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2 Theory and Practice of Music: Severinus Boethius and Guido D'Arezzo

2 Theory and Practice of Music: Severinus Boethius and Guido D'Arezzo

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6 With the Latin Alphabet, Above All



undoubtedly favoured by the tragic events that occurred to its author. The moral

interpretation of his work as a philosopher was Christian indeed, and he had a

brilliant political career. But as a result of this, he was accused of betrayal before

the court of Theodoricus, and consequently he was executed.

In the field of music, Latin scholars hardly translated anything from Arabic.

Although treatises of algebra and medicine by them were put into the new dominant

language, they ignored the pages about music which were sometimes attached.

“: : : in their translations of various Arabic treatises, they omitted the portions that

regarded music! As a result, the section about music in the Šifa by Avicenne was

never translated.”6 The neo-Platonic tradition was directly followed and maintained

fresh by Marcus Tullius Cicero (106–43 B.C.), Ambrosius Theodosius Macrobius

(early fifth century), and Proclus (410–485). At the end of his work De Republica,

the famous orator, polemicist and politician of the pre-imperial period added a

Somnium Scipionis, where he described the music of the heavenly spheres.7

“: : : ‘quis est, qui conplet aures meas, tantus et tam dulcis sonus?’ ‘Hic est’ inquit

‘ille, qui intervallis coniunctus imparibus sed tamen pro rata parte ratione distinctis,

impulsu et motu ipsorum orbium efficitur et acuta cum gravibus temperans varios

aequabiliter concentus efficit. Nec enim silentio tanti motus incitari possunt, et

natura fert, ut extrema ex altera parte graviter, ex altera autem acute sonent. Quam

ob causam summus ille caeli stellifer cursus, cuius conversio est concitatior, acute

et excitato movetur sono, gravissimo autem hic lunaris atque infimus. Nam terra,

nona, inmobilis manens una sede semper haeret conplexa medium mundi locum.

Illi autem octo cursus, in quibus eadem vis est duorum, septem efficiunt distinctos

intervallis sonos, qui numerus rerum omnium fere nodus est. Quod docti homines

nervis imitati atque cantibus aperuerunt sibi reditum in hunc locum, sicut alii, qui

praestantibus ingeniis in vita humana divina studia coluerunt. : : :’ ”8 [“: : : ‘what is

this sound, so great and sweet, that fills my ears?’ ‘This’ he replied ‘is the sound

which is produced by the impulse and the movement of the orbits, by tempering

together intervals that are unequal, yet calculated precisely in their ratios; by mixing

the acute with the deep, various harmonies of sounds are similarly created. Such vast

movements cannot take place silently indeed, and nature causes the extremes at one

end to sound deep, and at the other end, acute. For this reason, that supreme starry

course in the skies whose change takes place most rapidly moves with an acute,

stimulating sound, whereas the deeper sound accompanies the lower course of the

Moon. The Earth, the ninth heavenly body, which remains immobile, and confined to

one spot, occupies the central position in the world. Instead, the other eight courses,

in two of which the same force resides, create sounds that may be distinguished into

seven intervals, whose number is the essence of almost everything. By reproducing

this with singing and strings, wise men opened up the way to return to this place,



6



Burnett 1990, pp. 87–88.

Cicero 1992.

8

Macrobius 1893, pp. 657–658.

7



6.2 Theory and Practice of Music: Severinus Boethius and Guido D’Arezzo



261



like others who cultivated studies of the divine with outstanding intellects during

their human life’ : : :”.]

In the Christian environment, readers disregarded the ancient context of the Punic

Wars between Carthage and Scipio Africanus, who appeared to his descendant

Scipio Aemilianus in a dream. They preferred to interpret the story in favour of

the immortality of the soul, which returns to heaven. The most famous commentary

on this work is that of Macrobius, in which we can find some of the most permanent

occurring topoi that accompanied Pythagoreanism in music.

