian wanton and the Ionic soft, in which Ut–fa. Whence Pliny (bk. 2, ch. 22) said that Saturn is moved by the Dorian, Jupiter by the Phrygian, Mercury by the Lydian. Further, all the modes, simple and mixed, are reduced to 12 by Kircher, or to 15 by Euclid, Cassiodorus, and Capella:

[…continues on p. 515 (PDF 550) with the catchword “Ionius” (the Ionian mode), completing the catalogue of the musical Modes, still within Chapter V.]

(printed p. 515 — Chapter V continued. The catalogue of Modes ends with the Ionian and Hypoionian; then the three famous Genera of music — Diatonic, Chromatic, and Enharmonic — are expounded, with their inventors, characters, and tetrachord structures, and the species of each genus after Aristoxenus and Kircher. The right column gives the tetrachord paradigms of each species with string-length numbers and interval ratios.)

But according to Euclid, Cassiodorus, and Capella there are fifteen [modes], numbered thus: Dorian, Iastian, Phrygian, Aeolian, Lydian, Hypodorian, Hypoiastian, Hypophrygian, Hypoaeolian, Hypolydian, Hyperdorian, Hyperiastian, Hyperphrygian, Hyperaeolian, Hyperlydian. But on these [see] more in Kepler (bk. 3 of the Harmonics, chs. 14–15).

[Margin: The 7th Division, into the genera Diatonic, Chromatic, and Enharmonic.]

[III.] Seventhly, Music is divided into three most famous genera — namely the Diatonic, Chromatic, and Enharmonic (Greek διατονικόν, χρωματικόν, ἐναρμονικόν) — as Vitruvius has them (bk. 5, ch. 4), naming three genera of modulation (διάτονον, χρῶμα, ἁρμονίαν; where see Daniele Barbaro); Ptolemy (Harmonics 1, ch. 13), attributing this division to Archytas the Pythagorean; Martianus Capella (bk. 9, in the chapter on the Genera of Tetrachords), who calls these three genera of tetrachords ἐναρμόνιον, χρῶμα, διάτονον; Boethius (bk. 5); Macrobius (bk. 2 on the Dream of Scipio, ch. 4); Zarlino (part 2, chs. 9 and 16); and Kircher (Musurgia 3, p. 119, and more fully in the whole of ch. 13). This division is taken from the diverse manner of arranging the tetrachords in ascending from a grave sound to an acute one.

[Margin: The Diatonic genus.]

The Diatonic, by Plutarch’s testimony, is the most ancient and most natural — its invention ascribed by Zarlino to Terpander of Lesbos or to Pythagoras. This genus ascends by two tones and a lesser semitone; and because it proceeds by intervals a tone apart and abounds in tones, it is called Diatonum or Diatonic. It is severe, grave, and constant, displaying manly characters and habits, and is today most in use, as it was also in the times of Martianus Capella and Macrobius.

[Margin: The Chromatic.]

The Chromatic genus was invented by Timotheus of Miletus the Lyric poet, as Suidas and Boethius relate — wherefore Aristotle says in the Metaphysics that, had Timotheus not been, we should have been forced to lack many melodies. Now chroma in Greek signifies color; whence this genus is so named, because it introduces various colors into the diatonic, standing between the Diatonic and Enharmonic as the variety of colors between white and black. It proceeds by two hemitones (greater and lesser) and a semiditone — that is, three hemitones; it is far more artful than the Diatonic, and fit for stirring various affections; whence Vitruvius says of it: “By subtle skill and the frequency of its modulations it has a sweeter delight”; but Barbaro calls it soft and plaintive.

[Margin: The Enharmonic.]

