VITRUVIUS, BOOK V, CHAPTER 4:
On harmony.



1. Harmonia autem est musica litteratura obscura et difficilis, maxime quidem quibus graecae litterae non sunt notae. Quam si volumus explicare, necesse est etiam graecis verbis uti, quod nonnullae eorum latinas non habent appellationes. Itaque ut potuero quam apertissime ex Aristoxeni scripturis interpretabor et eius diagramma subscribam finitionesque sonituum designabo, uti, qui diligentius attenderit, facilius percipere possit.

Translation

1. Harmony is an obscure and difficult branch of musical literature especially for persons unacquainted with Greek. If we wish to explain it we must use Greek words and some of these have no Latin renderings. Therefore I shall translate (as well as I can) from the works of Aristoxenus subjoining his diagram, and I shall indicate the definitions of the musical notes, so that an attentive reader can the more easily understand.

2. Vox enim mutationibus cum flectitur, alias fiat acuta, alias gravis; duobusque modis movetur, e quibus unus effectus habet continuatos, alter distantis. Continuata vox neque in finitionibus consistit neque in loco ullo, efficitque terminationes non apparentes, intervalla autem media parentia, uti sermone cum dicamus: sol lux flos vox. Nunc enim nec unde incipit nec ubi desinit, intellegitur; sed quod ex acuta facta est gravis et ex gravi acuta, apparet auribus. Per distantiam autem e contrario. Namque cum flectitur, inmutatione vox statuit se in alicuius sonitus finitionem, deinde in alterius, et id ultro citro crebre faciendo constans apparet sensibus, uti in cantionibus cum flectentes vocem varietatem facimus. Modulationis itaque intervallis ea cum versatur, et unde initium fecit et ubi desiit, apparet in sonorum patentibus finitionibus, mediana autem patentia intervallis obscurantur.

Translation

2. For when the voice is changed and modulated it may sometimes become high, sometimes low. it moves in two manners, of which one is continuous, the other by intervals. For the continuous voice neither stops in definite notes nor indeed anywhere, and comes to no clear endings. There are, however, intervals apparent between one sound and the next; as when we say : sol lux flos vox. For now it is not perceived whence it begins nor where it ceases. But that it passes from high to low, and from low to high, is heard by the ears. The case is opposite with intervals. For when the voice is modulated, the voice in changing is directed first to one determinate sound and then to another. Doing this often backwards and forwards it appears consistent to the sense of hearing, as when in singing we modulate the voice in various ways. When therefore the voice is modulated by intervals, the manifest limits of the notes make clear where it begins and where it breaks off; but the notes within the intervals, although clear in themselves, are not heard.

3. Genera vero sunt modulationum tria: primum quod Graeci nominant harmoniam, secundum chroma, tertium diatonon. Est autem harmoniae modulatio ad artem concepta, et ea re cantio eius maxime gravem et egregiam habet auctoritatem. Chroma subtili sollertia ac crebritate modulorum suaviorem habet delectationem. Diatoni vero, quod naturalis est, facilior est intervallorum distantia. In his tribus generibus dissimiles sunt tetrachordorum dispositiones, quod harmonia tetrachordorum et tonos et dihesis habet binas (dihesis autem est toni pars quarta; ita in hemitonio duae diheses sunt conlocatae); chromati duo hemitonia in ordine sunt composita, tertium trium hemitoniorum est intervallum; diatono toni duo sunt continuati, tertium hemitonium finit tetrachordi magnitudinem. ita in tribus generibus tetrachorda ex duobus tonis et hemitonio sunt peraequata, sed ipsa cum separatim uniuscuiusque generis finibus considerantur, dissimilem habent intervallorum designationem.

