Introduction: Silence and Sound

ÚSTAV HUDEBNÍ VĚDY, FILOZOFICKÁ FAKULTA, MASARYKOVA UNIVERZITA V BRNĚ

MARTIN CELHOFFER

MAGISTERSKÁ DIPLOMOVÁ PRÁCE

SILENCE AND SOUND: ESSAYS ON THE ONTOLOGY OF MUSIC

Vedoucí práce: doc. PhDr. Lubomír Spurný, Ph.D.

Konzultant: Dr Elizabeth Eva Leach

BRNO 2006

Prohlašuji, že jsem pracoval samostatně, s použitím uvedené literatury.

Martin Celhoffer

V Brně, dne 19. června 2006

Summary

This writing deals with one of the most problematic issues in musicology - the

ontology of music. The themes selected are developed on the background of antinomy

between sound and silence. This antinomy was understood as (i) audible and inaudible

categories of music during Antiquity and Middle Ages; (ii) object (sound-concepts, sound-

structures) and subjective condition (‘silence’ of a priori givenness of perceptual and

cognitional faculties of a man) during the modern era. Chapters are organized chronologically

showing the evolution of the idea of world harmony from Antiquity till the early empirics in

the first part; and the theories of modern philosophical concern in metaphysics of music in the

second part. The study also reflects how music was apprehended methodologically: as (i) a

multidisciplinary field incorporating music, mathematics, astronomy, astrology; (ii) a

philosophy of music integrating epistemology and ontology.

Práce je věnována snad nejdiskutabilnější otázce muzikologie - ontologii hudby.

Vybrané tematické okruhy jsou rozvíjeny ve světle základního protikladu mezi zvukem a

tichem. Tento protiklad je pojímán jako (i) otázka kategorizace hudby na ‘slyšitelnou’ a

‘neslyšitelnou’ v období antiky a středověku; (ii) otázka vztahu objekt (zvukový koncept nebo

struktura) a subjekt (‘ticho’ apriorních daností lidského vnímání a umu) v období novověku.

Jednotlivé kapitoly jsou řazeny chronologicky, v první části práce vypovídají o vývoji

myšlenky ‘harmonie kosmu’ od antiky až po raný empirismus; ve druhé části o různých

novověkých filozofických teoriích zabývajících se metafyzikou hudby. Práce také odráží jak

byla ontologie hudby chápána z metodologického hlediska: jako (i) multidisciplinární přístup

zahrnující hudbu, matematiku, astronomii a astrologii; (ii) filozofie hudby zahrnující

epistemologii a ontologii.

Contents

PREFACE.............................................................................................................................................................. 1

INTRODUCTION: SILENCE AND SOUND .................................................................................................... 3

PART ONE: THE COSMOLOGY OF MUSIC................................................................................................. 9

Pythagorean tetractys ........................................................................................................... 10

Plato’s World-Soul ............................................................................................................... 16

Boethius’ Musica Mundana ................................................................................................. 21

Kepler’s Planetary Polyphony.............................................................................................. 26

PART TWO: POST-COSMOLOGICAL CONCEPTIONS ........................................................................... 31

Immanuel Kant: Mind as a ‘string instrument’ .................................................................... 33

Schopenhauer: Music as representation of the Will............................................................. 40

Phenomenology and ontology of Music............................................................................... 46

CONCLUSION.................................................................................................................................................... 52

BIBLIOGRAPHY ............................................................................................................................................... 56

Preface

The aim of this paper is to interpret some of the basic assumptions of evaluation the

ontological status of music. This issue never stood alone among the other disciplines, but

became an indispensable part of our interpretations of all phenomena, whether related to

music directly or not. When I had asked myself the question why is the ontology so

fascinating and important for musicology, the well-known Schopenhauer’s statement arose in

my mind:

For in every mind which once gives itself up to the purely objective

contemplation of the world, a desire has been awakened, however concealed and

unconscious, to comprehend the true nature of things, of life, and of existence.

(Schopenhauer, 1958, p.406)

This ‘concealed desire’ is a prime mover of our investigation. The fact that satisfactory

answer to the questions concerning ‘true nature of things’, particularly the ontology of music,

could not be provided does not make the attempt of this writing quixotic. The questions are

not to be answered, simply because there is no answer to comprehend all the dimensions of

real world in one individual theory.

As I propose later, examining the ontology of music is not considered as independent

and integrated theory, but might provide us with understanding of basic premises for various

consecutive theories. A causa de cy the approach I have chosen quadrates with series of

essays of individual subjects. The essays are organized chronologically and are arranged into

the two parts: (1) The cosmology of music and (2) Post-cosmological conceptions. The

cosmology of music is a gradually developing concept with common axioms. On the contrary,

post-cosmology consists of various, occasionally contradictory theories, refusing the axiom-

wise heritage of Antiquity and Middle ages.

The common thread implicitly running across this writing is the idea exposed by the

title: the antinomy between the terms ‘silence’ and ‘sound’. The emphasis of this antinomy is

given in the introduction. The reason for such a literary and not ‘scientific’ title I found in

fact, that audibility and inaudibility of music was one of the key issues in cosmology in

accordance to ontology. On the other hand, the theories of post-cosmology deal with sound in

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terms of sound-constructs or sound structures of musical work, and with silence in terms of

subjective and general conditions, the question of audibility and inaudibility no more holds

sway.

I have omitted extensive throng of philosophers and music theorists that have

contributed to reception of the ontological issue of music. I did not intend to present a

comprehensive enumeration of theorists, but I have pursued the tracks of some important

tendencies.

Last but not least, I would like to express my thanks going to supervisors of this

writing, Dr Elizabeth Eva Leach and doc. PhDr. Lubomír Spurný, Ph.D., who have given so

generously of their time in granting so many advises and guidance upon my work.

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Introduction: Silence and Sound

‘It is silence here’, statements like this or similar are used to describe a particular state

of exchanging information between subject and environment. The semantic context of this

utterance may differ: a suspicious silence, a pleasant silence, or an embarrassing silence. In

fact, ‘silence’ means ‘relative silence’ as there is ultra-sound and infra-sound lying beyond the

grasp of man ear. On the contrary, sound itself is conditional on a complicated process of

perception. Thus silence and sound could be considered vice-versa: sound as silence and

silence as sound. Consequently, the dichotomy of hearing is accepted as relative. While

silence has always the same quality in terms of acoustics, sound has many forms and patterns

sometimes evading from hearing. We built our ‘realm of sound’ on the basis of contingent

perceptual options.

As a subject transforms environmental forces into sophisticated perception, this might

be considered as disruption of subject’s equilibrium resulting generation of information. This

act is made through differentia, a kind of ‘mirrored’ activity whereabouts conditions below

the axis of disturbance are reflecting their nature above. Thus silence and sound refer to actual

process rather than to particular phenomenon as an object by itself. Accounts of this, absolute

silence and absolute sound are abstract theoretical notions.

Silence and sound are not being further set out from acoustical point of view as might

have been expected. The approach to these categories by means of philosophical speculation

may uncover basic facets of our assumptions for understanding music. In addition, ‘silence

and sound’ hint at dynamical dichotomy of inherency, particularly in music. Music arises

from a dialogue between them, from their interaction. Does music tacitly mean peculiar

paradigm of sound otherwise can music be in specific case silent? This issue occurs when

approaching to Pythagoras, Plato, Boethius and many other theorists.

It is possible to imagine many things by the term music: a well-known melody, a

popular hit, soundtrack, musical, opera, a village song or a great symphonic work. We hardly

ever imagine something else quite different from the notion of sounding structure. Our

understanding of music is exclusively perceptual. However, for Pythagoreans the term music

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means mathematics. Music was for them a science par excellence, a science providing the key

for understanding the cosmos, a universal harmony holding and uniting everything. These two

conceptions, one based on perceptual quality and another pointing out its ontology, represent

perceptual and meta-perceptual paradigm of understanding the term music.

Music is unpromptedly associated with an act of hearing. Thus the purpose of music

was described as ‘to delight the human ear’ in many treatises, emphasizing the aspect of

aesthetic perception. However, music was also considered as ‘a science’ dealing with act of

understanding and meta-sensual experience. Another conception is that of the Memoria:

music can be stored in human memory and contrariwise restored from it. Moreover, on the

mediaeval concept of memory is based the creative ability - inventio (Ziolkowski 2002,

p.297).

The relations of these antimonies discussed thus far are presented in table 1. The

horizontal axis ‘x’ describes the perceptual and meta-perceptual dichotomy. The vertical axis

‘y’ divides the bilateral phenomena of sound and silence. Music is described as a set

containing determinate areas of every category involved.

Table 1.

If we are trying to understand what the word music actually means, it would be

unavoidable to establish an ontological dispute. In a general way, what is the nature of any

given real particularity? ‘The nature of something’ in terms of ontology refers to quality not to

quantity and therefore is immeasurable. Therefore is not possible to define the word music as

the succession of coded pitches in spatial and temporal organization. Anyway, how should the

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ontology of music then be construed? As we come to a resolution that music can be

considered as an ontological entity there is an intrinsic difference between treating this entity

as an object or as a homologue (Wallin, 1991) between the two or more objects. Namely the

term ‘object’ associates a natural entity with spatial and temporal organization that is possible

to perceive through the senses. On the contrary, a homologue means a correspondence which

can be to some extent abstract as well as measurable, for instance through mathematical

equation. Therefore, music is accepted as a multiple set of heterogeneous phenomena. In

order to investigate the ontology the examination is focused to the correlations among them.

Was this issue a crucial task for theorists during the antiquity and Middle Ages and

how was it aproached? Quid est Musica? - appears in various Latin writings on music usually

at the very beginning of treatise. The answer mostly refers to the reinterpretation of Greek

thought that portrays music as an activity of the Muses or as a reflection of cosmic harmony

or harmony by itself ruled by Creator - a supreme being. But the ontology of music eo ipso,

as a discrete discipline, was never a principal and outstanding issue for such philosophers as

Pythagoras, Plato, Plotinus or Boethius. In this sense the ontology of music had an

interpretative quality of evaluating the aesthetic potential of music or like a ‘theory of

everything’ - integrating axiom of all phenomena.

It is possible to provide a satisfactory answer to the question of what music is? Why is

this question considered irrelevant in musicology and beside the point of science? The

ultimate limit for acceptability of knowledge is given not explicitly by verification but in a

certain extent by operative paradigm in terms of common convention. Probably the whole of

knowledge has an abstract nature in the sense of projecting subjective notions onto reality. For

instance, a cube with scaling of 2 x 2 x 2 units represents a three-dimensional object of

cubage 8 units. This knowledge is mediated by empirical experience can be verified and

simply imagined. But mathematicians are already manipulating with more than three-

dimensional objects at the present time. That is to say, knowledge could be drawn from each

empirical experience, and applied consequently to the field where is no direct verification

based on classical empirics. The knowledge is not measurable by itself but through empiric

(table 2):

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Table 2.

Empiricism provides a limited sum of verified data whereupon theories are construed.

Consequently, these theories are supposed to confer a noticeable order to the particular data.

In certain circumstances might the specific theory explain phenomena which are not possible

to verify empirically. For example, the ‘string field theory’ in physic is ‘verified’ by

mathematics and not by experiment. On the other hand, an empirically verified theory may

fail analogous to thermodynamics. This reflection is not being an attempt to contest with

verification in science but points out the very thin line disentangling acceptable and non-

acceptable theories. Thus satisfactory resolution of the issue in terms of utter definition seems

to be a quixotic investigation.

Music is the discipline that undoubtedly has an empirical base when focusing on the

angle of sound structure. But this positive facet might detract the understanding of its nature.