The Enharmonic was invented by Olympus (by the testimony of Aristoxenus and Plutarch, On Music) — being of all the most excellent to use and fullest of authority, of the highest art and skill, and (for its difficulty) used by very few, and on that account called par excellence (αὐτονομαστικῶς) harmonic or enharmonic. It proceeds by a Diesis and a ditone. Treating of these lightly, Kepler (Harmonics 3, ch. 6, at the end) thinks the Diatonic corresponds to hard song [major] and the Chromatic to soft song [minor]; or that there were two species of the Diatonic, Hard and Soft, intermixed in the Chromatic; but that the Enharmonic corresponds to nothing in ordinary Music except the vibrations of the human voice, the tremor of organs, and the mordent on the strings of the Pandura, and the like. Finally, Macrobius (bk. 2 on the Dream of Scipio, ch. 4) says: “Since there are three genera of musical melody — Enharmonic, Diatonic, and Chromatic — the first, for its excessive difficulty, has fallen out of use; the third is infamous for its softness; whence the middle, that is the Diatonic, is by Plato’s doctrine ascribed to the mundane [world-]music.”

Further, Aristoxenus subdivided the Diatonic into Soft and Incited (Sharp), and the Chromatic into Soft, Sesquialter, and Tonic — which subdivisions, like those of Didymus, Archytas, and Eratosthenes, are disapproved by Ptolemy (Harmonics 1, chs. 12–13, and 2, chs. 13–14), Boethius (bk. 5, chs. 15–17), and Zarlino (part 2, ch. 16). Kircher, however (Musurgia 3, ch. 13), says that the more skilled Musicians receive five subaltern genera or species of the Diatonic — the Pythagorean, Soft, Syntonic, Toniac, and Equal; three species of the Chromatic — the Ancient, Soft, and Syntonic; and finally two of the Enharmonic — the Ancient and Ptolemaic; whose paradigms he sets out in tetrachords with their own proportions, in greater and lesser numbers.

The Tetrachord Paradigms

(the four strings — I = Hypate hypaton, II = Parhypate hypaton, III = Lichanos hypaton, IV = Hypate meson — with their string-length numbers; each ascending interval and its ratio shown between them)

In each chain below, the numbers are the string-lengths (I → IV), and each ”— interval (ratio) →” is the step between consecutive strings; every tetrachord spans the Diatessaron (3 : 4 from I to IV).

Diatonic — Diatonum, or Pythagorean: I = 6144 — Tone (sesquioctave, 9:8) → II = 6912 — Tone (9:8) → III = 7776 — lesser Semitone (256:243) → IV = 8192

Diatonic — Soft: I = 63 — sesquiseptima (8:7) → II = 72 — sesquinona (10:9) → III = 80 — sesquivigesima (21:20) → IV = 84 (beside strings III and IV the original also prints the smaller figures 45 and 48; their basis is not made explicit — they coincide with strings III–IV of the Syntonic tetrachord below, 36:40:45:48.)

Diatonic — Incited (Sharp), or Syntonic: I = 36 — minor Tone (sesquinona, 10:9) → II = 40 — major Tone (sesquioctave, 9:8) → III = 45 — lesser Semitone (sesquidecimaquinta, 16:15) → IV = 48

Diatonic — Toniac: I = 168 — Tone (sesquioctave, 9:8) → II = 189 — sesquiseptima (8:7) → III = 216 — sesquivigesimaseptima (28:27) → IV = 224

Diatonic — Equal: I = 9 — sesquinona (10:9) → II = 10 — sesquidecima (11:10) → III = 11 — sesquiundecima (12:11) → IV = 12

Chromatic — Ancient: I = 6144 — Trihemitone (trisemitonium) → II = 7296 — Semitone → III = 7776 — lesser Semitone → IV = 8192

Chromatic — Soft: I = 105 — sesquiquinta (6:5) → II = 126 — sesquiquartadecima (15:14) → III = 135 — sesquivigesimaseptima (28:27) → IV = 140

[Translator’s note: in the Pythagorean tetrachord string III is printed “7777,” evidently for 7776 (= 6912 × 9⁄8), so that III → IV is the limma 256:243 (7776 × 256⁄243 = 8192). The Ancient-Chromatic numbers are the Pythagorean-derived values, whose intervals (trihemitone, semitone, lesser semitone) do not all reduce to simple superparticular ratios. The Soft-Diatonic secondary figures (45, 48) are recorded above as printed.]