Translation

3. The kinds of modulation are three: first that which the Greeks call harmonia; second chroma; third diatonon. Now harmonic modulation is artificialiy constructed; singing in this style has a very solemn and impressive influence. Chromatic modulation, by the refinement and "closeness" of its transitions, produces an impression of more sweetness. The diatonic modulation is closer to nature and has a more easy distance of its intervals. In these three scales, the arrangements of the tetrachords differ. The harmonic scale has two tones in the tetrachord and two quarter-tones. (Now two quarter-tones make a semitone.) The chromatic tetrachord has two consecutive semitones and the third interval is of three semitones. The diatonic tetrachord has two consecutive tones, and the third interval a semitone completes the amount of the tetrachord. Thus in the three scales the tetrachords are equivalent to two tones and a half, but when they are considered separately within the limits of each scale, they vary in the arrangement of the intervals.

4. Igitur intervallo tonorum et hemitoniorum et tetrachordorum in voce divisit natura finitque terminationes eorum mensuris intervallorum quantitate, modisque certis distantibus constituit qualitates, quibus etiam artifices qui organa fabricant, ex natura constitutis utendo comparant ad concentus convenientes eorum perfectiones.

Translation

4. Therefore by the intervals of tones, semitones, and tetrachords, nature has divided and defined their limits for the voice, measuring them by the quantity of the intervals; and has fixed their quality in certain distinct modes. Craftsmen who make instruments use these proportions which nature has fixed, and make perfect their instruments with a view to suitable concords.

5. Sonitus, qui graece phthongi dicuntur, in unoquoque genere sunt X et VIII, e quibus VIII sunt in tribus generibus perpetui et stantes, reliqui X, cum communiter modulantur, sunt vagantes. Stantes autem sunt, qui inter mobiles sunt interpositi. Continent tetrachordi coniunctionem et e generum discriminibus suis finibus sunt permanentes; appellantur autem sic: proslambanomenos, hypate hypaton, hypate meson, mese, nete synhemmenon, paramese, nete diezeugmenon, nete hyperbolaeon. Mobiles autem sunt, qui in tetrachordo inter inmotos dispositi in generibus ex locis loca mutant; vocabula autem habent haec: parhypate hypaton, lichanos hypaton, parhypate meson, lichanos meson, trite synhemmenon, (paranete synhemmenon,) trite diezeugmenon, paranete diezeugmenon, trite hyperbolaeon, paranete hyperbolaeon.

Translation

5. Sounds (which in Greek are called phthongi) are eighteen in number for each kind. Of these, eight are perpetually fixed in the three kinds; the remaining ten, when they are modulated in common, are found to vary. Now those are fixed which are interposed betwteen the variable sounds; they determine the combination of the tetrachord, and in accordance with the differences of the kinds remain in their own limits. Their names are these: proslambanomenos; hypate hypaton; hypate meson; mese; nete synhemmenon; paramese; nete diezeugmenon; nete hyperbolaeon. Those sounds are shifting which are arranged in the tetrachord between the fixed sounds, and change from place to place in the three kinds. Their names are these: parhypate hypaton; lichanos hypaton; parhypate meson; lichanos meson; trite synhemmenon; paranete synhemmenon; trite diezeugmenon; paranete diezeugmenon; trite hyperbolaeon; parenetfe hyperbolaeon.

6. Ei autem qua moventur, recipiunt virtutes alias; intervalla enim et distantias habent crescentes. Itaque parhypate, quae in harmonia distat ab hypate hemitonium, in chroma tramutata habet hemitonium. Qui lichanos in harmonia dicitur, ab hypate distat hemitonium, in chroma translata progreditur duo hemitonia, in diatono distat ab hypate tria hemitonia. Ita X sonitus propter translationes in generibus efficiunt triplicem modulationum varietatem.

Translation

6. But those sounds which shift, gain various qualities; for they have increasing intervals and distances. Thus the parhypate which in the enharmonic is half a semitone from the hypate, has a semitone when it is changed to the chromatic. What is called lichanos in the enharmonic kind, is distant a semitone from the hypate; transferred to the chromatic, it advances two semitones; in the diatonic, it is distant three semitones. Thus the 10 sounds, because of their transpositions in the three scales, produce a triple variety of modulation.