It is not surprising that in the modern era, whenever emphasis on empiricism in terms of a

touchstone is generally accentuated, it is currently the art most difficult to define in spite of its

material substance. By contrast, mathematics even though dealing mostly with abstract

numbers and theoretical dimensions eventually not possible to imagine is considered to be the

positive science. On what matter of fact rests this paradox? It is certainly not due to music

itself, i.e. to its acoustical structure and nature, but to the fact that music includes the

perception and understanding of a man’s subjectivity. Volker Kalisch states:

...if we speak about music we automatically have to deal with humans, with

human conditions, with ourselves. And vice versa: when we start to reflect upon the

nature of man we automatically reach a point where music intervenes. Being human

and experiencing music are clearly inseparable. (Kalisch, 2000, p. 309)

Therefore, music does not exclusively rest in sound and at least one facet of it is non-

empirical. On the proviso that music includes specific human perception and understanding, it

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will be necessary to deal with these phenomena. According to Cooke (1957, p.5), music is a

‘language of sub-consciousness’. Both terms are problematic alone and even more in their

juncture. It is a literary explanation, a sophisticated metaphor and therefore it should not be

taken au pied de la lettre. Simplistically said, a language is just a tool mediating particular

semantic notions. Its syntax can be understood by music theory and acoustics. It is not

necessary to emphasize how useful this would be in terms of musical analysis. But

investigation like this cannot shed a light to the nature of music. On the other hand, inclusion

of the assumption of subconsciousness’ existence seems to contribute to our ontological

dispute. This refers on basic antimony of this discourse: sound as a conscious phenomenon,

and silence as an unconscious phenomenon. From this point of view, Musica humana can be

interpreted as ‘subconscious music’ - ‘inaudible consonances’ of human mind subordinated to

higher quality of Musica mundana.

However, the nature of subconsciousness - or whatever we call it - is to a particular

extent an immeasurable part of the realm of our existence impenetrable with actual

measurements but perhaps penetrable with imagination, inspiration and contemplation.

Notably in the arts, imagination and inspiration have a crucial role and there are indispensable

parts of both creative and perceptive processes. If these qualities of subconsciousness

participate on music it might be the reason for exclusivity of phenomena such as aesthetics in

terms of unaccountability of its nature. Does it mean that these phenomena considering being

beyond actual methodological grasp are less important?

As it can be seen from previous allusive explanations, an approach to the ontology of

music can be pursued from various directions. However, the basic intention of them is to

supply a background for interpretation of cosmology of music. A number of key notions

(Pythagorean tetractys, Plato’s World-Soul, Boethius’ Musica Mundana, and Kepelr’s

Planetary polyphony) ranked chronologically will be presented as representation of particular

conception of ontology. A common thread of these conceptions is the idea of cosmology and

how this was reinterpreted in antiquity, Middle Ages, and Renaissance. The structure of study

was deliberately set up on a number of essays and therefore it is not intended as a

comprehensive study on ontology of music. I tried to avoid generalizations and

simplifications although more extensive historical background would be desirable for

advanced and more accurate research. Intention of examining ontological issues is to provide

paradigms for understanding music, for drawing courageous parallels between the past and

present. Aspiration of this study is not in presenting the notion of ontology as a scientific

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method but as a cognitive-literary dialogue between mind and imagination, the reason and the

art, and between silence and sound.

8

PART ONE: THE COSMOLOGY OF MUSIC

The cosmology of music is an interdisciplinary achievement bringing together

mathematics, astronomy (eventually astrology), and music. Although the first essay is devoted

to Pythagorean doctrine of tetractys, we should bear in mind that the formal sources of

Pythagoreans are running back to Babylonians (McClain, 1984). The cosmology presupposes

a series of common premises, which were gradually shifted in pursuance of new empirical

data. This progression is recorded in four following essays, from Pythagorean tetractys to the

theory of Kepler’s ‘harmony of the world’.

The hypotheses about the cosmology of music were set out on the basis of

contemporary understanding of the universe. Neugebauer (1969, p.171) noted that:

To a modern scientist, an ancient astrological treatise appears as mere

nonsense. But we should not forget that we must evaluate such doctrines against the

contemporary background. To Greek philosophers and astronomers the universe was a

well defined structure of directly related bodies. The concept of predictable influence

between these bodies is in principle not at all different from any modern mechanistic

theory.

However, the Greek view on cosmos drew its formal conception either from

mythology. It was generally accepted that the universe was settled by mythical beings. And

celestial music was their expression. Forasmuch as the empirical data were missing in

Antiquity and Middle Ages, and therefore there was no physical conception of sound, the

antinomy of silence and sound – the audibility and inaudibility of this music varied among

authors. The theory of musical cosmology was, in fact, an attempt to discover ‘the theory of

everything’ - the universal knowledge conferring the sense to all phenomena. Sound was

metaphorically confused with immaterial harmonious order of random phenomena.

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Pythagorean tetractys

The essence of all things rests in numbers - this was a rudimental premise for

Pythagoreans. A notion of everything penetrating immaterial numeric principle was holding

sway among the Pythagoreans for nearly the whole millennium. Pythagoreans considered

music as the most reputable discipline due to its possibilities of discovering the numerical

ratios and verifying their hierarchy. However, this theorem of multilateral correlation between

the number and music was also noted by Babylonians and Egyptians probably about two

thousand years or even more before Pythagoras (McClain, 1984). This suggests that

Pythagoras (c.560 - c.480 BC) was not inventor of this knowledge, but rather its importer to

Greece, and hints on his possible scholarship in Middle East. Though Lippman (1963) holds

the view, that ‘as difficult as it is to specify the older constituents of Pythagorean thought, it is

still more difficult to determine the precise achievements of Pythagoras himself’. This is even

complicated by the fact that of no authentic writing of Pythagoras has been preserved.

Therefore, the investigation and evaluation of Pythagoras’ own contribution is thrown upon a

number of secondary sources, which were written by his followers and other philosophers.

Pythagorean thoughts were transmitted to Christian mystics thanks to Plato’s (c.429 -

347 BC) writings, especially his Republic. Also Aristotle (384 - 322 BC) mentions some of

Pythagorean’s ideas in Methaphysics. Euclid (c.325 - 256 BC) presented the theory of

numerical ratios in Elements, books 7-9 based on Pythagorean music theory. Also

Nicomachus (c.60 - c.120 AD) discussed Pythagorean ratios in his Introductio arithmetica.

Ptolemy (c.90 - c.168) in his Harmonics - a summary of Greek knowledge on music, points

out Pythagoras’ contribution in terms of noting that music is the direct link ‘between the

microcosm and the macrocosm, between man’s soul and the universe’ (Gamwell, 2004). The

idea of the music of the spheres and codification of the regular proportional relationships

between particular tonal pitches is also generally accredited to Pythagoras (Harap, 1938;

Kinkeldey, 1948). Nevertheless, several myths about Pythagoras’ life emerged inevitably and

became legends. Unarguably, the most famous legend is the ‘hammer story’ found in

Nicomachus’ Manual of Harmonics and in many other writings. Another myth considers

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Pythagoras as the inventor of monochord, but according to Waerden (1943) and Dykast

(2004), monochord emerged as late as in the third century BC.

Generally, Greeks imagined the earth as a flat disc confined by the river Oceanus

while Gods lived at the top of the mountain Olympus. The stars were assumed to be orbiting

around the earth. Ever since the notion of their trajectories being determined by certain

relations emerged, the particular celestial bodies were associated with particular spheres. It

was believed that a Siren was sitting on each sphere, or respectively, each sphere was ruled by

an individual deity. To how many spheres was the Pythagorean cosmos understood to be

divided is disputable. Meyer-Baer (1970, p.44) suggests an interesting hypothesis on a

possible view on cosmos:

In the south of Italy, a number of bronze vortices, or spindles, have been

found which consist of eight disc on an axis, their circumferences forming a kind of

double cone. It is probable that these, like the golden tablets found in the same area,

were used in the rites of the Pythagoreans, a sect which had several centers in southern

Italy and Sicily. Although the details of these rites have remained a secret, it is known

that the idea of the cosmos constructed in eight layers was a basic dogma of

Pythagorean belief. The image of the seven or eight spheres was derived from the

Babylonians, but the Pythagoreans added a new concept of numbers as a ruling

principle of the cosmos and also identified them with musical intervals.

However, no source seems to illustrate in greater detail, how is the mechanism of

spheres in ‘Pythagorean cosmos’ understood in terms of arithmos. Forasmuch, due to the lack

of sufficient and attested data in the ancient astronomy, the organization of the universe was

believed to follow the same rules as the organization of material in music, where the actual

measurements confirm the conception of arithmos and harmonia. Pythagoreans assumed all

things to be originated in numbers, and this axiom was applied to the ontology of all

phenomena. Thus music was a key, a gateway to a higher understanding – a ‘theory of

everything’.

Pythagoreans proposed a distinction between the notions of unity - immaterial being,

and multeity - material being. This basic antimony constitutes an ontological differentia,

which results in the act of creation:

...material world, being a physical entity, must have a limit. This limit is

inherent in the numbers 1, 2, 3, 4. They create the point, the line, the plane and the

volume. Adding up these dimensions, 1 + 2 + 3 + 4 = 10, we exhaust the limits of

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physical extension. There is no number following 10 that is not incapsulated in the

tetrad. Nothing can be added that does not exist as a combination of these four

numbers. Tetrad and decad are therefore the models of perfection. They create unity

out of multeity, and multeity out of unity. They originated in the unlimited, absolute

world, but when they extend into the physical world, they create a limited, yet perfect,

unified system, a universe. (Berghaus, 1992, p.45)

This very accurate interpretation of the tetractyl, i.e. a set of four numbers regarded as

the source of all things, suggests the basic constituents of Pythagorean thought. The dynamic

aspect of tetractyl and emergence of time quality is described as follows:

Time, or the fourth dimension, enters when the idea of number is given

physical extension. Chronological time (chronos) proceeds from eternity (aion), just

as finite space proceeds from infinity. The metaphor for this process is creation. The

act of creation establishes the monad in time and space. Time is a corollary product of

the creation of the physical world, and it prevents the created universe from remaining

static. The cosmos is dynamic, ever-changing. However, this constant motion is

ordered. The dimension of temporality is structured just like the spatial world. The

patterns of movement obey a scheme. All changes are phases proportionate

propensities. (Berghaus, 1992, p.45)

The Pythagorean conception of the genesis of universe shifted the traditional Greek

world-view and also the role of deity to a great extent. However, the only touchstone available

for experimental support of this doctrine was through music, especially the specification of

numeric ratios in musical intervals. There are two basic categories of ratios: superparticular,

defined by formula ; and reciprocal . With regard to this formulas,

superparticular ratios are 2:1, 3:2, 4:3 etc.; reciprocal 1:2, 2:3, 3:4 etc. These ratios are

equivocal according to string length (or cubage of air column) and frequency. Where

superparticular ratios determine the frequency, the reciprocal determine the string length and

vice versa:

diapason diapente diatessaron

string length 1:2 2:3 3:4

frequency 2:1 3:2 4:3

Table 3.

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This table represents the first three harmonics. Naturally, as the ratio sequence

continues further, frequency increases and, respectively, string length decreases. But only first

three ratios are considered as the perfect consonants. This is mathematically proven by the

fact that these ratios of ‘tetractycal’ numbers exclusively. Moreover, tetractys (1, 2, 3, 4 /

1+2+3+4=10) is a ground for basic numbers that constitute the ratios of consonances in

whichever combination: 4:1= double-octave, 3:1= octave + fifth, 2:1 or 4:2= octave, 4:3=

fourth, 3:2= fifth (addition of fifth and fourth results the octave and difference between them

the whole tone 9:8). The fact that what is sensually perceived as consonant and plausible

harmonious sounds can be expressed mathematically, suggests the hypothesis that everything

has its base in numbers. For all of the above, mathematics became the most reliable method of

codifying the rules of music and, consequently, the rules determining all phenomena.

Providing that the whole universe originates in number, multeity of all things is

unified by basic numerical patterns. Of course, this includes individual human beings: a body

and a soul. It is assumed, that Pythagoras believed that listening to the music has a specific

effect on the soul. The dynamic process in music evokes the congeneric process in the human

soul. Censorinus (early third century AD), a neopythagorean, states that music has a similar

effect on the soul as the stars. Similarly as music, astrology was understood to be determined

by numbers and geometrical figures (De die natali, XI-XIII, ed. O. Jahn, Berlin, 1845. IN:

Godwin, 1986, 19). Iambichus (c.250 - c.325 AD) points out ‘that music contributed greatly

to health, if it was used in an appropriate manner’ (Life of Pythagoras, translated by Thomas

Taylor, London, 1818, pp. 43-8, 80-3., IN: Godwin, 1986, p.28):

And there are certain melodies devised as remedies against the passions of the

soul, and also against despondency and lamentation, which Pythagoras invented as

things that afford the greatest assistance in these maladies. And again, he employed

other melodies against rage and anger, and against every aberration of the soul. There

is also another kind of modulation invented as a remedy against desires. He likewise

used dancing; but employed the lyre as an instrument for this purpose.