“Deinde tonus per naturam sui in duo dividi sibi aequa non poterit. Cum enim

ex novenario numero constet, novem autem numquam aequaliter dividantur, tonus

in duas dividi medietates recusat : : :”.9 [“Therefore, due to its own nature, the tone

cannot be divided into two equal parts. As it is formed by the number nine, and

the number nine can never be equally divided, the tone refuses to be divided into

two halves : : :”]. The conclusion presents us with the same prohibition of dividing

the tone into two equal parts. But now, far from the sources of Euclid and Ptolemy,

or incapable of following the reasons partly justified by mathematics, the argument

used became worse than mistaken, unless the text is corrupt, or errors have been

made by the copyists. Macrobius seems do not understand that dividing an interval

of a geometrical progression means extracting the square root in order to obtain the

proportional mean. Thus 9 would give the excellent whole

p number 3, whereas it is

8 that does not produce the whole number, but contains 2. Furthermore 9, which

clearly cannot be divided into two whole numbers like 8, all the same contains two

rational parts that are equal. In other words, Macrobius is confusing the geometrical

progression with an arithmetic one.

Ancient Pythagoreanism was declining to pure verbal rhetoric, losing its bearing

mathematical skeleton. Only a showy Platonic dress was left visible, which however

continued to perform its advertising function effectively. As in Plato’s Republic, now

through the end of Cicero’s De Republica, the choice of the intervals for scales and

the modes of music made it possible to justify the melodies considered to be moral

and suitable for that particular social organisation, refusing the others. Mathematical

sciences again served for the prohibition; whether they were right or wrong did not

seem to be of any importance to them.

“: : : cum sint melodiae musicae tria genera, enarmonium, diatonum et chromaticum, primum quidem propter nimiam sui difficultatem ab usu recessit, tertium

vero est infame mollitie, unde medium, id est diatonum, mundanae musicae doctrina

Platonis adscribitur.”10 [“: : : seeing that there are three genres of musical melodies,

enharmonic, diatonic and chromatic, the first has actually become detached from

use due to its difficulties, whereas the third is shameful because of its effeminacy

and its licentiousness; as a result, the intermediate one, that is to say, the diatonic, is

attributed by Platonic doctrine to the music of the universe.”] Now music’s task was

to open up to the soul the doors of the heavenly paradise, whether this was Platonic



9



Macrobius 1893, p. 586.

Macrobius 1893, p. 598. Cf. Flamant 1977, pp. 351–381.



10



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6 With the Latin Alphabet, Above All



or Christian. But wasn’t there a risk that all those different micro-intervals, used in

the lascivious modes and admitted by the rival theory of Aristoxenus, might become

extremely dangerous keys? They were definitely ready to open up quite different

paradises, visible and tangible, since they were earthly ones. Macrobius despised

all the arts of the senses; he condemned the art of singing, and dancing, and even

cookery. Honest men and women should not practise them. He believed that ears

should be closed to the temptations of a sensual melody. For him, the only music

should be the heavenly kind of the spheres, abstract, transcendent and inaudible.

He had largely taken his inspiration from Plato.11

Compared with Macrobius, Proclus was more important for the mathematical

sciences, above all in view of his commentary on Euclid’s text, though he has not left

us anything dealing with music. As has already been said, this scene was dominated

by Boethius, in whom we find the commonplaces of Pythagoreanism, together with

the relative errors of Macrobius.

In the tradition of the quadrivium, Boethius now placed Arithmetic before Music.

He wrote all the numbers in Roman numerals, and used them to present the few

notions that were needed to define the usual Pythagorean ratios. Rapidly freeing

himself from the task, he indicated the difference between music and the other mathematical disciplines. “: : : cum sint quattuor matheseos disciplinae ceterae quidem

in investigatione veritatis laborent, musica vero non modo speculationi verum etiam

moralitati coniuncta sit.” [“: : : as there are four mathematical disciplines, while the

others attend to investigations into the truth, music, on the contrary, is not only

concerned with speculation, but also with morality.”]

In customs, the extreme positions were a “lascivus animus” [lascivious spirit]

and an “asperior mens” [more rigid, proud mind]. The former enjoyed lascivious

melodies, and “when he heard them, he often became effeminate, and weak”.

