Chapter 29

Continuation of the cosmological law of harmony.
How it is formed in animality.

1568. We need to investigate more thoroughly the origin of harmony in animality. Although I have indicated its elements and their psychological or cosmological origin, I have still not explained the origin and formation of harmony.
Time and space are as it were the seat of multiplicity in animal feeling, a multiplicity to which the soul gives unity. But there would be no harmony unless there were enjoyment, which must be sought in feeling's 'feel'. This, however, is still not sufficient to complete the concept of sensible harmony. Although every individual feeling has its own 'feel', harmony is the result of several feelings. Even the enjoyable unity of these different feelings comes from the soul. If harmony is to be present therefore, the soul must give its own unity not only to space, which is continuity, and to time, which is duration, but also to multiplicity of feelings. In fact the soul gives unity to this multiplicity, whether the feelings, which arise deep in a calm, fundamental feeling, are of different or of the same 'feel'.(317) But, in order to produce harmony it must do even more: the kind of unity it must give to several feelings (it always and necessarily gives some unity to feelings, of which it is the identical subject), must be an enjoyable unity. This is the kind of unity I wish to explain and distinguish from the unity always present as a result of the identity of the sentient subject.

1569. To explain the nature and origin of this pleasurable unity, we must turn to the universal (ontological or cosmological) laws governing the action and passion of every substance. These laws, applicable also to the sensitive and rational principle, are the following.

1570. The first law states: 'An ens loves the act it has begun, and is distressed if it encounters some impediment which cuts its action short. On the other hand, it experiences enjoyment if the whole act can be unfolded in accordance with its free movement.'

1571. I say 'An ens loves the act which it has begun' because it could not be distressed by an act it had not started. It would simply lack the enjoyment which pertains essentially to every act of a sensitive ens.

1572. I say 'if the whole act can be completed in accordance with its free movement' because, when an ens is about to begin an act, its motion is limited in kind and degree by its own virtuality. The act has a natural conclusion where its motion comes to rest.

1573. The explanation I gave about pain comes under this law, when the law is applied to the sensitive principle. The animal principle, intent on positing its fundamental feeling as fully as possible (life instinct), is distressed if it is impeded from doing so totally; this distress is pain.

1574. The second law is: 'The act begun by an ens is sometimes multiple through succession, that is, results from a series of links which can be considered as a single act through the unity of the ens unfolding its activity in several communicating potencies. In this case the ens seeks to complete the whole series of links right up to the last; it is distressed if its progress is cut short.'

1575. The action of the rational principle, to which the sensitive principle is connected and subordinate, is an example of this law. The action is composed of three links: 1. judgment, 2. affections, 3. external movements. Sometimes however there are four links: 1. judgment, 2. affections, 3. decrees of the will, 4. external acts. The activity of the principle does not normally stop at pure judgment but, seconding the judgment (first link), conceives some affection (second link) for the thing judged good or bad, etc. Nor does it stop here; either it activates decrees of the will followed by the external actions, or affections instinctively produce corresponding movements in the body (third link). Among corporeal movements are vocal sounds, which explains why we are inclined to follow up a vivid feeling with a sound, a natural completion of our sensitive activity drawn into movement.

1576. These sounds, intimately bound as ultimate effects with thought and affection, become natural, external signs by which people who have the same experiences can know what we are thinking and feeling interiorly. But before sounds fulfil this office, they are the spontaneous, natural completion of the human, sensitive, rational act seeking completion and wanting to go as far as it can. We see this principally when we are moved interiorly by some marvellous feeling: we emit a great sound or expression which strictly speaking has no tie with our thought or feeling except as its final expression. For example, in anger we can utter blasphemy or an imprecation against something totally different from what causes our anger, or we may proffer some obscene word or make a meaningless sound, such as babai, papae, capperi. More commonly however we use the name of God to relieve our feelings, that is, we name the greatest thing we can find. Thus in Hebrew 'God' is added as a superlative to all words, for example, 'mountain of God', 'prince of God', etc. meaning the highest mountain, the great prince, etc.(318) The Arabs and all oriental peoples follow the same usage,(319) as does Euripides.(320) We also have an explanation for the origin of swearing and of exclamations instinctively emitted; for example, the Latins used words like Pol, Edepol, Jupiter, etc. A positive law was needed to forbid people taking such an august name in vain, and to restrain human instinct, which could hardly desist from emitting such exclamations. Similarly, in English we make use of whatever is great; we say, 'By heavens!', 'By Jove!', 'My God!', etc. Swearing by someone's head or by a creature almost divinises the thing, and was forbidden for this very reason.