Therefore, the instrumental and vocal imitation of the music of the spheres was

considered as the ‘early music therapy’ (particularly in terms of mental health), through which

the harmonia between body and soul and between soul and cosmos was achieved. Censorinus

(Godwin, 1986) mentions that Pythagoras himself might have been used to play his lyre

before sleep and upon waking up ‘to imbue his soul with its divine quality’.

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Another disputable issue emerges in connection with audibility of music of the

spheres. Various sources refer to the myth of Pythagoras’ exceptional ability to hear ‘celestial

harmony’. However, there are two quite different suggestions, and both can be found in

Simplicius’ (fl. first half of 6th c.) commentary on Aristotle’s On the Heavens (trans. by Th.

Taylor in The Theoretic Arithmetic of the Pythagoreans, London, 1816, IN: Godwin, 1986,

p.51):

Pythagoras, who is reported to have heard this harmony, should have his

terrestrial body exempt from him, and his luminous and celestial vehicle, and the

senses which it contains, purified, either through a good allotment, or through probity

of life, or through a perfection arising from sacred operations, such a one will perceive

things invisible to others, and will hear things inaudible by others.

Though Simplicius is quite skeptical about this possibly influenced by Platonic view

on disputable materiality of spheres. He assumed that if any sound emerges from superlunary

spheres (i.e. those of immaterial celestial bodies), it should be neither ‘percussive nor

destructive’ but it activates the ‘powers and energies’ of sublunary sounds (i.e. material), and

also affects the senses in terms of harmonization. Accordingly, there are the two types of

sound in the Pythagorean theory: material and immaterial. ‘If then, sound is not passive there

[i.e. in superlunary spheres] it is evident that neither will the sound which is there be passive’.

However, Simplicius suggested yet another view: he mentions that Pythagoras might have

said that he hears the harmony of the spheres as ‘understanding the harmonic proportions in

numbers, of the heavenly bodies, and that which is audible in them’.

The proportions which constitute human beings are homologous to proportions of the

universe, nature and music. The Pythagorean theory, leastwise as comes to us, incorporates an

ontological issue. From this point of view it was not only descriptive analysis of music, but

searching for ‘primordial principle’ that ‘extends into the material world and becomes

multeity’ (Berghaus, 1992, p.45). The musical sound is considered as an audible

representation of this principle. On the other hand, ‘ontological immaterial music’ rests in

number in the state of rest and becomes audible through the dynamics of tetractys - sound

emerges from silence, music of the spheres becomes audible and recognizable on the basis of

homology.

Pythagoras, in fact, established the numerical basis of acoustics. The generalizations of

intervallic proportionality were also applied to dance, sculpture and architecture. The visual

arts follow proportionality defined by the golden section, tetragonal figure designed on the

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basis of Pythagorean numeric ratios. Pythagorean conception of cosmic harmony influenced

Neo-Platonists, astronomers, astrologers, humanist scholars, poets and musical theorists. His

thoughts, as driven on by his followers, traveled in two directions: those who followed his

mathematical conception and those who followed his ethos theory (Harap, 1938).

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Plato’s World-Soul

Prior to number becoming a matter, the idea appeared. Platonian idea provides a

sophisticated plan for numeric underpinning of the material world. It is believed that all of

Plato’s (c429 - 347 BC) authentic writings are preserved. The most remarkable sources of his

thoughts on music are Timaneus, Laws and Republic. However, Plato mentions the term

music (mousike) in many places in his dialogues and the meaning of this term may vary from

often condemned sensual pleasure to speculative music as a supreme wisdom (Fubini, 1990).

The immense range of Neo-platonic sources also accounts for the further development of his

ideas during the Middle Ages and Renaissance.

Generally, Plato was continuator of two Greek conceptions of music: (i) the

Pythagorean numeric ontologism and (ii) the Damonian doctrines of musical ethos. Plato’s

approach to music was marked by his tendencies of searching the ideal social structure. Thus,

he implemented the ideas about music into wider context of education and politics. He was a

traditionalist, censorious towards the individualism in ‘modern’ music, which might break

integrity of the society. On the contrary, he viewed the traditional music as acieraging the

society, having a collective character and therefore being an important element of the social

sustainability. Plato criticized decadent style of music, apparently in practice in Greek society,

which he perceived as corruptive, threatening the social welfare of society. These ideas about

the social role of music are explored on the background of musical ontology, which is the

synthesis of Pythagoreism and Plato’s doctrine of ideas, particularly the doctrine of the world

soul as a universal plan of all things described in Timaneus.

In his Laws, Plato provides the first epistemological antimony between rationalism and

sensualism, when criticizing astronomers for theirs methods of verifying the arguments

through sensual experience. However, his rationalism is not well marked but is rather based

on intuitivism and mysticism. The most remarkable of all Platonian thoughts is undoubtedly

the doctrine of the ideas. Ideas are non-material archetypes, primordial prototypes, invariable,

perennial units that are qualitative superior to all phenomena and subjects of visual and

sensible world, which is only the imperfect imitation of them. Whereupon the reality is

divided into two spheres: (i) world of ideas, which are the primordial existence - an

16

ontological basis of all phenomena and (ii) world of spatial-temporal phenomena, which can

be recognized through the senses. The Platonian ontology can be summarized in four basic

premises:

• All things have an autonomous existence.

• The ontologisation of the notion: the subject of every notion has to be the idea - an

inalterable being.

• The hypostasis of the notion: notions exist outside the world.

• The knowledge has rational nature and not sensual in terms of recalling the divine

substance settled in the human soul.

The first preserved formulations of the theory of cosmology can be found in Plato’s

Timaneus (the word ‘music’ is not mentioned, but Plato used the term ‘harmony’, Kinkeldey,

1948), and in his Republic. The Plato’s view on Cosmos was based on the same assumptions,

but differs from that of the Pythagorean view in some details. The main difference is that

Plato defined the model for physical universe - a world-soul, as mediation between numerical

base of all things and physical universe. Therefore numbers became a matter through world-

soul, which is constructed in accordance to a numeric plan. The physical lay-out of the

universe is very similar to that of the Pythagorean one. The whole universe has a shape of

globe as the most perfect form in terms of symmetry. Cosmos consists of eight circular orbits

- spheres: the first sphere consist of fixed stars running in opposite direction to the others, the

second is occupied by Saturn, follows by Jupiter, Mars, Mercury, Venus, Sun, and the eight

sphere is occupied by Moon.

And of each of its circles there was seated a Siren on the upper side, carried

round, and uttering a single sound on one pitch. But the whole of them, being eight,

composed a single harmony. (Republic, X, 614b-619b, translated by Thomas Taylor in

The Works of Plato, London, 1804, vol. I, pp. 466-75., IN: Godwin, 1986).

Therefore the individual spheres are not producing basis for musical ‚cosmic scale‘,

but are moving in harmonious proportions. Godwin (1986, p.3) suggests that:

If we allow that these “spheres” may represent not only the physical orbits of

the planets, but also the powers of those planetary archetypes - the Mercurial, the

Solar, etc. - within the human soul itself, then the journey [journey of souls described

in the Myth of Er] takes on new meaning as an inner pilgrimage through the layers of

17

the psyche to the divine center within, which is also the all-encompassing

circumference of the Spirit.

This may hint at possible contemporary conceptions of astrology, reflecting very close

relations between macrocosm and microcosm and the universal validity of the basic creative

principles displayed through the visible cosmos.

The universe, human beings and also music are built upon the world-soul, in

accordance to its harmonious proportions. The structure of the world-soul consists of the two

basic numerical ratios: 1:2, 1:3 and of their squares, which constitute the basic numerical

consequence: 1, 2, 3, 4, 8, 9, 16, 27, 32 and so on. This sequence can be divided into two lines

according to double or triple squares ordering from 1 to 729 (Dykast, 2005):

2 4 8 16 32 64 128 256 512 1

3 - 9 27 - 81 243 - 729

Table 4.

The number one represents the fundamental number from which all other numbers are

generated. The ascending sequence of these numbers (1, 2, 3, 4, -, 8, 9, 16, 32, -, 64, 81, 128,

243, and 256) constitutes the numeric plan of word-soul expressed in numeric ratios:

1:2:3:4:8:9:16:27:32:64:81:128:243:256

The individual ratios of this sequence determine the musical intervals:

1 = unison 64:81 = major third

1:2 = octave 81:128 = minor sixth

2:3 = fifth 128:243 = major seventh

3:4 = fourth 243:256 = half-tone.

4:8 = octave

8:9 = whole tone

9:16 = minor seventh

16:27 = major sixth

27:32 = minor third

32:64 = octave

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The last two numbers are not included in the world-soul, because their ratio 512:729

defines diminished fifth which is the delimitative point for acceptance. The first four numbers

of this sequence are, in fact, the numbers of Pythagorean tetractys. In general, the closer the

ratio is to its source (number 1) the more perfect is the ratio and the more plausible is the

musical interval based on it.

The fact that ratios of world-soul can be applied to determine the musical intervals

indicates the ontological status of music and its inextricable link to mathematics. In

accordance to Platonian doctrine, audible music is just imperfect imitation of music of the

spheres, music that rests in the ‘silence’ of world-soul. On the contrary, inaudible music is

expression of harmony and symmetry and can be considered as a general quality of

phenomena, and as a desirable state of human soul. Thus, musician is not only the one who

plays or sings, but also the one who has reached the ‘perfect harmony within his soul’ (Fubini,

1990, p.39) and who has acquired the capability of higher understanding closer to vision of

the subject-matter. Moreover, playing the instrument does not necessarily mean performing,

but has the symbolic meaning:

The lyre ultimately became a popular symbol of the harmony of the cosmos. It

appears in the hands of Muses, or Eros, or Orpheus... The lyre becomes the means for

harmonizing the cosmos, and the figure that governs the cosmos rules it by playing the

seven strings of the lyre, harmonizing the seven spheres. (Meyer-Baer, 1970, p.68)

Nevertheless, Plato understood music as being in a close juncture with the other arts:

poetry, dance and theatre. Music is audible and non-audible (as sound and silence)

representation of world-soul’s numeric proportions. Each art displays the same proportionality

in different way. However, Plato proposed ontological contrast between material and non-

material, visible and non-visible, audible and non-audible world through antimony of idea and

matter on the same numerical base. Platonian ontological hierarchy can be designed as

follows:

• Number: ratios, mathematical formulation - analogous to probable patterns of

oscillation of the string, which is the most fundamental known particle in physics.

• Idea: primordial prototypes - analogous to genetic patterns.

• Matter: audible and visible things - analogous to spatial-temporal phenomena.

Plato believed that music has a magic influence on human soul. Every human soul has

been wandering in supernal world of ideas and numeric entities before its birth (this can be

19

understood in terms of modern science as ‘genetic being’). When came into material and non-

eternal world, the soul is recollecting the past through experience and gradually penetrates

through the layers of the soul analogous to the spheres of the universe. This might be the

aspect of inner journey in the Myth of Er (as suggested Godwin above). ‘The harmony within

music echoes the harmony within the soul, and at the same time the harmony of the whole

universe‘ (Fubini, 1990). The motion in music is corresponding to the motion within the

human soul and therefore music has not primarily the function of entertainment but serve as a

tool for refinement of the human affects and for the ethical improvement. Thus music rounded

out the divine plan in humans. Platonian tradition came to Middle Ages as the antinomy of

idea and matter, soul and body, and became transformed by Christian conception of world-

view as being synonymous with the terms of good and evil. Therefore Neo-Platonist

philosophers doubted the sensual perception of music and appreciated music as a

mathematical discipline.

20

Boethius’ Musica Mundana

The influence of Boethius’ conception of musica on the following generations of Latin

writers on music is undisputable. He is regarded by modern scholars as perhaps the most

profound writer and translator of Greek tradition into Latin culture, needless to say, besides

the other philosophers of the early Christian Age, as were Iambichus of Chalcis, Augustine,

Martianus Capella and Cassiodorus. At first, one question comes to foreground: to which

extend is Boethius translator and compiler of Greek knowledge, or contributor of new ideas

and theories. According to Karpati (1987, pp.6-7) ‘there was no comprehensive work in Latin

which could contain high-level theoretical matter and from which Greek music - theory could

be thoroughly learnt’ at the time of Boethius. Contemporary Roman writings were merely

focused on grammar and rhetoric, in not comparable range to mathematical field, wherein

music was counted. This might be the reason, why Boethius devoted himself to the

mathematical disciplines. He put the four mathematical sciences under the umbrella term

quadrivium (‘quadruvio vestigatur‘, chapter: Proemium, in quo divisio mathematicae, De

institutione arithmetica, book I) for the first time, and which includes arithmetic, geometry,

astrology and music. He regarded arithmetic as the superior discipline to the others:

Quae igitur ex hisce prima discenda est nisi ea, quae principium matrisque

quodammodo ad ceteras obtinet portionem? Haec est autem arithmetica ... ut animal

prius est homine (De institutione arithmetica, book I).