The latter, on the contrary, preferred rousing tunes, and “took strength from

those that were more stimulating”. These were, respectively, the Lydian and the

Phrygian modes.12 Besides these ideas, Boethius also followed the other topoi of

Pythagoreanism and Platonism. He discussed the variants, like those of Ptolemy,

and refused the opposite position of Aristoxenus.

Unlike human instrumental music, the music of the heavenly spheres did not

arrive at man’s ears. Nevertheless, the sound was defined as “: : : percussio aëris

indissoluta usque ad auditum” [“: : : the connected striking of the air as far as

the organ of hearing”]. Some movements were faster, others slower, some more

frequent, others more spaced; this was the derivation, respectively, of the sounds that

were more acute or deeper. “In quibus autem pluralitas differentiam facit, ea necesse

est in quadam numerositate consistere.” [“In which the multiplicity is different; this

is necessarily composed of certain numbers”].13 The ratios for music were thus



11



Flamant 1977, pp. 355–356.

Boethius 1867, pp. 179–180.

13

Boethius 1867, pp. 189–190.

12



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263



made of numbers; in this way, they distinguished between the various consonances

and dissonances, as we have seen in the Greek tradition.

Boethius repeated, and established through the centuries, the legend of Pythagoras, who “: : : divino quodam nutu : : :” [“: : : as a result of some divine will : : :”] is

said to have understood that the different sounds of hammers in a smithy depended

on their different weights. Such indisputable authority made it superfluous for him

to verify whether it was really the double weight that produced a sound an octave

lower, and whether the other ratios of consonance were obtained by changing

the weights proportionately. All the consonances were then fixed by the Roman

numerals XII, VIIII, VIII, VI. Pythagoras is said to have investigated what “ratios

corresponded to all the consonant relationships”.14 “Nunc quidem aequa pondera

nervis aptans eorumque consonantias aure diiudicans, nunc vero in longitudine

calamorum duplicitatem medietatemque restituens ceterasque proportiones aptans

integerrimam fidem diversa experientia capiebat.” [“He got the most genuine

certainty by means of different experiments, at times adapting suitable weights to

the sinews, and judging their consonances with the ear, and at times creating pipes

twice or half as long, and preparing other ratios.”]15

There would be too many earthly sounds, because they form a continuum.

“Continuae enim voci terminum humanus spiritus facit, ultra quem nulla ratione

valet excedere.” [“Thus the spirit of man places a limit to the continuous sound,

beyond which it is not appropriate to go for any reason.”] In order to explain how

sound arrives at the ear, Boethius made a comparison with the ripples produced by

a stone in water. Some codices also included a figure (Fig. 6.1) to describe the ratios

of music.16

The belief that, according to this theory, the tone could not be divided into two

equal parts was repeated several times. “Rursus tonus in aequa dividi non potest

: : :” [“Again, the tone cannot be divided into equal parts : : :”]. “: : : quod tonum

in gemina aequa diceremus non posse disiungi.” [“: : : we will say that the tone

cannot be broken down into two equal parts.”] “: : : ut tonum sequioctavam facere

proportionem [9:8] eumque in duo aequa dividi non posse, sicut nullam eiusdem

generis proportionem, id est superparticularis [n+1:n];” [“: : : the tone is composed

of the sesquieighth ratio, and it cannot be divided into two equal parts, seeing that

no ratio of the same kind exists, that is to say, superparticular;”].17

Consequently, for this orthodox tradition, “Non est igitur diapason [octave]

consonantia constans sex tonis, ut Aristoxenus arbitratur. Quod in numeris quoque

dispositum evidenter apparet.” [“The consonance of the diapason, therefore, is not

composed of six tones, as Aristoxenus believes. That is clearly apparent also in

the order of numbers.”] Having defined the ratio of the comma, the quantity by

which six tones exceed the octave, as DXXIIII.CCLXXXVIII:DXXXI.CCCCXLI



14



Boethius 1867, pp. 197–198.

Boethius 1867, p. 198.

16

Boethius 1867, pp. 199–201.

17

Boethius 1867, pp. 202–203 and 223.

15



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6 With the Latin Alphabet, Above All



Diapason.

I.



Diapente.

II.



II.



Diatessaron.

III.



III.







um 1

Dupla.







Sesqualtera.