This release of feeling terminating in a word pertains, it must be noted, to the rational principle, and is continued by the sensitive principle. Hence, whatever word or expression is used, the speaker always intends to say something, not simply to make a noise; he intends to say and indicate something exceedingly great, even when the word per se has no meaning. It is a new word invented precisely to terminate the act of the thought which cannot remain shut in but wants to become sensible, to be bound to a reality which makes it more vivid and more consistent with the person who has the thought. As we have seen, this office is usually fulfilled by imagined or, generally speaking, sensible realities expressing internal thoughts. This need to terminate, in a real external act, the act begun in our thought is so great that even when taking God's name in vain is forbidden by divine law, the best human beings still feel the need to do so and, almost to deceive themselves, substitute similar words. Some people, for example, have substituted 'My giddy aunt!' for 'Good God!', and Italian Capuchins came out with the innocent exclamation 'Buzzards!' to express their amazement.

1577. Human instinct seeks to complete the act which is begun in thought, passes to affection, sometimes moves our will to decisions, and terminates in the external act, where we find some expression to emphasise it more vividly. This extremely powerful instinct suffers considerably when so opposed and crippled that it cannot complete its act. It explains many facts of human action.

The law I have mentioned is precisely the reason why people who have suffered some great catastrophe scream and howl, injure and harm themselves, tear their clothing, soil themselves with ashes and mud, beat their forehead, pull out their hair, roll about on the ground, bite and cut themselves, and even commit suicide. It is indeed one of the causes of suicide, as shown by those Indian widows who burn themselves to death on the funeral pyre of their husband.(321) Perhaps people who harm themselves, that is, add more suffering to themselves, are seeking relief from the pain they already suffer. The cause of such incredible cruelty to oneself is the internal act of great sorrow which cannot however be contained and restricted to the first stage. It must pursue its way, be carried out in all its natural extension, increased, finalised, signified and allowed to raise a kind of eternal monument in the wounded person. The hurt we do to ourselves in these conditions is easier to tolerate than restraining our instinct by containing the act of sorrow which begins in thought and finishes in the body as a result of the unity of the animal-intellective subject. This dynamic bond binds together our various potencies, so that the movement of one passes and continues into another. Thus, when people experience great joy, they express their joy externally: they make themselves look good, dress up, dine and wine and converse expansively; and we should not think that they do these things simply to be able to enjoy them better. Instinct plays a large part in making the act of interior joy pass through all its natural cycle, as it were, releasing and exhausting its activity.

1578. What Seneca says is true: 'Small and trouble-free cares are talked about; tremendous cares stupefy.' This stupor is explained by the same law, partly because vehement animal passion upsets the organs which then lose all virtue to further the spirit's movement, and partly because the intensity of the internal act compensates for its extension. Instinct, by increasing the intensity of the act, as it were feeds on and finds satisfaction in its desire and effort to perfect the act of internal sorrow. Consequently, the sorrowing person, unable to find strength to develop the act and communicate it to his external potencies, becomes interiorly hard and unfeeling.

1579. Solitude is loved and sought by those who are deeply afflicted; they can never stop thinking about what causes their sorrow, nor speak of anything except their catastrophe; they have to dissect it, reflect on it in all its minute details, and those who claim to diminish this sorrow become intolerable. All this is the result of the same law, of the same instinct which, using all the activity available to it, strives to complete and perfect the act of sorrow already begun. The act does not remain simply as a seed, but develops a body and grows to fullest maturity.
The same law must also be seen as the cause why tears bring relief to an unhappy person, for whom perhaps nothing is more welcome than weeping. Here the act is finally exhausted. If there were no weeping the incomplete act would remain full of power and bent on coming to fruition.