7. Tetrachorda autem sunt quinque: primum gravissimum, quod graece dicitur hypaton, secundum medianum, quod appellatur meson, tertium coniunctum, quod synhemmenon dicitur, quartum disiunctum, quod diezeugmenon nominatur, quintum, quod est acutissimum, graece hyperbolaeon dicitur. Concentos quos natura hominis modulari potest, graece quae synphoniae dicuntur, sunt sex: diatessaron, diapente, diapason, et disdiatessaron, et disdiapente, et disdiapason.

Translation

7. Now the tetrachords are five : the first is the lowest which in Greek is called hypaton; the second is the middle which is called meson; the third which is joined to these is called synhemmenon; the fourth being separated is called diezeugmenon; the fifth which is the highest is called in Greek hyperbolaeon. The concords (in Greek symphoniae) which the human voice can modulate are six: diatessaron (fourth); diapente (fifth); diapason (octave); disdiatessaron (octave and fourth); disdiapente (octave and fifth); disdiapason (two octaves).

8. Ideoque et a numero nomina ceperunt, quod, cum vox constiterit in una sonorum finitione ab eaque se flectens mutaverit et pervcnerit in quartam terminationem, appellatur diatessaron, in quintam diapente [in sextam diapason in octavam et dimidiam diapason et diatessaron, in nonam et dimidiam diapason diapente, in XII dis diapason].

Translation

8. These have taken their names from numbers. For when the voice has rested in one fixed sound, and then modulates and changes from itself, and comes to the fourth sound it is called diatessaron; when it comes to the fifth, it is called diapente; [to the eighth, diapason; to the eleventh, diapason with diatessaron; to the twelfth, diapason with diapente to the fifteenth disdiapason].

9. Non enim inter duo intervalla, cum chordarum sonitus aut vocis cantus factus fuerit, nec in tertia aut sexta aut VII possunt consonantiae fieri, sed, uti supra scriptum est, diatessaron et diapente et ex ordine disdiapason convenientiae ex natura vocis congruentis habent finitiones. Et ei coventus procreantur ex coniunctione sonituum, qui graece phthongi dicuntur.

Translation

9. For concords cannot arise between two intervals, when the sound of strings or the song of the voice is uttered, nor between three or six or seven; but, as we wrote above, the diatessaron and diapente up to the disdiapason are concords which have limits arising from the nature of the voice. And these concords are produced from the conjunction of sounds which in Greek are called phthongi.

COMMENT

This is a long and difficult chapter in which Vitruvius summarizes the music theory of the Greek Philosopher Aristoxenus. It is the introduction for the next chapter in which Vitruvius describes the position and pitch of bronze sound vessels that - according to his theory - should be incorporated into a theatre to enhance acoustics. This is not the place to give a full account about Greek music, only some basic ideas are given here for a better understandig of Vitruvius' text.

Greek music is based on the tetrachord which is derived from the number of chords on a lyre. Basically a lyre had seven chords which could produce two tetrachords. Each tetrachord had 2 1/2 tones and each tone was further divided in 12 parts. So in the tetrachord there are 30 intervals. Only the first and last notes of each tetrachord are fixed tones and each last note of the tetrachord is the first note of the next tetrachord. The position of the two intermediate notes can change depending on the modus of the music. The names of the notes where also derived from the position of the chords on the lyre. Hypate was the first note of the tetrachord, the parhypate was the note closest (para-) to the hypate, the lichanos was named after the chord of the lyre that was touched with the index finger and finally mese was called after its central position in the lyre and can be called hypaton of the next tetrachord.

The diagram below gives the different possible divisions of a tetrachord. The fixed notes (hypate and mese) are not indicated; the stay respectively on position 1 and 30. The position of parhypate and lichanos can change.

BIBLIOGRAPHY

F.GRANGER, Vitruvius, On architecture, Cambridge - London, 1931
T.PETERS, Vitruvius, Handboek bouwkunde, Amsterdam, 1999
S.GIBSON, Aristoxenus of Tarentum and the birth of musicology, New York, 2005

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