Tonus.



Sesquioctava.

Quadrupla.

II.

IIII.







Sesquitertia.

Tripla.

III.

II.



VIII. VIIII.



Dupla.

II.



VIII.





Sesqualtera.



IIII.







III.



VI.



IIII.







Sesquitertia.



Fig. 6.1 The Roman numerals used by Boethius for musical intervals (Boetius 1867, p. 201)



[524,288:531,441], Boethius insisted: “Sed de his, quid Aristoxenus sentiat, qui

auribus dedit omne iudicium, alias commemorabo. Nunc voluminis seriem fastidii

vitator adstringam.” [“But I will recall another time the beliefs of Aristoxenus, who

entrusted all judgement to the ears. Now, to avoid tedium, I will limit the series of

the volume.”]18

And yet our philosopher dedicated another two chapters, in Book 3, to the subject

“Adversus Aristoxenum”, and one to the proof of Archytas that a ratio of the kind

9:8, that is to say, superparticular, could not be divided into two equal parts. In the

first chapter, he stated that the tone 18:16 could be separated into the ratios 18:17

and 17:16, but these are not the same. Thus he selected only rational numbers as

legitimate, without mentioning them by name, though.19 He always limited himself

to these, when he again wrote that Aristoxenus was wrong in sustaining that the

interval of the fourth was composed of two tones and one semitone, or that the

octave was six tones. And he again indicated by how much they exceeded the octave,

i.e. the value of the comma.20

For the demonstration that a superparticular ratio, such as 9:8, could not be

divided into two equal ratios, he even appealed to Archytas: “Superparticularis

proportio scindi in aequa medio proportionaliter interposito numero non potest.

Id vero posterius firmiter demonstrabitur. Quam enim demonstrationem ponit

Archytas, nimium fluxa est.” [“The superparticular ratio cannot be broken up into

equal parts by inserting a proportional number in the middle. This will proved



18



Boethius 1867, pp. 265–267.

Boethius 1867, pp. 268–270.

20

Boethius 1867, pp. 273–275.

19



6.2 Theory and Practice of Music: Severinus Boethius and Guido D’Arezzo



265



with certainty below, seeing that the proof offered by Archytas is too weak.”] “: : :

quoniam minimi in eadem proportione sola differunt unitate, quasi vero non etiam

in multiplici proportione minimi eandem unitatis differentiam sortiantur, cum plures

videamus esse multiplices praeter eos, qui in radicibus collocati sunt, inter quos

medius terminus scindens aequaliter eandem proportionem possit aptare.” [“: : : as

minimal ratios in the same proportion differ only by one unit, as if minimal numbers

did not share also proportionately the same difference of unit as multiples, when we

see that there are many more multiples, excepting those expressed in roots, among

which the median term may be adapted which divides the same ratio into equal

parts.”]21 This sentence appears to be obscure. Perhaps he meant that the proof can

be based on a ratio in which the terms, like 9:8, differ by only one unit, when the

same relationship could be written in many other ways with the multiples 18:16,

36:32, etc. What is, however, clear is that roots are excluded, even if Boethius knew,

therefore, that they could successfully divide the tone into two equal parts. He later

tries to justify this by resorting to consonances and geometry.

After thus criticising Archytas, Boethius for the umpteenth time calculated the

comma: the difference between the two unequal parts (the apotome, or greater

semitone, and the diesis the lesser semitone), in which the tone could be divided.

In his opinion, that was the only legitimate way. Then he tried to calculate how

many times those intervals contained the comma. But instead of considering them,

as he had done so far, as ratios between numbers, he took the difference between

the terms. Thus, instead of being represented by the two considerable figures,

524,288:531,441, the comma was reduced to a much more manageable VII.CLIII

[7,153].