One might expect that the first of his writings was De institutione arithmetica, which

is written after Nichomachus’ work on arithmetic reflecting Pythagorean view of ontology. It

is not known whether he wrote also about geometry and astrology, but treatise on music De

institutione musica is preserved, even incomplete (five books preserved from supposed

original seven books), and become the most quoted treatise on music during the Middle Ages.

De institutione musica is probably written after Nicomachus’s lost work on music

Introduction to music and the fifth book is a compilation of Ptolemy’s Harmonics. His treatise

is a synthetic work reflecting Neo-Pythagorean and Neo-Platonic tradition. He understood

music as a pure theoretical discipline - philosophical speculation. Counting music as a

quadrivium discipline he contributed to music theory in terms of mediaeval systematical

21

knowledge and his Latin typology of music based on Greek cosmology become the general

theoretical framework of mediaeval concept of music theory. This background information is

important for proper understanding of different methodology of music.

The concurrence of various disciplines, particularly those of quadrivium, in one

common universal knowledge, simply imply that his thoughts about music should be scanned

not only in De institutione musica, as it is usually realized, but as Chamberlain (1970)

correctly suggests, also in other sources, notably in De institutione arithmetica and in

Consolatio philosophiae. According to exploring the ontology of music, we can found

fragmentary information in De institutione musica as Boethius himself noted that he will

provide the further explanations of musica mundana and musica humana, but he did not

mention where. Boethius, analogous to Pythagoras and Plato, understand numbers as

primordial principle. According to his Christianity, of course, numbers become the primary

tool of creation:

...Conditor deus primam suae habuit ratiocinationis exemplar et ad hanc

cuncta constituit, quaecunque fabricante ratione per numeros adsignati ordinis

invenere concordiam (De institutione arithmetica).

The fact that numbers are construed as primordial beings is also important for

ontology of music as the musical intervals are derived from numeric ratios. In chapter De

substantia numeri he states that ‚omnia quaecunque a primaeva rerum natura constructa sunt,

numerorum videntur ratione formata.‘ Therefore Boethian conception of music is based on

mathematical underpinning of nature and influenced by methodology of quadrivium, which

reflects the analogy of epistemological organon to the four senses, four seasons, four

elements, and to the four creatures below the throne of God. It means that there are four ways

how to approach to the reality according to hierarchy of quadrivium:

• Arithmetic: ontology - superior to all phenomena

• Geometry: pure forms - spatial phenomena

• Astrology: cosmos - spatial-temporal phenomena

• Music: perceivable quality of spatial-temporal phenomena

Boethius, probably under the influence of Aristotle, emphasizes the sensual dimension

of music and considers the ability of perception through the senses as a natural attribute of all

22

‘living creatures’. However, he assumes that perception itself is linked to the mind rather than

to the object and poses ontological issue:

It is obvious that we use our senses in perceiving sensible objects. But what is

the exact nature of these senses in connection with which we carry out our actions?

And what is the actual property of these objects sensed? The answers to these

questions are not so obvious; and they cannot become clear to anyone unless the

contemplation of these things is guided by a comprehensive investigation of reality.

(De institutione musica, Introduction, IN: Godwin, 1986, p.44)

As Woodcock mentions (1943, p.32), ‘The battle between reason and the senses still

rages.’ Boethius presumes that through the mathematics it is possible to gain the

understanding of the essence of all sensually perceived phenomena:

...if someone sees a triangle or square, he can easily identify it by sight. But

what is the essence of a triangle or a square? This he must learn from a mathematician

(Godwin, 1986, p.44).

But when hearing, perceived sounds are not only recognized in terms of their

structure, but also in terms of aesthetic judgment made by subject. This may be plausible ‘if

the are in the form of sweet and well-ordered modes’, or implausible ‘if the sounds heard are

unordered and incoherent’. Therefore, as Boethius states, the other disciplines (quadrivium)

are related to ‘the investigation of truth’ and music to speculation and morality: ‘musica vero

non modo speculationi verum etiam moralitati coniuncta sit‘. The basis for such an aesthetic

judgment is considered in fact that ‚amica est enim similitudo, dissimilitudo odiosa atque

contraria‘. This can be understood as ‚the principle of similarity‘ between the structures

within the subject and perceived object who are supposed to have, consequently, generic

numerical origin. With accordance to ‚the principle of similarity‘, as it was explaned by Neo-

Platonists Plotinus, Boethius clearly adopt Plato’s ethos theory:

For there is no greater path whereby instruction comes to the mind than

through the ear. Therefore when rhythms and modes enter the mind by this path, there

can be no doubt that they affect and remold the mind into their own character.

(Godwin, 1986, p.45)

The ethos theory is unavoidable consequence of hierarchy of phenomena and of

generic numerical underpinning of the reality. Music is presupposed being everywhere, in

both macrocosmic and microcosmic dimensions. Thus Pythagorean and Platonic thoughts

about music and cosmology are prerequisites for Boethian classification of music. This,

23

perhaps the most quoted classification of music in mediaeval literature, can be found not only

in De institutione musica, but as Chamberlain (1970) suggests, the other relevant definitions

can be found in Consolatio. Either few further explanations can by drawn from De institutione

arithmetica. Boethius describes in De institutione musica three types of music (Tres esse

musicas): musica mundana, musica humana and musica instrumentalis. This typology is not

quantitative, but either qualitative in the terms of dimensional ontology. Thus the music

mundana and humana have different ontological status as instrumentalis. Musica

instrumentalis is in its definition closest to the modern term of music and therefore is not

further explained in this essay. On the contrary, the two other types of music are disputable in

terms of ontology. Musica mundana includes three distinctive forms:

‘The first type [musica mundana], that is the music of the universe, is best

observed in those things which one perceives in heaven itself, or in the structure of the

elements, or in the diversity of the seasons’. (Godwin, 1986, p.46)

Either according to Consolatio (Chamberlain, 1970), musica mundana consists of

three forms or categories:

1. Motions of celestial bodies - not audible for human ear.

2. The binding of the elements - inaudible harmony.

3. The alteration of the seasons - inaudible.

In De institutione arithmetica Boethius explanes the generic numerical base for

elements, seasons and celestial movements: ‚Hinc enim [numerorum ratione formata] quattuor

elementorum multitudo mutuata est, hinc temporum vices, hinc motus astrorum caelique

conversio‘. However, Boethius does not distinguish the category of sound in such ontological

hierarchy as the types of the musicas themselves. This regards the first type of musica

mundana:

How could it possibly be that such a swift heavenly machine should move

silently in its course? And although we ourselves hear no sound - and indeed there are

many causes for this phenomenon - it is nevertheless impossible that such a fast

motion should produce absolutely no sound, especially since the orbits of the stars are

joined by such a harmony that nothing so perfectly structured, so perfectly united, can

be imagined. (Godwin, 1986, p.46)

Chamberlain (1970, p.82) assumes that ‘the philosophic tone of this music, like that of

the world, would seem to be largely physical and mathematical’. This confirms that Boethius

24

emphasizes the perceptual aspect of hearing and construed it as a part of ‘world music’. Thus,

as Woodcock (1943) suggests, evaluation of consonance depends on both ear and science.

In De institutione musica he only poses questions with regard to musica instrumentalis

but does not provide a satisfactory answer:

For what unities the incorporeal existence of the reason with the body except a

certain harmony (coaptatio) and, as it were, a careful tuning of low and high pitches in

such a way that they produce one consonance? What unites the parts of man’s soul,

which, according to Aristotle, is composed of a rational and irrational part? In what

way are the elements of man’s body related to each other or what holds together the

various parts of his body in an established order? (Godwin, 1986, p.47)

However, with reference to Consolatio, musica humana, similarly as mundana, has

three forms, too (Chamberlain, 1970, p.82):

1. ‘The fit proportioning or blending (“coaptatio” and “temperatio”) of the

“incorporeal life of reason” with the body, like one musical consonance of high

and low notes’.

2. The second ‘is the joining of parts within the soul itself, of rational and irrational

parts’.

3. The third ‘is both the thorough mixing of the elements and the fixed proportioning

of members in the body alone’.

This type of music is inaudible, and therefore rests in silence. Boethian conception of

musica humana is far from simplification that of the harmony between the body and soul. It

indicates the structural convexity within the living system on the basis of highly sophisticated

mediation which Boethius assumes being conveyed by mathematical proportions. The four

basic elements of genetic information and their combinations are the basic constituents of

such living system - a microcosm itself, what seems being analogous to Pythagorean tetractys

as the source of macrocosm. Boethius was much more Pythagorean as it is thought according

to his treatise De institutione arithmetica. His classification of music should not be

understood literary, but through the background information of arithmetic, numerology, Neo-

Pythagorean and Neo-Platonic mysticism.

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Kepler’s Planetary Polyphony

Johannes Kepler (1571-1630), German astronomer and philosopher, was the last

adherent of Greek tradition of Music of the spheres. His prolific and courageous attempt was

to link together the idea of harmonious organization of the cosmos and the latest astronomical

observations based on empirical data. However, Kepler’s first great work Mysterium

Cosmographicum (1596) reflects deviation from Ptolemaic cosmological theory in favor of

the heliocentric theory of planetary motion invented by Nicolaus Copernicus. The

contemporary astronomers, such as Galileo Galilei, and Tycho de Brahe, took advantage of

modern telescope equipments due to the improvement of optics. In 1600, Kepler became the

assistant to Brahe in well-found astronomical observatory in Prague. After the death of Brahe

in 1601, he assumed his position as court astronomer and mathematician to Rudolf II, and he

had opportunity to use the most modern telescope in that period.

Kepler sketched a comprehensive hypothesis of geometrical organization of planetary

motions and distances among their orbits. He knew only five planets: Saturn, Jupiter, Mars,

Venus, and Mercury. If there are included also Sun, Earth, and Moon, it is similar planetary,

respective spherical, system as in Greek cosmology. However, the role of deities has shifted

under the influence of new theories and observations. The spherical motion focused around

the Earth became the orbital motion of particular planet around the Sun and was not

autonomous henceforward. The Sun became not only the center of this new view of cosmos,

but he considered it as the basic motive power which decreases proportionally with the

distance of particular planet from the Sun. Later on, Isaac Newton established his theory of

gravitational force on Kepler's theories and observations.

During his service on the court of Emperor Rudolf II he wrote one of his major works

Astronomia Nova (1609). This work contains formulations of two of so-called Kepler’s three

laws of planetary motion, which are best known nowadays, although Kepler himself regards

his explanations of ‘world’s harmony’ more important than his formulations of the three laws

of planetary motions (Brackenridge & Rossi, 1979). The first law is that he discovered the

planetary orbits have to be elliptic and not circular as he had presupposed before. The Sun is

stationary focus of these elliptic orbits. The second law states that an imaginary line from the

26

Sun to a planet terminates equal areas of an ellipse during equal intervals of time, accordingly

an orbital speed of a planet is not constant and depends on distance from the Sun: the closer a

planet comes to the Sun, the more rapidly it moves. The formulation of the third law was

introduced in Harmonices Mundi (1619), it states that the ratio of a cube with face equal to a

planet’s distance from the Sun and the square of the planet’s orbital period is a constant valid

for all planets.

According to his discoveries, Kepler believed that the universal harmony could be

found in planetary structure. He devoted himself fully to research the geometrical laws

accountable for distribution, organization, and motions of celestial bodies. In The

Cosmographic Mystery he posed the question why there are only five planets in the solar

system. He found the reason in the fact that there are only five regular three-dimensional

solids with identical faces all joined with identical angle. These solids are: (1) Cubus, (2)

Tetrahedron, (3) Dodecaherdon, (4) Icosihedron, and (5) Octohedron. In the fifth book of

Harmonices Mundi, De harmonia perfectissima motuum coelestium, chapter De quinque

solidis regularibus he drew a parallel between the intervals among the planetary spheres and

these regular solids in following order: Saturn - cube - Jupiter; Jupiter - tetrahedron - Mars;

Mars - dodecahedron - the Earth; the Earth - icosihedron - Venus; and Venus - octahedron -

Mercury. Further investigation proved that data fits only approximately and not exactly.