1580. The same law must also explain the origin of sacrifices to the divinity and particularly of human sacrifices (whose role was subsequently replaced by immolation to God of things very dear to human beings). The feeling of profound humility, of a Lord supreme over all things, and particularly of our need to acknowledge the guilt of our sin before that most powerful and infinite sovereign, requires more than a sterile, cold act of pure thought. It has to be expressed in a very real act which penetrates and dominates the whole of the human being, an act which is naturally infinite because it corresponds to the concept of an infinite ens. The only way a human being can perform this act perfectly is by self-destruction and, more imperfectly, by destruction of his possessions. Strictly speaking the essence of sacrifice, whether the sacrifice is a holocaust or sin-offering, requires the human being himself as the victim; other sacrifices are only a surrogate for the perfect sacrifice. In fact in a holocaust, the act of feeling begins from the thought that 'in comparison with the Creator, the creature is nothing; only the Creator is an ens.' The feeling of nothingness can be expressed sensibly and, so to speak, monumentally, only by destruction. In sacrifice for sin on the other hand the act of feeling begins from another thought: 'The creature who has offended the Creator must not exist'. The thought of undue existence receives its final actuation only by making non-existence real, that is, by destruction. Finally, sacrifice is also an expression of a supreme love. Because there is no act in which love is more intense and operative than in suffering for the loved one, the great lover seeks this act as the ultimate loving effort given him to accomplish. He is invited to this above all when the desperate sorrow for the lost loved one gives him resolve and launches him into cruel acts. Thus, at the death of Patroclus, Achilles' soldiers shaved their heads and covered his body with their hair. The same applies to the cruelties found among all ancient peoples in their burial rites or in their feasts for the dead [App., no. 15].

1581. The third law of harmony, that is, of the fitting action of entia is: 'A simple or multiple act, carried out through several communicating potencies, does not always cease suddenly, but regresses according to a certain law by which it passes through different ordered states in successive series. This gradual passage, right up to the total extinction of the act, is natural and hence pleasant for the subject of the act. When the gradual passage is impeded however, the subject is under stress.'

1582. In Anthropology, I demonstrated this law with an example of imagined colours and sounds.(322) I will make some further observations about these.
Fresnel and Arago's theory about the wave system to explain the phenomena of light was considered very probable. But they limited their studies to laws governing the action of luminous waves of fluid which, they supposed, was diffused through all nature. This however is not sufficient to explain vision. Vision arises in the visual sensory and not in the ether, whose only function can be that of stimulator. The psychologist must therefore avail himself of their efforts in order to know or suggest the way in which the visual sensory might operate when luminous sensations arise in the soul. I think that this difficult question would be considerably illuminated if the findings or conjectures of those two enlightened physicists concerning what happens in the above-mentioned fluid outside the sensory were applied to the sensory itself.

1583. According to this concept the optic nerve would be a bundle of nerve-filaments. The bundle would be filled with an extremely elastic substance (or perhaps fluid) whose molecules received the impression of the ethereal waves and vibrated longitudinally like the string of a violin. The size, speed, number and different contrasts of these vibrations would explain the phenomena of vision.
First of all, different colours would be the result of different numbers of vibrations made by the molecules in the nerve- filament. This number would correspond to the number of ethereal vibrations. We can accept as demonstrated that the number of ethereal vibrations varies according to different colours, for example, those of yellow light are more numerous than those of light which stimulates red.

1584. The speed and size of the waves is in proportion to their number. Their diversity of speed, size and number must mean therefore that similar vibrations take place in the molecules of the nerve substance and, by producing different stimulations, result in different colours. This explains how each nerve- filament is capable of giving the sensation of all the colours by means of the different stimulation it receives from different luminous rays.(323)

1585. Furthermore, vibrations propagated along the nerve-filament would be reflected and turned back on themselves when they reached the extremity, in conformity with some law. Their return would explain how imagined and complementary colours, whose image we have,(324) remain when the external sensation ceases. In fact, a vibration which breaks against an obstacle before completion produces a reflex vibration whose velocity must differ from the first according to a complementary law.