He proceeded in the same way with the terms of the other musical intervals,

modified here for convenience in their proportions, obtaining, for the difference of the tone LVIIII.XLVIIII [59,049], for the difference of the apotome

XXXIII.DCCLXXVII [33,777], and for that of the lesser semitone XXVI.DCXXIIII

[26,624]. He undoubtedly facilitated the comparison between the intervals: the

scholar thus rapidly concluded that the lesser semitone was more than three commas

and less than four, that the apotome naturally became more than four and less than

five, and lastly, that the tone contained more than eight, but less than nine. To arrive

at this result, he simply multiplied 7,153 by 3, 4, 5, 8, and 9, and compared the

product with the relative differences of the preceding musical intervals (Fig. 6.2).22

For example, 7;153 3 D 21;459, which is less than 26,624.

The proof of Archytas using semitones may have been fluxa [weak], but this one

of Boethius using commas seemed to be worse, because it was errata [mistaken]. In

other words, seeing that the notes are fixed in the Pythagorean model by numbers

arranged in a geometrical succession, and not in an arithmetic succession, adding

or taking away an interval means multiplying or dividing the terms (appropriately),

and not adding or subtracting. The differences between numbers in a geometrical



21

22



Boethius 1867, pp. 285–286.

Boethius 1867, pp. 291–299.



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6 With the Latin Alphabet, Above All



Fig. 6.2 How Boethius calculated the commas contained in the Pythagorean tone (ibid., p. 295)



succession increase proportionately, and do not remain the same. Boethius should

have multiplied his fine Roman six-figure numerals nine times together, and not

simply by nine, and then have compared the result.

In the tradition of Pythagorean arithmetic, so fond of whole numbers, the comma

was making the theory of music uncomfortably asymmetrical, and registered the

incompatibility between the fifth of 2:3 and the octave of 1:2. But could the comma

at least have become, for music, that kind of basic unit, father/mother of the rest,

as 1 was interpreted at the time for all the numbers? The treatises tried at the

time to measure the other intervals by the comma, as the Greeks had done, and as

Boethius was repeating. Yet in general, they only gave the results, without proving

them adequately. Though the procedure in theory appeared to be clear, in practice

it became almost impossible to follow without a good technique of multiplication,

and considerable patience. The temptation to take easy short-cuts, which led to the

same results, must have been irresistible. Thus we shall see the passage of more than

1,000 years, before we find a good, brief, elegant proof, without the need to perform

all these calculations.23

At the end of Book III, Boethius proclaimed that he had proved what he

had promised.24 However, the search for a solidus [solid] argument about the

impossibility of diving the tone into two equal parts remains vain. Here we

find, rather, a clear case of how the arguments and reasons proposed, even in

mathematical sciences, derive critically from general rules and principles, often

accepted tacitly, as they are widely believed and taken for granted. Actually, the

presumed proof depended on what number was considered to be at the time, and

what relationship was thought to exist between the different disciplines under study.



23

24



Tonietti 2006b, pp. 153–156; see below, Sect. 6.5, and Appendix C.

Boethius 1867, p. 300.



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267



Fig. 6.3 The monochord of Boethius (ibid., p. 349)



In the pattern of the quadrivium, music followed arithmetic, and the latter dealt

with discrete quantities, that is to say, whole numbers and fractions. Continuous

quantities, like incommensurable magnitudes and roots, were considered to be parts

of geometry. Nobody could have taken the liberty of using them for music without

departing from orthodox theory. Thus remaining exclusively inside these limits, it

would be impossible to divide the tone into two equal parts: because the proportional

mean between 8 and 9 is an incommensurable magnitude, which can be measured

only by means of the (irrational) square root of 2.

While the tone could be safely divided

p into two equal parts for heretics like

Aristoxenus, or for those who admitted 2 among the numbers, orthodox scholars

were using whole numbers to deny the heretics this possibility that they claimed.

The grotesque aspect was that in this period, orthodox Pythagoreans were not even

capable of expressing the question in correct mathematical terms. But right this

event made the nature of the conflict even clearer. Not that this musical heresy was

really impossibilis more mathematico [impossible according to mathematics], but

consequently, it appeared to be prohibita [prohibited]. Many centuries were to pass,

and other events are to be told, before the prohibition was allowed to drop.