Nevertheless, Kepler believed that ‘God the Creator is the Geometer and speaks in the

universal language of geometry’ (Brackenridge & Rossi, 1979, p.113).

The Keplerian geometrical forms, which are in basic correspondence to musical ratios,

are derived from astrology. It comes to this that the layout of two particular planets or stars

forms a geometrical or a non-geometrical angle by connecting the imaginary vectors of these

bodies with the Earth. (Brackenridge & Rossi, 1979) A harmonic angle is the angle derived

from one of eight harmonic ratios of motion (0o, 60o, 72o, 90o, 120o, 135o, 144o, and 180o;

schemes):

27

Table 5. (according to Brackenridge & Rossi, 1979, p.114)

Implicitly, these harmonic angles are indubitable due to inevitability of their causal

existence, but their interpretations are axiomatic. The circle is divided by inscription of

regular polygons into identical fragments, which constitute the ratios and angles, as it is

presented in the schemes above. These angles and ratios implied from them are the basic

terms of astrological interpretation of planetary constellation:

Constellation conjunction opposition trine quartile sextile quintile biquintile sesquaquadrate

Angle 0o 180o 120o 90o 60o 72o 144o 135o

Interval unison octave fifth fourth minor

third

major

third

major

sixth minor sixth

Ratio 1:1 2:1 3:2 4:3 6:5 5:4 5:3 8:5

Table 6.

Kepler wrote: ‘Perhaps God himself has invariably expressed these proportions

[regular polygons inscribed into circle] in bodies and motions’ (Harmonices Mundi Lber III,

28

Source: Godwin, 1986, p.149). He accepted all the harmonic ratios derived from harmonic

angles as musical consonances, in accordance to music theory of early 17th century.

Kepler at first had believed that planets’ orbits are circular, but latter the observations

data did not fit to this assumption and hint on the new theory that these orbits have to be

elliptic (the first law of planetary motion) and therefore ‘imperfect’. This imperfection must

have some reason and Kepler proposed a bit curious hypothesis: each planet does not

represent particular tone (because the distance from the Sun is not constant) but melodic

pattern in dependence of the range between the aphelius (farthest point from the Sun) and

perihelius (closest point from the Sun) distances. This hypothesis of music of the spheres was

new at all and based on empirical data. He adjudicated the musical scale – the fundamental

sequence of ascending and descending notes for each planet in correspondence with their

elliptical orbits, and within the range equal to the deviation of perihelion and aphelion

distances:

Table 7.

The individual notes of these melodic patterns are selected points of permanently

changing pitches (in terms of ‘planetary glissando’) within its range. The closer is the planet

to the sun the higher is the pitch. The lowest note of each pattern represents aphelius point,

the highest note perihelium. Therefore each pattern repeats simultaneously with one orbital

period which is different for each planet (according to Kepler observations presented in

Harmonices Mundi): Mercurius 87 days, Venus 224, the Earth 365, Mars 686, Jupiter 4332,

and Saturnus 38769 days. The ‘musical’ range is very small in the case of Earth’s orbital

course - only the semitone – mi fa. According to Kepler’s interpretation, the semitone sounds

29

sad, and symbolizes the decline and corruption of earthly sphere with its imperfection (misery,

famine, Gamwell, 2002). Forasmuch as each planet has its own melodic subject, the music of

the spheres, of Musica mundana, has to be polyphonic. Walker (1967, p.232) noted that:

For Kepler just intonation and polyphony had finally prevailed because they

were natural, that is, they corresponded to the archetypes in the mind of God, on

which the created world was modeled, and which are also in the mind of man, the

image of God.

Kepler’s intention was primarily not focused to prove celestial music, but to find and

prove harmonic proportions of planetary system in terms of their spatial and temporal

organization. His speculations about music were based on astronomical research and

astrologic interpretation of the universe. Is the Keplerian analogy among the regular solids,

harmonious angles and musical consonances a metaphor or a real correspondence between the

macrocosms and unifying principle based on universal harmony? Majority of Kepler’s

observations and conclusions are valid till nowadays, but his ‘cosmic polyphony’ is symbolic,

because he did not believe that celestial harmonies are audible: ‘The source of the human

response to music is to be sought in the soul and intellect, not in physical matter’ (Harmonices

Mundi Lber III, Source: Godwin, 1986, p.149). The important part of Kepler’s theories about

music is his interpretation of a sound:

How a plucked string will transfer its sound to another unplucked one if they

are consonant with one another, but leave it immobile if they are dissonant. Since this

cannot be the work of any mind, because a sound thus caused has neither mind nor

intellect, it follows that we must say that it is caused by a simultaneity of motions... If

the speed of one string can serve to move the other one tuned to it, though it be

untouched as far as the eye can see, will not the same speeds of both strings serve for

the pleasant stimulation of the ear, because the latter is in some way moved uniformly

by the two strings, and two impulses from the two sounds or vibrations meet at the

same moment? (Harmonices Mundi Lber III, Source: Godwin, 1986, pp.150, 151)

The medium of transferring particular vibration Kepler took as species immateriata -

the etheric emanation from object. Movement of e.g. a string causes this phenomenon. If a

string of particular length and tension is potentially influenced by species immateriata, then it

would be perhaps possible to transfer the powerful cosmic vibrations into human mind. The

idea of simultaneity of motions was later treated by Athanasius Kircher in his great work

Musurgia Universalis (1650). He described an imaginary instrument ‘enneachord of nature’

on which every string, if plucked, resounds through all levels of the beings.

30

PART TWO: POST-COSMOLOGICAL CONCEPTIONS

As soon as philosophy became an autonomous discipline, by the result of establishing

the positive natural sciences based on empirics during the 18th and 19th centuries, the

metaphysic dimension of music was apprehended in separation from theory and practice of

music, and from other sciences such as astronomy, mathematics and physics. Jean-Philippe

Rameau noted in Preface to his remarkable Treatise on Harmony (1722):

However much progress music may have made until our time, it appears that

the more sensitive the ear has become to the marvelous effects of this art, the less

inquisitive the mind has been about its true principles. One might sad that reason has

lost its rights, while experience has acquired a certain authority. The surviving

writings of the Ancients show us clearly that reason alone enabled them to discover

most of the properties of music. Although experience still obliges us to accept the

greater part of their rules, we neglect today all the advantages to be derived from the

use of reason in favor of purely practical experience... Conclusions drawn from

experience are often false, or at least leave us with doubts that only reason can dispel

(Rameau, 1722/engl. ed. 1971, p.xxxiii).

Contrary to the cosmology of music, where all disciplines were integrated in their

methodology, the disciplines of modern science forked into arts and exact science. The

methodology used in post-cosmological conceptions of musical ontology stems from

philosophy: (i) epistemology, concerned with role of subject in cognition, (ii) ontology

focused on subjective perception in terms of a priori givenness, and on the objectivity of

music. Therefore the ontological issues lost their simplicity based on common premises, and

became sophisticated disputes trying to comprehend the complexity of all phenomena and

provide an acceptable paradigm for them.

Metaphysic of music is apprehended from various points of view, represented by three

subjects selected: (i) Immanuel Kant’s integration of rationalism and empirics, his rejection of

metaphysics, (ii) Arthur Schopenhauer’s ‘modern’ cosmology understanding music as a

‘direct copy’ of everything-penetrating will, and (iii) phenomenology of music providing

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several solutions of the ontological issue. Music was apprehended as a perceptual

phenomenon, i.e. subjective perception of objective sound concepts. The metaphysic

dimension of this perception was sought no more in cosmology but in human subject.

However, the antimony of silence and sound became less and less recognizable and a new

antinomy appeared: objective sound and perceived sound. The inaudible music of universe

was lost.

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Immanuel Kant: Mind as a ‘string instrument’

One of the most influential philosophical theories concerning metaphysics and

transcendental aesthetics was set up by Immanuel Kant, notably in his writings The Critique

of Pure Reason (1787) and The Critique of Judgment (1790). Although Kant is not generally

regarded as ‘philosopher of music’, his contributions in the field of epistemology (rational and

empirical), relations of cognition and perception, explanations the categories of object and

subject are indisputable. The consequences of his proposed ideas on philosophy and aesthetics

of music became essential concepts for following generations of scientists and philosophers.

His works, especially the three of Critiques, are a bridge between rationalist and empiricist

traditions.

Kant stated what was formerly indicated by Descartes, that objective knowledge can

be apprehended exclusively as a consequence of the cognitive acts of a subject. Rational

human subject is situated in the centre of cognition. Although he understood the aesthetics as

a science concerning the perceptional quality of objects, rational order of the world could

never derive from accumulation and organization of sensual perceptions. While in traditional

cosmological theories the human subject is a part of whole universe, a mirror of it,

‘microcosmical representation of macrocosm’, and therefore the same rules are applied for

them, Kant drew a methodological difference between them, and not a parallelism.

Consequently, ‘...he situates beauty not in the object but in a psychological experience of the

subject: the “determining ground” of the beautiful “can be no other than subjective” (Reed,

1980, p.566).

If the intelligibility of objects in the world can be brought about only via

synthesizing acts of the mind, the mind can no longer be just the imitator of pre-

existing objects... Kant rejects claims about nature's inherent structure, arguing that we

ourselves ‘give the law’ to nature as it appears to us, so that we cannot know nature as

it is ‘in itself (Bowie, 2006).

This is the most fundamental contradiction to cosmology of music. The correlation

between the human being and the universe has categorically been changed. Kant made a

separation of ‘supersensible realm’ from phenomenal world. Therefore, his conception of

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transcendental aesthetics (Critique of pure reason) does not presuppose any ‘existing forms of

beauty, whether natural or artificial’ (Reed, 1980, p.568). The gateway to understanding lies

in exploration of cognitional facility of a man. Thus ontology of music is concerning with the

human subjectivity, especially in its pure form of cognition.

He made a distinction of the knowledge into (i) categorial (a priori): pure without

addition of empirics, independent from experience and impressions; (ii) empirical: originated

in experience. He noted out that even if any knowledge does not anticipate experience in

terms of temporality, knowledge itself is not entirely originated in experience. This

contradiction is resolved by the fact that the quality of our cognitive faculty contributes by

itself to knowledge. The mathematics serves as an example that a priori recognition is

possible without the dependence of experience, even though mathematical judgments

themselves are synthetic. Therefore reason is faculty providing a priori principles of

knowledge.

The transcendental knowledge, about to be a priori possible, is concerned with no

objects or phenomena, but with the process of our recognition of objects. The objects are

given to us through the medium of the senses which provide us with perception. A pure form

of this perception is possible to deduce as follows: if we eliminate from the representation of a

solid (i) what reason thinks about it, and (ii) sensations like color, impenetrableness etc.; the

remanentia of the representation are shape and spatial dimension (Kant: Critique of pure

reason). Similarly, the time is not regarded as empirical notion derived from experience,

because we could not perceive the actual time and the consecutive time if they are not based

on a priori notion of time. Therefore space and time are essential notions, substances of all

perceived sensory data. These substances are not autonomous as well as attributes of

phenomena, but are the form, an ‘inner sense’ of a man’s perception. As a result of

implication this theory into ontology, the ‘real world’ was split into (i) phenomena -

appearances, experience, and (ii) nomena - things themselves. All of the nomena are

incognosible, thereupon the existence of primordial musical structures are rather uncertified.

On this account, the existence of music, or musical phenomena, is conditional to human mind.

However, Kant was rather skeptic about music as a mind becoming phenomenon. In

his Critique of Judgment, §51 ‘Of the division of the beautiful arts’ he proposed the

classification of the fine arts into three categories: ‘the arts of speech’ - rhetoric and poetry;

‘the formative arts’ - sculpture, architecture, and painting; and ‘the art of the play of

sensations’ - Tonkunst. The first two categories present no analytical problems, but in the

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third (play of sensation: tone and color) Kant finds that there is no certain utterance whether

colors and sounds consist of disordered bundles of sensations, or possess determinate forms:

If we think of the velocity of the vibrations of light [color] or in the second

case of the air [tone], which probably far surpasses all our faculty of judging

immediately in perception the time interval between them, we must believe that it is

only the effect of these vibrations upon the elastic parts of our body that is felt, but that

the time interval between them is not remarked or brought into judgment; and thus that

only pleasantness, and not beauty of composition, is bound up with colors and tones.