1586. This would enable us to understand why complementary, accidental colours oppose and cancel each other, that is, produce black instead of white. If a complementary, reflex vibration returns in the nerve-filament, while the eye is impressed by the same colour, a vibration must be produced in the opposite direction, leaving the pupil at rest. Let us consider an experiment known to physicists.
Suppose that two small, coloured squares, one violet and the other orange, each with a black spot in the centre, are placed on a black background. If we look alternately at each spot for a second and then close our eyes, we will seem to see three squares, one yellow (which is the complementary colour of violet), the other blue (the complementary of orange), and the third (in the middle) green, the result of the composition of yellow and blue. On the other hand, if the two squares themselves are complementary colours, for example violet and yellow, or orange and blue, the middle square is no longer visible, that is, it becomes black.

The explanation of these phenomena seems to be the following:

1. When we look successively at the two coloured squares, our optic axes have different directions. The squares therefore strike the retina in different spaces so that each eye has the impression of two squares, in all four impressions. But two of these impressions, one of one square, the other of the other square, strike the same space in each retina, because the optic axis of one eye has the same alignment on one colour as the optic axis of the other eye has on the other colour. As a result the impressions of two colours strike the same space of the retina of both eyes. Nevertheless, as long as both eyes are fixed on the squares, they see only two squares, either because the impressions have no time to combine, or because the spontaneity of the soul does not co-operate in producing images in the phantasy, or because the attention is turned solely to looking at the two squares without interest in anything else.

This is not the case with the imaginary colours that follow. The impressions on the three different spaces in the two retinas must result in three series of longitudinal vibrations in the nerve-filaments. The two spaces impressed by a single colour must each produce the complementary colour as an imagined or reflex colour, because the reflex vibration must complement the stalled vibration. The space between, impressed contemporaneously by the two colours, must produce reflex vibrations complementary to the individual colours. These reflex vibrations are not confused because they vary in size and speed. Now, since a nerve-filament can produce only one sensation at a time proportioned to the number of its molecules, the result must be a colour composed of the two complementary colours. But if the two colours of the squares are themselves complementary, it is clear that the vibration caused by one of the colours must, while on its way from the outside to the inside, meet the perfectly equal reflex vibration of the other colour moving in an opposite direction from the inside to the outside. In this way the two series of vibrations cancel each other: the two series moving outwards destroy alternately the other two reflected series which are returning.

1587. The same hypothesis would also explain why a colour, before ceasing in the eye, leaves behind other colours, for example white becomes yellow, then red, indigo, blue and finally green, when it disappears. If we consider that the molecular vibration which reflects from the external extremity of the nerve-filament is complementary to the colour impressed on the retina, we can conceive that the reflex, complementary vibration breaks once more as soon as it reaches the extremity of the nerve-filament. It must then return from the outside to the inside with a different speed. This outward and inward movement of ever-changing waves must result in different, imaginary colours until excitation entirely ceases or the vibration becomes so small that it is insufficient to produce a distinct colour.(325)

1588. Similar reasoning could be used to explain the laws of mechanics according to which the acoustic nerve is stimulated by sound. I think it also very probable that the sensations of all the other sensories arise from similar vibrations and obey analogous laws.

1589. Now, if every subject enjoys its act (first law) so that any impediment to the progress of the act or any disturbance which forces the subject to cut short one act and undertake another is distressful, then the sensitive soul must welcome 1. vibrations of sensory molecules which produce a greater feeling in the soul, 2. vibrations which develop harmoniously without clashing, and finally, 3. vibrations which work together to increase stimulation as much as possible. This explains the pleasure we receive when some colours and sounds harmonise, and our various levels of displeasure with other colours and sounds. As I said in Anthropology, natural and spontaneous vibrations must produce pleasing colours and sounds. This is true also for imaginary and complementary colours and sounds, that is, those to which the mechanics of the nervous system are spontaneously determined. Because these are pleasant, the external impression simply associates itself with the sensitive spontaneity, which it helps by alleviating the effort contributed by the sentient principle's activity. On the other hand, the sentient principle is distressed and suffers discord and disharmony when it experiences 1. contrary excitations, or 2. excitations which are confused and mutually obstructive, so that it cannot complete the sensitive acts it has begun, or when new excitations force it to change to different acts and abandon the first.