In that period, the reasons of orthodox Pythagoreans were sustained by a series

of affirmations, which Boethius dutifully noted down. Having reduced sounds

to the numbers of ratios, depending on whether these were either multiples or

superparticular, the note of music were as a result heard to be consonant in some

cases, and in others dissonant. Consonances were then those notes “: : : quae simul

pulsae suavem permixtumque inter se coniungunt sonum.” [“: : : which, struck at the

same time, mingle together in a pleasant, integrated sound”].25 Boethius took pains

to repeat to us the well-known musical ratios of the Greeks, calling the notes by

both their Greek and their Latin names. He distributed their scales among the three

genres, diatonic, chromatic and enharmonic, derived from the relative divisions of

the monochord in accordance with the respective tetrachords.

In order that the ears could judge consonances with certainty, he explained

how to construct a monochord with regula [ruler], magadas [hemispheres] and

nervus [sinew]. The various vibrating lengths of the string, necessary to generate

the different notes, were obtained by shifting the central hemisphere (Fig. 6.3).26

After stating that something confused arrived from the ears, whereas the ratio

[reason] could judge the purity of them, perceiving even the smallest differences,



25

26



Boethius 1867, pp. 301–302.

Boethius 1867, pp. 348–349.



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6 With the Latin Alphabet, Above All



Boethius concluded that it was impossible to trust the ears completely. This

ratio guided and corrected the erring senses. And yet, there was considerable

disagreement among theoreticians about the harmonic rules. The followers of the

Pythagoreans preferred reason, while Aristoxenus, on the contrary, judged through

the senses. Lastly, to Ptolemy did not seem that harmony could be contrary neither

to the senses nor to reason. We know that he tried to reconcile both together. But

then the latter, like the Pythagoreans, placed the differences between sounds in the

quantity, that is to say, in whole numbers, while Aristoxenus was left alone to decide

on the basis of quality.27

In the arguments offered, the following dualistic opposition assumed greater

mathematical significance. Like the colours of the rainbow, for which it cannot be

said with certainty where they finish, if sounds for music formed a continuous spectrum, whether deep or acute, they would not have a designated place which would

fix them precisely. Only discrete sounds, like distinct, unmixed colours, occupy

an exact, fixed place. “Continuae quidem non aequisonae voces ab armonica [sic!]

facultate separantur. Sunt enim sibi ipsis dissimiles nec unum aliquid personantes.

Discretae vero voces armonicae [sic!] subiciuntur arti.” [“Then the continuous notes,

not in unison, are far from the possibility of harmony. They are different from

themselves, and are not capable of sounding in some unit. Indeed discrete notes

are subject to the art of harmony.”]28 On this basis, both the Pythagoreans and

Ptolemy had established the consonances, even though the former excluded one

like the octave united to the fourth (as its ratio 8:3 is not superparticular), which was

admitted by the latter.

The conclusions of Boethius are all against Aristoxenus, who did not use

numbers, “: : : sed aurium iudicio permitit : : :” [“: : : but allowed the ears to judge

: : :]”.29 Now taking his inspiration from Ptolemy, our medieval philosopher believed

that he could in this case represent the error of Aristoxenus more convincingly

(Fig. 6.4).

The strings represent the octave and its division into the six Pythagorean tones.

But to us this appears to be just a translation into geometrical segments of previous

calculations with ratios between numbers. Of course the string long GP (the six

tones) would sound more acute, because it is shorter than the octave HR.30 But

why prevent Aristoxenus from using six other strings of different lengths ‘equally’

distributed between AK and HR? Nobody could make any geometrical objections to

this operation, because these lengths exist, and can be constructed relatively easily,

even if they are naturally incommensurable magnitudes that can only be measured

by means of roots. The argument of Boethius based on the figure thus became

double-edged, and was reduced to the affirmation that continuous magnitudes did



27



Boethius 1867, pp. 352–355.

Boethius 1867, pp. 356–357.

29

Boethius 1867, p. 363.

30

Boethius 1867, p. 364.