(Kant, §51, p.169)

This statement is like to be a ‘phenomenological’ analysis of composition, the same

issue employed medieval writers on music, but in rather different conception in ‘grammar of

music’ (add reference!) The issue was related, similarly to Kant, to the question whether

music consists of some kind of dividable commposita or not, et inde whether music is art

conveying particular meaning or not. Parret (1998, p.260) on this account suggests:

It is clear that music requires no activity of thought, since it has no semantic

component: a musical sequence has no propositional content such as is found in

language (including the most “beautiful” language possible, namely poetry). Music

does not make us think; rather, it causes us to reflect and to dream more than any other

art.

According to this task, Reed (1980, pp.569-570) mentioned the problem of the nature

of sound in connection with the first and second editions of the Critique: ‘In the first he

[Kant] says “ich zweifle gar nicht” that sound vibrations possess a form, but in the second he

says “ich zweifle gar sehr”. If sound vibrations have a form, than it would be possible make a

judgment and music would be considered as fine art. Kant offered a compromise: music

possess to a particular extend both form and sensation. However, Kant placed music at the

lowest place among the other arts ‘because it merely plays with sensations’ and therefore is

not constituted in pure rational acts (see phenomenology of music):

The formative arts produce ‘lasting impressions (Eindrücke),’ while music

produces only ‘transitory impressions’. And this oscillating degree of presence

appears to be related to the difficulties Kant has had in situating music in his analytical

categories. However, both comments are governed by a structure that continually

discounts the worth of music with respect to that of the bildenden Künste, which thus

represent a kind of mean of presence (even though we are to take no ‘interest’ in their

existence) between a glut and a dearth. (Reed, 1980, p.575)

35

It seems to be paradoxical that Kant understood music as sound and perception, and

the fact that music have from this point of view transitory, not lasting existence, led him to

exclude music from rational speculation and therefore he abases music as an formative art.

His theory lacks some kind of ‘higher paradigm’ of music (e.g. cosmology) in terms of

rational rule that would be able to confer judgments about its quality. However, music is still

a cultural phenomenon in that it proposes to human beings new orders of perception.

While music is abased as a play of sensation not conveying rational form, the

cognitional faculty of a man itself can be understood in ‘musical’ terms. Kant often used in

his Critique of Judgment such terms as ‘harmony’, especially ‘harmony of cognitional

faculties’ in accordance to the ability of aesthetic judgment. Both Reed (1980) and Parret

(1998) proposed a speculative (at least) interpretations of Kant’s text:

When one takes account of the materiality of Kant’s text, it is evident that for

one of the most complicated elements of his terminology, Gemüth, musical imagery is

omnipresent: the mind (Gemüth) is presented to us as itself a musical instrument, more

specifically a stringed instrument. The same thing could be said of the Anthropologie,

where sensibility, as the first property of the mind, is presented as a bodily organ on

which something like music is played. (Parret, 1998, p.262)

Kant thus imagines the mind as a sort of musical instrument, more precisely a

stringed instrument (or perhaps the psychological equivalent of the vocal chords), the

principle strings being understanding (shown vibrating here), reason, and imagination.

That is why in the same paragraph he calls a ‘state of mind’ a ‘Gemütsstimmung,’

literally a ‘pitch’ or ‘tone of mind,’ and speaks elsewhere of the ‘beide Gemützustände

zusammenstimmen (two mental tones harmonizing, in accord)’ ([§]16), or a

representation that ‘places the cognitive faculties in a proportionierte Stimmung’ with

each other through its harmony (Zusammenstimmung) with the ‘conditions of

universality’ supplied by the understanding ([§]9). The activity of our cognitive

faculties generally is thus called a ‘Spiel,’ a play of mental strings. Within this

structure Kant defines beauty (that is, the subjective experience of something as

beautiful) as the mental tone that results from the harmonious interplay of the string of

imagination and the string of understanding. (Reed, 1980, pp.579-580)

It is improbably that Kant’s intention was to hint on this interpretation deliberately.

However, are then the proportion and the functionality of human mind, determined by

‘general rules of harmony’, an a priori attribute of pure reason? Is the harmony an a priori

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unconscious presumption of mind in like manner as time and space are conscious? The

question Kant asked himself is:

...in what way we are conscious of a mutual subjective harmony of the

cognitive powers with one another in the judgment of taste - is it aesthetically by mere

internal sense and sensation, or is it intellectually by the consciousness of our designed

activity, by which we bring them into play? (Critique of Judgment, §9)

If ‘the given representation’ activating through our senses the judgment of taste, was

concept ‘uniting understanding and imagination’, the ‘consciousness of this relation would be

intellectual.’ But, as Kant later mentioned, this kind of judgment is not that one of the taste,

because it lacks reference to ‘pleasure and pain’. On the contrary, if the ‘subjective universal

communicability of the mode of representation in a judgment of taste’ is possible to

presuppose without particular concept, then it should refer to ‘nothing else than the state of

mind in the free play of the imagination and the understanding.’ Therefore the basis for

aesthetic judgment is not a ‘concept’ but ‘harmony’:

This merely subjective (aesthetical) judging of the object, or of the

representation by which it is given, precedes the pleasure in the same and is the

ground of this pleasure in the harmony the cognitive faculties. (Kant, Critique of

Judgment, §9)

In the original text, Kant used in many places in stead of the term ‘harmony’ -

Harmonie, other, quite synonymic terms such as Zusammenstimmung, Einstimmung,

Übereinstimmung, or Beistimmung. (see also Reed 1980, pp.578-579) Although these terms

have apparently no reference to music, the meaning is almost the same as in music,

representing particular dynamic correlation according to particular rules.

Forasmuch as it is not possible to prove the intelligibility of musical perception, Kant

suggested different point on this issue in §54 of his Critique of Judgment. He described the

psychological mechanism of laughter with relation to musical experience. He stated that both

laughter and musical experience are based on corporeal activity with cathartic effect and

therefore cause physical pleasure generated by releasing of a state of tension: ‘Laughter is an

affection arising from the sudden transformation of a strained expectation into nothing.’

(Kant’s italics, 54§) Accordingly, Parret (1998, p.263) suggests that ‘musical experience can

also be described in terms of tenseness (expectation, tension, release).’

One might ask why music represents such methodological problem in Kant’s text. For

this purpose may be useful to design a paradigm with reference to Critique of pure reason.

37

OBJECT

noumenon ‘thing of itself’

BODY

senses, physical equilibrium (principle of laughter)

MIND

cognitive process, phenomena (thinking about objects)

PURE REASON

a priori knowledge, time & space

Table 8.

The pure reason is situated in the center representing the ability of pure knowledge,

and of a priori judgments. The problem occurs if this paradigm is adapted to Critique of

judgment, namely to the aesthetic judgment, and more specific to the judgments about music -

play of sensations. While in the formative arts space (concept, form) and time (lasting

impressions) in the terms of a priori attributes of the pure reason are definable, in music

space (no concept) and time (transitory impressions) are indefinable. Therefore Kant

suggested that there has to be harmony between mind and body - a play of sensations, and

harmony between mind and reason - a harmony of cognitive faculties. However, there is no

subset of pure reason in terms of a priori harmony in Kant’s text, and therefore the harmony

is among the other sets (pure reason, mind, and body) and by this correlation is outside the set

of pure reason.

Generally, Kant thoughts were autonomous, without dictates of external authority. He

designated the methodological difference between the universe of all things and their

temporal and spatial representations in the human subject. Consequently, he isolated the

cognitional options of universe in term of ontology from those in human subject. The music

of the spheres was not a mirrored model for harmony of ‘cognitional faculties’ that were, in

fact, a modification of musica humana. On the contrary, the human subject is a model for

universal harmony:

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...all of nature must be read in terms of the subject’s mental structure. Or put it

differently, the vibrations of the cognitive faculties spread out and resonate through all

of nature - it being of the nature of music always to extend and impose its existence.

(Reed, 1980, pp.580-581)

Harmony and music became the attributes of interaction between mind and sensual

faculty. The metaphysic aspect of this act is hidden in a priori givenness of the mind.

Therefore, there is no reason to assume that music exists outside this mind, because the

common genesis between the universe and subject is missing. However, Kant’s text, indeed,

presupposes a general assumption of harmony. Whether this assumption is an attribute of pure

(conscious) reason or unconscious general condition of subject, is not possible to define. The

reason for this consists in impossibility of excluding the subjective from unconscious general

condition.

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Schopenhauer: Music as representation of the Will

Arthur Schopenhauer (1788-1860), was one of the first Western philosophers of

modern history who had access to the translations of Indian philosophical treatises, namely

those belonging to Buddhist and Vedic traditions. This fact might have contributed to

formulation of his conception of the ‚will‘, and phenomenal world as its representation. Some

of his thoughts have been undoubtedly drawn from Hindu theory of Maya, notably those of

the illusionary nature of phenomenal world and that people do not have individual wills but

were rather simply part of a vast and single will that pervades the universe, that the feeling of

separateness that each of has is but an illusion. The main core of his philosophical output is

included in his famous work The World as Will and Representation published in 1819 and

later on, the new edition of two volumes published in 1844.

Schopenhauer was to a certain extent follower of Kantian idealism in the terms of

distinction the reality into phenomena and noumena, namely the things as they appear to us

and the things-in-themselves as they are beyond the grasp of a man’s reason. Schopenhauer

negotiated this ontological agnosticism and turned the whole Kantian ontology at new,

metaphysical direction through his interpretation of Kant’s thing-in-itself as ‘will’.

Schopenhauer’s classification of all beings and his view on universe differs from that of the

Kantian in many respects. The thing-in-itself as the will has an active role in its

representations; all phenomena are in dependence of the will’s objectification. The hierarchy

of beings can be simplified as follows:

The universe

appearances = representations of the will

objects

thing-in-itself = will

subjects

ideas (Plato’s ideas) phenomena (space & time)

Table 9.

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According to this table, out of all the categories only phenomena are governed through

a priori attributes (space & time) of pure reason. Experience includes phenomenal world,

appearances and representations. Although experience has a serious ontological problem: how

to recognize the inner nature of things? Schopenhauer mention in his The World as Will and

Representation (trans. E. F. J. Payne, 1969, pp. 98-99):

We want to know the significance of those representations; we ask whether

this world is nothing more than representation. In that case, it would inevitably pass us

by like an empty dream, or a ghostly vision not worth our consideration. Or we ask

whether it is something else, something in addition, and if so what that something in

addition, and if so what that something is.

By the term ‘something else’ Schopenhauer meant ‘inner world’ or ‘inner nature’ of

all the phenomena, id est things out of empirical nature. He apprehended human body as a

physical phenomenon, or ‘physical object among physical objects’ (Alperson, 1981, p.156).

However, self-consciousness represents more than physical phenomena, because it expresses

will: ‘The action of the body is nothing but the act of the will objectified, i.e., translated into

perception’ Human will is ‘knowledge a priori of the body, and that the body is knowledge a

posteriori of the will’ (Schopenhauer, pp. 100-101). This categorization Alperson (1981,

p.156) characterizes as ‘epistemological dualism’.

Schopenhauer apprehended the human being as embodied will and emphased the fact

that the human behavior is subjected to it. The will itself governs a metaphysical dimension of

the world, and therefore confer an ontological status to all its appearances and representations.

The will is a universal principle at the same time in unity with phenomenal world and apart

from it. It is also an essence-mover of the phenomenal world:

One can see the will manifesting itself in the blind forces of the inanimate

world such as gravitation, magnetism, and electrical attraction and repulsion, as well

as in the forces of germination and vegetation in the plant world, and in the

personalities and actions of men. The world is at once will and representation.

(Alperson, 1981, p.156)

The acts of the will’s objectification are in peculiar hierarchy according to complexity

and clarity how they are expressing the will. They are, in fact, Platonic ideas, the ‘original and

unchanging forms and properties of all natural bodies, whether organic or inorganic, as well

as the universal forces that reveal themselves according to natural laws.’ (Schopenhauer,

World, Vol. I, p.169.) Ideas are the archetypes, the individual objects, then, are copied in

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accordance to them. The hierarchy of the arts is organized in the same order as the hierarchy

of clarity and complexity of the objectification of will. Hierarchy of the arts (from low to

high), according to Schopenhauer:

• Architecture (gravitation, stone material, proportion).