[The catchword “Te-” points to p. 516 (PDF 551), which continues with the remaining tetrachords (Syntonic Chromatic; the two Enharmonic species), after which Chapter VI begins.]

(printed p. 516 — Chapter V concludes, then Chapter VI begins. The tetrachord paradigms are finished and the last divisions of music given: hard versus soft song (major and minor) and plain versus figured song, with a brief history of notation from Boethius through Gregory to Guido of Arezzo. Chapter VI, on the strings, voices, and musical notes of the harmonic system, then opens with the accidents of modulation — voice types, note-durations (with a table of the nine note-values), and pitch, introducing the ancients’ five tetrachords of the Greater Perfect System.)

(conclusion — the last tetrachords, and the 8th and 9th Divisions of Music)

The Tetrachord Paradigms (continued from p. 515)

Chromatic — Syntonic (Sharp): I = 66 — sesquisexta (7:6) → II = 77 — sesquiundecima (12:11) → III = 84 — sesquivigesimaprima (22:21) → IV = 88

Enharmonic — Ancient: I = 6144 — Ditone → II = 7776 — Diesis → III = 7984 — Diesis → IV = 8192

Enharmonic — Ptolemaic: I = 276 — sesquiquarta (5:4) → II = 345 — sesquivigesimatertia (24:23) → III = 360 — sesquiquadragesimaquinta (46:45) → IV = 368

These were the foundations of the remaining Tetrachords, from which the whole system or musical scale was so composed that it consisted of five tetrachords, the fourth string of the first being the first of the second, and the fourth of the second the first of the third, and so on — as we shall set forth in the example of the following chapter, where we shall explain the names and order of the strings.

[Margin: The 8th Division, of Hard and Soft (song).]

[IV.] Eighthly, the genus of melodies is divided into Hard and Soft Song (Cantus Durus ac Mollis) — a division famous among more recent [musicians]. Hard Song is that in whose system the intervals are ordered, from the lowest voice, by the major Third and Sixth — that is, the consonances 5:4 and 5:3 — which are also called hard and harsh. Soft Song is that in which the intervals are ordered, from the lowest voice, by the minor Third and Sixth — that is, the consonances 6:5 and 8:5 — which are called the soft Third and soft Sixth; of which you have examples in Kepler (bk. 3 of the Harmonics, ch. 6), whom let anyone consult who desires these things.

[Margin: The 9th Division, of Plain and Figured Song.]

[V.] Ninthly, Music is divided into Plain (or Firm) Song and Figured (or Harmonic) Song. Plain Song is that in which the passage from sound to sound is made by the simple raising and lowering of the voice, without any inquiry into Consonance per se, and without variation of time; or in which the difference of high and low is attended to, but without the symmetry of many harmonically-consonant voices through various time-delays. Figured Song is that whose modulation is made through many voices harmonically consonant with one another, and through time-delays concinnously ordered in voice or sound; and because this is done by means of certain notes and figures, this song is therefore called Figured — a genus reckoned to have been invented in the last centuries.

Further, Plain Music is subdivided into Boethian, Gregorian, and Aretinian — all of which, for their gravity and perspicuity, are most fit for divine worship and for exciting devotion. Boethius, imitating the Greeks, established 15 divisions on the monochord, distributing 15 strings into four tetrachords, and admitting a semitone between the first and second [tetrachord]; whom among the Latins Saints Ambrose and Augustine followed. Afterward St. Gregory the Great, about the year 594, devised the seven letters of the alphabet A B C D E F G, repeating them up to the number 15. But Guido of Arezzo, about the year of the Lord 1024, established the hand or musical scale of 20 letters and six syllables — Ut, re, mi, fa, sol, la — of which [we shall say] a few things in the following chapter.

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