28



6.2 Theory and Practice of Music: Severinus Boethius and Guido D’Arezzo

A



B



C



D



E



F



G



269

H



P

O



R



X

N

M

L

K



Fig. 6.4 How Boethius proved that the octave sounded deeper than six tones (ibid., p. 364)



not produce consonances. Was he making a prophecy, rather, about the music of the

twentieth century?31

Aristoxenus went so far as to make divisions into quarters of a tone, which

he distributed in the genres like the enharmonic mollius [softer, more effete] and

the diatonic incitatius [more stinging, stimulating]. The former was also called

spissum [slow]. Boethius reported that Aristoxenus had been blamed by Ptolemy

for proposing divisions that could not be perceived by the hearing. In fact, the

latter seemed to be his favourite theoretician of music.32 After being converted

to Christianity, he translated some books by Aristotle and the NeoPlatonics into

Latin, trying to reconcile them, as they would have done in Arabic countries. With

him, the concept became famous that distinguished music into three species. The

highest, mundana, was the music of the spheres, generated by heavenly bodies and

not discernible with the ears, but only with the mind and the soul. The intermediate,

humana, species descended inside us. Whereas the instrumentalis music appeared

inferior to him because it was created by the hands of players of instruments.

Whether they were appreciated or not, the orthodox theories of music were

becoming a stiff, empty slough that prevented growth or change. The characters

like Boethius are interesting because they are capable of showing us the dominant

opinions of the period, but they do not tell us much that is new. Five centuries later,

on the contrary, to cut a long story short, a novelty arrived which was to produce

a profound change in musical activity, in the direct practice of composers and

musicians. Guido D’Arezzo (early 1000–c.1050), the famous monk, re-elaborated,

perfected and modified previous ideas in a form of notation that was destined to

establish itself in view of its effectiveness in the writing of music, which up to

that time had essentially been limited to memory and oral transmission. As we are



31

32



Tonietti 2004. See Part II, Sect. 12.4.

Boethius 1867, pp. 365–366 and 370–371.



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6 With the Latin Alphabet, Above All



Fig. 6.5 How Guido D’Arezzo wrote the notes of music on the lines (Guido D’Arezzo 1963,

p. 10)



narrating, we know quite a lot about the musical theories of the Greeks and of the

Arabs, but their ancient music is largely unknown to us, and can only be described

by means of words and with a great effort of imagination.

How was the tempo to be indicated? For music, it is necessary to write not only

the height of the notes, but also the way in which they run one after the other,

creating the tempo. Gradually and slowly, the modern stave was now born. From

Fig. 6.2, we can see that Boethius indicated the notes by means of the letters A, B,

C, D, : : :. The Latin letters were to go on being used in the Anglo-Saxon musical

world. Whereas the Latins, following Guido, were to adopt new names, such as

ut (subsequently do), re, mi, fa, sol, la, [si], taking the first syllables of a hymn

dedicated to s[ancte] i[oannes]: Ut queant laxis resonare fibris : : : [In order to be

able to resound with relaxed strings : : :]33 The hymn-book presented to Pope John

XIX and the Micrologus contained the most famous novelty, destined to spread all

over the world. The succession of notes was represented on parallel lines read from

left to right (Fig. 6.5).34

Here, time became space; it transformed itself into a geometrical line capable

of stringing together like pearls the heights of the sounds, one after the other, in a

regular, rhythmic succession. At last, it was possible to put down on paper even the

most important characteristic of music, the most difficult one to seize: musica sine

lineis est sicut puteus sine fune [music without lines is like a well without a rope].35

Guido was interested in teaching young people how to sing. His notations are useful

and intuitive to succeed in intoning the notes and remembering them. If A indicates

a note (la), a indicates the octave above it (another la). Three tones one after the

other, as there are between fa and si, are difficult to sing, because they sound rough,

since they form one of the hardest dissonances. Actually this tritone was called the

diabolus [devil] in musica. Then the note creating the roughness, si natural, was

represented with the square symbol \, while between this note and la, another round

note was introduced, indicated by b ([), would sweeten the interval fa b, making

it now equal to the fourth do fa.

Our monk recognized that music was appreciated thanks to its variety, like

colours for the sight, smells for the sense of smell, or tastes for the sense of taste.



33



Guido D’Arezzo 1963, p. 45.

Guido D’Arezzo 1963, p. 10.

35

Guido D’Arezzo 1963, p. 31.

34



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2 Theory and Practice of Music: Severinus Boethius and Guido D'Arezzo

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