• Painting (landscape painting = imitation of the world of plants; human bodies =

imitation of humans, expression of the man’s character).

• The literary arts (expression of emotions and actions).

• Music has an outstanding position, because ‘in it we do not recognize the copy, the

repetition, of any Idea of the inner nature of the world’. Ideas are the objectivity of

will (see table above); music is not repeating them but will itself and therefore

differs from the other arts repeating the Ideas. Schopenhauer apprehended Plato’s

Ideas apart from world of experience and therefore they are out of knowledge, too.

However, they may become an ‘object of knowledge in aesthetic contemplation’,

particularly in the other arts.

Schopenhauer stated that ‘parts of all harmony’ are the four voices: bas, tenor, alto,

soprano or: fundamental note, third, fifth, and octave, and are in correspondence to ‘four

grades in the series of existences: mineral, plant, animal, and human. Bass ‘moves heavily,

rises and falls only by large intervals, thirds, fourths, and fifths, and is guided here by fixed

rules in each of its steps’, and therefore represents naturally the ‘inorganic kingdom of

nature’, while soprano with ‘great flexibility’ bears the melody and represents the ‘highest

stage of the scale of beings’. So, the hierarchy of parts in music reflects the hierarchy of the

other arts. Music itself is an independent art, has its own resources.

Another issue Schopenhauer was concerned with is the combination of music and text

in vocal music and opera. The relationship of tone and speech or music and poetry is

problematic due to their conceptual inconsistency. ‘The words are and remain for the music a

foreign extra of secondary value, as the effect of the tones is incomparably more powerful,

more infallible, and more rapid than that of the words’ (Schopenhauer, engl. transl. 1958,

448). Schopenhauer, of course, follows the hierarchy of the arts proposed by his own before,

and therefore regarded music as the most capable medium of expressing the inner contents:

...the musical art at once shows its power and superior capacity, since it gives

the most profound, ultimate, and secret information on the feeling expressed in the

words, or the action presented in the opera. It expresses their real and true nature, and

42

makes us acquainted with the innermost soul of the events and occurrences...

(Schopenhauer, engl. transl. 1958, p.448).

Accordingly, Schopenhauer suggests that it would be more appropriate to write the

text to already existing piece of music. However, he was acquainted with the usual and

practically convenient method of composing the music on already existed text or poem. He

finally concludes that music is able to express ‘every movement of the will, every feeling; but

through the addition of the words, we receive also their objects, the motives that give rise to

that feeling’ (Schopenhauer, engl. transl. 1958, p.449). It comes to this, that music does not

need the object to represent the content. Thus the classification of sound structure by itself as

musical phenomena was not the central idea; moreover, the role of physical sound as a

‘matter’ of music was neglected. Music does not have ‘matter’ in the terms of definable

phenomena representing the Ideas, expresses the ‘metaphysical to everything physical in the

world, the thing-in-itself to every phenomenon’ (Vol. I, p.262). Will as a noumenal mover of

phenomenal world is expressing itself in both phenomena and music, other arts are derived

secondary from phenomena, or are using its matter.

Contrary to Kantian conception of music as a play of sensations, music expresses

universal, pure form relating to the thing-in-itself and not to the phenomenon. According to

Green (1930, p.200),

...music must have deeper roots in human nature than the other arts, and that

whilst these are representations of external phenomena, themselves symbols of the real

essence of things, music is the representation of this essence itself, a parallel form,

therefore, of the World as our intellect perceives it.

Schopenhauer, then, understood music as the direct representation and objectification

of will:

Music, therefore, if regarded as an expression of the world, is in the highest

degree a universal language, which is related indeed to the universality of concepts,

much as they are related to the particular things... In this respect it resembles

geometrical figures and numbers, which are the universal forms of all possible objects

of experience and applicable to them all a priori, and yet are not abstract but

perceptible and thoroughly determined (The World as Will and Idea, translated by R.

B. Haldane and J. Kemp, 1883, vol. I, pp. 339-340.).

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The unity of will and multeity of its objectification induces that all phenomena have

identical ontogenesis. However, the organization of the pitches in the structure of musical

work does not suggest any ‘natural’ phenomenon.

‘We may regard the phenomenal world, or nature, and music as two different

expressions of the same thing [will], which is therefore itself the only medium of their

analogy, so that knowledge of it is demanded in order to understand that analogy.’

(Schopenhauer, The World as Will and Idea, translated by R. B. Haldane and J. Kemp,

1883, vol. I, pp. 339-342.)

This analogy is governed by musical proportion and melody, which reflects the ‘inner

spirit of the given phenomenon’. Melody has two dichotomical elements:

1. Rhythmical (quantitative): duration of the notes - vertical dimension.

2. Harmonious (qualitative): pitch and depth of the notes - horizontal dimension.

‘Rhythm is in time what symmetry is in space’ (Schopenhauer, 1958, p.453). This is

the only classification of phenomenal dimension of music in Schopenhauer’s text. Time and

space as the pure a priori forms which are prerequisites for perception, receiving object into

mind, might propose that rhythm and symmetry are the qualitative dimensions of these forms,

as well as a priori, while time and space are quantitative dimensions. Moreover, they might

be inextricably linked into rhythmic time and symmetrical space. The reason for this is that we

always are looking for proportions in time and space, for their organization. What is the

disadvantage of music for Kant - lack of definability in terms of concept and durability of

time; seems to be advantage for Schopenhauer - music is the essence, the pure form of the

will.

Music as the direct copy of the will has an influence on mind in qualitative different

way than phenomenal stimuli. The perceptual faculty does not contribute fundamentally to the

ontogenetical constitution of music. The musical reception suggests a process of recollection

of inner contents of the mind or memory rather than simple perception:

...that whoever gives himself up entirely to the impression of a symphony,

seems to see all the possible events of life and the world take place in himself, yet if

he reflects, he can find no likeness between the music and the things that passed

before his mind. For, as we have said, music is distinguished from all the other arts by

the fact that it is not a copy of the phenomenon, or, more accurately, the adequate

objectivity of will, but is the direct copy of the will itself, and therefore exhibits itself

as the metaphysical to everything physical in the world, and as the thing-in-itself to

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every phenomenon. (The World as Will and Idea, translated by R. B. Haldane and J.

Kemp, 1883, vol. I, p.340.)

Music ‘restores to us all the emotions of our inmost nature’, the listener under the

influence of musical stimuli is recollecting the primordial contents or a priori giveness of his

mind, which are, as Schopenhauer suggests, identical with the will. Music is also capable to

answer the most fundamental ontological questions more than ‘all the others [arts], since in a

language intelligible with absolute directness, yet not capable of translation into that of our

faculty of reason, it expresses the innermost nature of all life and existence.’ (Schopenhauer,

engl. transl. 1958, p.406) Schopenhauer ignored the phenomenal dimensions in music, its

‘sounding’ character, as well as its perceptional dimension, which later became the central

issue of phenomenology of music.

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Phenomenology and ontology of Music

While the last two chapters were devoted to the two contradictory but contiguous

philosophical conceptions of the metaphysical dimension of music, even not in terms of

autonomous philosophical sub-disciplines regarding ontology of music, the phenomenology

of music is implied discipline concerning with the two main spheres of interest: (i) the

examination of the way how is music perceptually constituted in a subject, emphasizing the

‘phenomenal dimension’ of music, and (ii) with the ontology of music occupied by

ontological status of musical piece.

Edmund Husserl (1859-1938), one o the most influential philosophers of the 20th

century, is regarded as foundator of philosophical phenomenology. Husserl’s interest in music

was restricted to the subjective temporal perception and inner constitution and temporal

organization of sensational data. However, as early as in the Antiquity and Middle Age, the

issue of mental organization of perceived data employed grammarians and philosophers to a

great extent in the discipline of ars memorandi. Aristotle, for example, wrote sole treatise On

Memory concerning the mental act of memory. According to Julius Victor, a fourth-century

grammarian, ‘memory is the firm mental grasp of things and words for the purpose of

invention’, (C. Julius Victor: ‘On Memory’ translated by Jan M. Ziolkowski 2004, p.297).

With reference to Carruthers and Ziolkowski (2004, p.3) ‘...as an art, memory was most

importantly associated in the Middle Ages with composition, not simply with retention.’

Memory was understood as cognitive faculty, which decomposes phenomena into simple

mental components. Husserl examination in phenomenology of music uses similar

methodology as that of the ars memorandi, although he tied up the rhetoric of modern

philosophers.

The phenomenology of music leads us back to the Kantian subjectivism - the

ontological dimension of the work is constituted in the inner action of subject. However,

Husserl refused the idea of exaggerative subjectivism, and did not believe that there are so

many worlds as they appear in individual subjective perceptions. He predicted ONE world

and ONE particular thing-in-itself but many appearances of it (Husserl, 1996, p.43). The

questions concerning with the metaphysics exceeds the borders of the world as a universe of

46

elementary facts (1996, p.31) He believed that the mathematical designation of pure nature

could be implemented through the methods of exactification the continuums, through

transformation of sensual causalities into mathematical causalities (1996, p.303), as it was

explained in the introduction to this writing. The methodology of natural sciences extracts the

truth from relativity of phenomena (1996, p.305), in consequence, the pure nature is

knowable. On the contrary, Kant refused the option of using pure notions of mind

transcendentally, so they could be applied exclusively to empirical experience (Kant, The

Critique of Pure Reason).

According to Husserl, the cognitional ability is invariably fixed to the consciousness

of object and therefore has an intentional nature. Consequently, the hearing cannot be

apprehended separately but with reference to the pitch. Any particular pitch depends on

quantitative specification, on mathematically definable and physically measurable parameters

such as the thickness of a string or its tenseness, and not on qualitative specification, such as

color or even sensational quality (1996, p.306). However, it appears that the ontology of

music differs from that of the pitch. The fundamental argument for this is that Husserl

distinguished between the pitch perceived and the hearing of the pitch. The antinomy between

sound and silence has a new, ontological dimension. Husserl accepted the existence of the

perceived pitch and sounding structures as objective, though this ‘materiality’ of the pitch and

sound structures is not apprehended as ‘music’.

According to Husserl, music has temporal and non-conceptual nature. Forasmuch as

music is constituted in the ‘inner subjective acts’, the subjective temporality became the

central issue of his examination.

It is indeed evident that the perception of a temporal object itself has

temporality, that perception of duration itself presupposes duration of perception, and

that perception of any temporal configuration whatsoever has its temporal form

(Husserl, Phenomenology, p.42, IN: Lippman, 1994, p.438)

The morphogeny of music and its real base lies in the acts of composition and

constitution of temporal sensational data into an object. This transformation is done through

cognitional and perceptual faculties. Husserl established the ontological contrast between

sound and music, between the temporal objectivity and materiality of sound structures and

inner temporal constitution. However, he did not provide further explanation concerning the

formal and conceptual sources of music.

47

Further investigation in phenomenology was concerned with the ontology of music.

Martin Heidegger (1889-1976), Husserl’s successor and critic, did not apprehend

phenomenology as an autonomous scientific discipline but as the method ‘how’ to examine.

However, his interest in the arts was restricted to the general question of its beauty, truth and

existence, music never stood in the main focus of his philosophical examination. Regarding

Husserl’s investigation in the terms of relation between sound materiality and its subjective

constitution, he considered that ‘the art work could not exist without the activity of the artist,

so the artist could not exist without the work of art’ (Stulberg, 1973, p. 257). This statement

reflects a bilateral dependency of objective status of a musical work and subjective status

representing by the artist.

Nelson Goodman and Roman Ingarden, were fully occupied themselves with

philosophical issue regarding ontological status of music. Roman Ingarden (1893-1970) dealt

also with related problems of performance, notation, and authenticity. For Husserl music,

according to its ontological status, was constituted through inner action of perception within a

subject, Ingarden posed quite different ontological point, regarding music not in general, but

music in particular, an actual musical work. The ontological status of a musical is inextricably

linked to the particular work. However, a new methodological problem arises: performance

versus ontological status of a work – the relation between an actual piece of music and its

multifarious performances.

...it is said that each time we hear that sonata [Chopin’s B Minor Sonata] in a

particular performance we hear the same sonata even though it is in every case a new

and somewhat different performance, since the performer and the conditions are

different (Ingarden, English transl.,1986, p.3).