1590. I will use this theory to explain harmony and consonance of sounds.

First, if several sounds began from the same point and at the same time, they would produce only one sensation corresponding to the vibrations of the nerve-filament they stimulated. This is proved by Savart's experiment. He made a ratchet turn in such a way that the teeth struck a rigid piece of paper. When the wheel turned slowly, the strikes made by the teeth against the paper could be distinguished because of the noticeable interval of time between them. But if the wheel's movement were greatly accelerated, only one continuous sound was heard, whose sharpness increased with the speed of rotation, resulting in a vibration of higher frequency. The explanation is that the individual strikes succeeded one another with the smallest interval of time, that is, smaller than the interval necessary for causing a sensation. Several acoustic sensations cannot harmonise unless the air vibrations strike the ear at the same time or begin from different points, in which case they act on a different nerve-filament.

1591. Harmony is possible both between successive sounds, provided they are separated by a very short interval, and between simultaneous sounds coming from different points, for example, from the different instruments of an orchestra. The harmony of successive sounds, such as those of an individual singer or instrument, must stimulate sensation in the same nerve-filaments, but there can be no pleasure unless the soul, which receives the different sounds, makes them simultaneous through its own nature which is immune from time. It is the soul which feels only a single feeling resulting from several successive sounds. This is a feeling of melody, another proof of the simplicity and identity of the sensitive principle at different times. In fact, the act of the fundamental feeling has a constant duration; successive sounds are simply modifications of this identical feeling. In this feeling successive sounds are compared and posit the pleasant harmony called 'melody'. Once again, we see how the unity of harmony is entirely psychological in origin.

1592. But according to the law I have enunciated, this pleasure arises in the essentially sensitive soul because two or more successive sounds are natural and spontaneous to it. The soul easily exercises its activity on them and produces sensitive acts without being cut short or obstructed, or forced to change them before they are completed. The reason is that 1. pleasure always arises in the soul from each of its acts, because feeling is always pleasant for it - this is not harmony but ordinary pleasure which suffers when individual acts are cut short - and 2. pleasure arises in the soul from several acts, provided one act helps rather than disturbs another - this is the pleasure of consonance or harmony.

1593. In fact the soul takes pleasure whenever it carries out its act with the greatest possible ease and least possible fatigue. This happens when it is not forced to change its act. Consequently the regularity of its acts is pleasing because regularity does not require change in the kind of action it is doing, but preserves the rhythm or form of its the action without additions and alterations.

1594. This explains why harmonic sounds consonant with each other are produced by a number of vibrations whose mutual relationship can be indicated by whole numbers, 1, 2, 3, etc. without fractions. As a result the size of the vibrations corresponds to those numbers, so that two or three or four, etc. vibrations of one sound are exactly equal to one vibration of another sound. Similarly, the velocity of the vibrations of one sound are precisely double or triple or quadruple that of another, with no remainder. Vibrations distributed in this way 1. are never confused or impeded, 2. have easily perceptible relationships, which 3. are always the same, so that the rhythm is of a constant measure. Hence the soul, which must co-operate with its activity in the production of these sensations, immediately finds the law for producing them. In other words, its action is regular. This regular form produces habit which makes the soul's action spontaneous and extremely easy. If we want to know which sounds harmonise best, it is sufficient to note the sounds produced by ethereal vibrations whose relationships are expressed by whole numbers. The octave, for example, corresponds to these numbers; its vibrations are 1 to 2. The harmony of a fifth has vibrations of 2 to 3; that of a fourth, vibrations of 3 to 4;(326) and that of a third, 4 to 5. The number of vibrations of the consonances called 'perfect' (fa-la-doh, doh-mi-so and so-ti-re) is always 4, 5 and 6.