Ingarden considered that ‘...musical work is not the same as its various

performances...’ (1986, p.9) Each performance of a certain musical work: (i) is a certain

individual occurrence (process) developing in time and placed in it univocally, (ii) is above all

an acoustic process, and (iii) is univocally fixed in space, both objectively and phenomenally

(1986, pp.10-11). Every musical work is than an object persisting in time (1986, p.15).

Ingarden, at last, was confronted with the ontological difference defined by sounding

and nonsounding qualities in music. Sounds (Ingarden uses a plural to underline particular

sounds in musical composition) are ‘spatially and temporarily individuated objects’; on the

contrary, a musical work is a ‘supraindividual and supratemporal structure’. The musical

48

work is a ‘multiphased structure in which the basic and elementary phenomena are sounding

or rustling (percussive) qualities’ (1986, p.83).

Ingarden describes the sound quality in music as the ‘chain of sound-constructs’.

However, these ‘sound-constructs’ do not ‘exhaust the work’s constitution, for there are also

various nonsounding qualities and constructs evidently superimposed upon the constructs’

(1986, pp.83-84). The totality of a musical work is constituted ‘when sound-constructs

combine with nonsounding ones’ (Ingarden, 1986, p.84).

The nonsounding elements are ‘not essential to all kinds of musical work just because

they do not appear in all of them’ (1986, p.88). Ingarden categorized the nonsounding

elements of a musical work as:

• Temporal or quasi-temporal structure of a musical work: closely connected with

the ‘properties of sound-constructs’. This temporal structure is also present in what

Ingarden calls ‘multiphased works of art’, such as literature, film, and drama.

• Movement: a ‘quite specific “motion” that accompanies the development of some

musical constructs’ (1986, p.90), e.g. the movement of individual voice in relation

to the others in Bach’s fugue.

• The forms of ‘specific musical constructs’, e.g. the shape and structure of melody

or chord.

• Emotional qualities: ‘They appear upon specific sound-constructs, both of a higher

and of a lower order…’ (1986, p.97).

• ‘Aesthetically valuable qualities’: they include all the nonsounding elements.

Music has an iconic, or representative functions if

a particular work does exercise the function of expressing the composer’s or

performer’s feelings, then the work evidently imparts information about something

other than itself, something which normally belongs to the real world (1986, pp.104-

105).

Ingarden apprehended a musical work as music itself, as the object of his examination.

However, he deviated from the point of his classification of nonsounding elements of a

musical work to the semantic aspects of a subjective perception of a musical work lying in

different methodological area. In the chapter ‘How does a musical work exist?’ of his The

Work of Music and the Problem of Its Identity, Ingarden specified the ontological status of a

49

musical work. Musical work originates in ‘specific, creative, psychosomatic acts by the

composer’. These acts culminate through notation or ‘immediate’ performance what Ingarden

characterized as ‘improvisation’. However, the musical work is not identical with the

‘arrangement of concrete sounds heard in specific performances’, it goes ‘outside the qualities

of concrete sounds’. A musical work is a ‘purely intentional object with its original source in

a specific real object and its ground of continued existence in a series of other real objects’

(1986, p.120).

Contrary to Ingarden, Nelson Goodman in his famous work Languages of Art (1976)

addressed himself to ontology in terms of authenticity and material delimitation of the arts. He

considered the ontological status of music as curious, because ‘music, unlike painting, there is

no such thing as a forgery of a known work’ (Goodman, 1976, p.112). He noted that

copies of the score may vary in accuracy, but all accurate copies, even if

forgeries of Haydn’s manuscript are equally genuine instances of the score.

Performances may vary in correctness and quality and even in ‚authenticity‘ of a more

esoteric kind; but all correct performances are equally genuine instances of the work.

In contrast, even the most exact copies of the Rembrandt painting are simply

imitations or forgeries, not new instances, of the work. Why this difference between

the two arts? (1976, p. 112-113)

On the basis of these and similar considerations, Goodman proposed nowadays

generally accepted categorization of the arts. The work of art might be:

• Autographic: distinction between original and forgery is significant; the most exact

duplication of work does not thereby count as genuine. Therefore, e.g. painting

belongs to the autographic art.

• Allographic: there is no distinction between the duplication of a work and its

original, e.g. music, literary arts.

The further division of the arts depends on the way of how work is done:

• One-stage: work is done by process of writing or painting (e.g. painting, writing)

• Two-stage: work is written but done though the performance (e.g. music, drama)

Therefore music is allographic and two-stage, painting is autographic and one-stage,

and literature is allographic and one-stage.

50

Contrary to the cosmology, phenomenology of music concerns exclusively with music

in particular, especially with musical work itself (Ingarden, Goodman) or with its perception –

particular sensual experience (Husserl). Phenomenology is focused to the ontological status of

musical work and subjective facets of its perception. The absorption in ontological status of

musical work, since the half of 20th century, may relate to augmentative historicism, early

music exploration, problems with definition of authenticity, and particularly to the ambition

of designation the concept of ‘Urtext’ as the clearest representation of composers’ intention.

Coessential for growing concern in ontology are questions of forgery, regarding artificial

work, and delimitation of copyright.

51

Conclusion

The antimony between silence and sound refers to the key issue of ontology of music:

is music explicitly a perceptual phenomenon or universal principle of primordial harmony?

Music as a sound-quality is apprehended perceptually, what can be verifiable empirically;

while music as silence-quality is a speculative, meta-perceptual music - this can be verified

through non-musical phenomena, e.g. planetary motions corresponding to musical

proportions. The basic problem of ontology, even of cosmology of music, is whether these

two opposite qualities are linked together in music, or if they can exist separately. Each

conception of cosmology, presented in this writing, is explaining the different way of linkage

between silence and sound qualities in music: Pythagoras suggests an ontogenetical unity of

all things; Plato believed that reality (sound) has a prototype existence in World-Soul

(silence); Boethius divided the phenomena of music in different categories in qualitative

order: Musica mundana (he believed that it is sonant), Musica humana (silent), and Musica

instrumentalis (sonant); and Kepler attempted to prove harmony of the world (silent)

empirically. On the contrary, Kant rejected knowability of metaphysical dimensions of music.

The Greek set of cosmological axioms could be summarized as follows (according to

Gentner & c., 1997):

• The Earth is at the center of the universe and is itself unmoving.

• The Earth is surrounded by physically real crystalline spheres, containing the heavenly

bodies, which revolve around the Earth.

• The heavenly bodies move in perfect circles at uniform velocity, as befits incorruptible

bodies. (Epicycles and eccentrically positioned circles were admitted into the system

to account for the observed motions.)

• All motion requires a mover. The outermost sphere, containing the fixed stars, is

moved by an ‘unmoved mover’, the Primum Mobile. Each sphere imparts motion to

the next one in; in the Aristotelian universe, there is no action-at-a-distance. In

52

addition, each sphere is controlled by its own spirit that mediates its motion. (The

heavenly bodies were known not to move in synchrony.)

• Celestial phenomena must be explained in entirely different terms from earthly

phenomena. Indeed, heavenly bodies and their spheres are made of different matter

altogether. They are composed not of the four terrestrial elements - earth, air, fire, and

water - but instead of a fifth element (the quintessence), crystalline aether (pure,

unalterable, transparent, and weightless). The further from Earth, the purer the sphere.

However, the exact scheme of the correspondence between the cosmos’ organization

and music has never been drawn. Thus we do not know whether each planet or sphere

represents particular tone or particular interval in dependence on the distance from the centre

(i.e. the Earth before Copernicus). This fact has two possible reasons: (i) the lack of

observational data and (ii) the view about the quality of cosmos. According to Greek tradition,

the universe was divided into two qualities: the ethernal spheres and spheres subjected to

permanent change. The usual distinction line was regarded to be the lunar sphere. The same

dimensions were attributed to human being, which took an inner journey accross the stages

identical with the spheres of the universe. Human being was a mirror of the universe; music

was an universal harmony linking the micro- and macro- dimensions together.

The role of deities in the cosmos was shifted in early Middle Ages. In 543, Justinian I,

Byzantine emperor, issued the decree of nine canons contra Origenem, the sixth canon

suppresses the belief that cosmos and celestial bodies are settled by rational beings (Grosse,

1994).

The first detailed proposal about celestial music was drawn by Johannes Kepler. His

interpretation of celestial music is more sophisticated in terms of modern science. He linked

together the Greek conception of musical numerology with empirics. This view on cosmos,

representing early empirics, was given by new observations and empirical data, and differs

from Greek view in these aspects:

• The centre of the universe is the Sun.

• The universe has a physical substance, and therefore is not divided into ethernal and

corruptive spheres.

• The planets move in elliptic orbits and their velocity is not constant.

• The mover of the solar system is the Sun.

53

• Celestial phenomena must be explained in the same terms as earthly phenomena. The

universe is made up from physical matter.

It is possible to draw parallels among various conceptions of musical cosmology as

well as with contemporary theories. Boethius wrote about the cycles and elements of nature as

a part of Musica Mundana. The same assumption that the variability of nature has its rules

subjected to the proportions of Musica Mundana can be found in Kepler: ‘...soul which we

call sublunary Nature, which controls meteorological phenomena according to the rules of

proportions which occur in the radiations of the stars.’ (Harmonices Mundi Lber III, Source:

Godwin, 1986, p.150). In spite of empirical data, Kepler still believed in astrological

influence on earthly phenomena and human being in terms of harmonic proportions identical

with those of music and carried by species immateriata.

Kepler also made contributions in the field of optics and developed a system of

infinitesimals in mathematics, which was a forerunner of calculus. The superparticular and

reciprocal musical ratios are, in fact, the two infinitesimals having identical limit: number one

- the mathematical basis for universe. Ratios derived from Pythagorean tetractys are

equivalent to the oscillating patterns of sub-elementary particles - so called strings - in string

field theory. The pattern of oscillation based on number or numerical ratio is believed to be

the key feature of the matter. The fact, that this oscillations are supposed to exist in more than

three-dimensional spaces substitute the former myth about metaphysical dimensions. In a

metaphorical sense, the string represents an equilibrial principle that penetrates the whole

cosmos. Once a string is plucked a many of dynamic qualities emerge from quiescent

condition. This is just a birth of sound from the realm of silence.

The early empirics of the end of 16th and beginning of 17th century brought in both

cognitive optimism and ontological skepticism. One might ask why such progressive scientist

as Galileo Galilei took recourse to relationship of simple craftsmen (Heer, 1965). The old

belief of epistemological unity between the universe - an objective world, and human being -

individual subject, was irretrievably lost. Modern scientists turned away from an ‘external

authorities’ and became to understand that experience has a key epistemological importance

dividing the reality into subject and object. This may be classified as ‘ontological schism’.

Kantian approach represents an antipole to the classical cosmology; he refused the

cosmology as an objective authority given to us and hyposthased the epistemological role of

subjectivity. For Kepler, the same rules were applied to the universe and to a man, but Kant

54

defined methodological difference between the universe and subject, between the thing-in-

itself and phenomenon - a thing as it is given to us. On the contrary, Schopenhauer turned

back to the ‘modern cosmology’, when he had introduced the concept of Will objectifying

itself in the universe. Will, analogous to Pythagorean tetractys, is an epigenetic source of all

phenomena.

Sound concepts and sounding structures are not considered to be music in itself

(Husserl, Ingarden). Sound does not exist in ontological terms; it only lasts for particular

period of time as a phenomenon (Kant). Sound is a ‘Heidegger’s phenomenon’ that hints at

something what does not represent by itself. Thus music is reflecting through something what

appears. The existence of sound is nothing but appearance by itself. According to Ingarden

and Husserl, music emerges through interaction between object (sound-concepts) and

subjective perception of this object.

The ontology of music does not mean that music exists in ‘ontological pre-shape’,

because our notion of perceptual music is simply not possible to adopt for ontological status

of music - thing-in-itself, but in epigenetic forms determining subjective perception (Wallin,

1991) there is a real basic - a potential for perceptual music - resting in the state of silence.

According to (i) cosmology of music, these potential epigenetic forms are in basic proportions

of numeric ratios; (ii) Kant, in a priori givenness of mind and (?) body; and (iii)

Schopenhauer, in Will and all its modifications. The primordial pre-shaping of perceptual

physiological options predetermines how music is perceived and predetermines also the

structure of music itself. The theory of ‚Ursatz‘ in Schenkerian analysis suggests implicitly

that music is believed or presupposed to exist in a couple of modifications of the primeval

stable model with many morphodynamic possibilities for further development.

55

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