1595. We see therefore that divine wisdom ordered external, corporeal things so that their laws might help the soul in its acts. We know for example that a vibrating cord not only vibrates as a whole, but also in halves and in quarters, etc. As a result, other sounds and harmonising sounds are felt together with the sound of the whole cord.(327)

1596. The same explanation applies to consonances which arise from simultaneous sounds coming from different points. Although we suppose that discordant sensations are received by different nerve-filaments to prevent their being confused, the soul's spontaneity nevertheless co-operates in producing them. If therefore the number of vibrations is not correctly and exactly interrelated, the soul is always obliged to act irregularly and to vary the rhythm of its action. This confirms and seals what I said, namely, that the unity of harmony is psychological in origin, although the spontaneity of the soul may be stimulated either regularly or irregularly by external stimuli which change its term.

1597. Finally the reason why the regular beat of time is pleasant is found in the same law governing the soul's action.

1598. From all this we can conclude:

1. The corporeal world, thanks to the wonderful order it has received from creative wisdom, can bestow order and harmony on feeling and on the rational principle.

2. This order lies not only in things external to us but in our own organisation (to which I will return later) and in the exquisite composition of our sensories, all of which are designed and arranged with such art and mastery of proportion that they correspond wonderfully to and accord with the proportions of the external, material world.

3. The sensitive principle itself accepts this wonderful order in the external world and in its term (the sensories), while with its own activity it posits form. The external world, which per se would not have the nature of order, proportion and harmony but only of separate, disjointed entities and actions, receives all these things from the sensitive principle through the unity created by the principle itself in that appropriate multiplicity. This last formal part of harmony, although not of rational origin, is nevertheless psychological in origin because it comes from the soul as sensitive.

Notes

(317) Feelings that have the same 'feel' are distinguished from each other only by 1. the different space which is their term in the calm-fundamental feeling, 2. the different time, when they are successive, and 3. the different intensity or degree.

(318) Gen 23: 6; Ps 35: 7; Ps 67: 16; Song 8: 6; Is 28 [27]: 2; Jn 3: 3.

(319) Cf. Schultens, Not. ad Haririi consess ., 4, n. 76.

(320) Eurip., Orest ., 5: 1172.

(321) It is well-known how difficult it has been for the English to abolish this custom in India, where the sublime act is repeated from time to time. Similarly ancient legislators had to enact very strict laws to forbid certain acts of cruelty in which people scourged themselves with serious consequences. The Twelve Tables prohibited women from cutting their cheeks: Mulieres genas ne radunto . 'In this place,' Festus explains, "cut" means "cut with their nails"'. Plutarch, in his life of Solon, narrates that Epimenides put a stop to the excessive cruelties which the Athenians practised on themselves at funerals. The Hebrews were forbidden to slash their limbs and tear themselves with their nails (Lev 19: 28) or shave their beards (Lev 19: 27), a sign of sorrow among the Egyptians. Nevertheless we see in the books of the prophets that the people could not totally abstain from practising such customs (Jer 41; Ezek 5; Gen 50).

(322) AMS , 443-454.

(323) AMS , 104.

(324) Cf. the theory I have put forward about phantasy in AMS , 350-366.

(325) It may perhaps be objected that nerve-filaments must vary in length in different-sized people, and hence the same phenomena are not verified in all human beings, as in fact is the case. I reply: the wisdom of the Creator was able to make the number of vertebrae, teeth and, generally speaking, bones, muscles, etc. the same in every human being. We can therefore suppose that with the same wisdom he made the number of elastic molecules in each filament of the optic nerve the same for us all. The vibrations must therefore be the same for a given number of molecules. That the molecules could vary in size, etc., would cause no difficulty. Nor can we say that optic sensations are perfectly equal in all of us; we can only say they are analogous. Indeed, to know whether the sensations in several human beings are totally and in every respect equal, we would need to compare them. This we cannot do because we have no awareness of others' sensations, only of our own. Moreover some diversity must evidently exist, if we note that when people see the same colours, they do not all have the same feelings; their feelings can vary at least in intensity.

(326) Professor Toscani assures me he has observed that babies begin by making a unisonal sound, after which their next baby noise jumps a fourth.

(327) Cf. AMS , 434 for the correspondence between the external world and the soul.