the search for meaning, mathematics, music, and ritual - frits staal

THE SEARCH FOR MEANING:MATHEMATICS, MUSIC,

AND RITUAL

FRITS STAAL

"Some say this is Napoleon, some Hitler, some Mussolini.For me it is simply allegro con brio. "

- Toscanini on Beethoven's Eroica

INTRODUCTORY NOTE

The Agnicayana, a 3,000 year old Vedic ritual, was performed in1975 in a village in southwest India by Nambudiri brahmans. Theceremonies, which lasted twelve days, were filmed, photographed,recorded, and extensively documented. Robert Gardner and Iproduced a 45-minute film entitled "Altar of Fire." A definitiveaccount was prepared in collaboration with the chief Nambudiriritualists and other scholars, and was published in two illustratedvolumes entitled Agni-The Vedic Ritual 01 the Fire Altar (Staal1983a).

While I was engaged in the preparation of Agni, itself primarilyan empirical account, I became involved in methodological andtheoretical issues and problems. I consulted the Indian Brhmal).aliterature, which has engaged in the interpretation of Vedic ritual onan extensive scale, albeit haphazardly. However, the structure of theceremonies, which to me had become intriguing, was not explained orelucidated by the Brhmal).as, just as it had not been explained orelucidated by the Nambudiri brahmans themselves. Since I foundnothing I could use in the works of modern scholars-whether theywere anthropologists, psychologists, or phenomenologists of religion

American Journal 01Semiotics, Vol. 2, No. 4 (1984), 1-57

2 FRITS STAAL

-I had to strike out on my own. In the second volume of Agni, Iincluded a chapter on ritual structure. I dealt with this topic in a morespeculative context in the Inga/ls Festschrift (StaaI1980a). I gave ventto my dissatisfaction with existing approaches to the study of ritual inan article in Numen (StaaI1979). The Indian science of ritual was thesubject of a monograph published by the Bhandarkar OrientalResearch Institute, Poona (StaaI1982a). In the present essay, some ofthe results of these earlier efforts are combined and integrated, theapproach is generalized, and the conclusions are more definite andpositive.

I am grateful to Terri Masson for comments on an earlier draft ofthis essay, and to Charles Chihara for scrutinizing the section on thefoundations of mathematics and for drawing my attention to the workof Saunders Mac Lane. The section on music could not have beenwritten without the generous assistance of Paul AttineIlo, who helpedme find books and examples, and who explained, played and sangmusical phrases and themes for my benefit. I am grateful to hirn andto Norm Furuta who suggested the reference to Doctor Faustus. Iremain responsible for the idiosyncracies of the exposition.

1. TRADITIONAL APPROACHES TO RITUAL

Ancient India developed a science of ritual that was primarilyconcerned with formal features.! The Western attempts atunderstanding ritual are of more recent date, and have not yet growninto a single scientific discipline. The practitioners of the disciplinesthat have studied ritual have generally regarded it as a symbolicactivity. The reason for this prejudice is that the first Westerners whospeculated about ritual were Christians, who regarded ritual as part oftheir religion, and assumed accordingly that it symbolized religioustruths and values. In India, this course could not be adopted becausethere is no concept of religion, and ritual has always been more basicthan truth or value. The sources of the Christian preoccupation withthe symbolic interpretation of ritual He in the CarolingianRenaissance, when the idea was first formulated that the ceremoniesof the church express and symbolize the coming of Christ and thehistory of salvation. With the Protestant emphasis on scripture andfaith, ritual receded to the background. However, in more recentdevelopments within Christianity, Protestant as weIl as Roman

THE SEARCH FOR MEANING 3

Catholic, the place of ritual or liturgy continues to be a topic ofdiscussion. In India, too, ritual or karman has been debatedceaselessly by philosophers and theologians. This goes back as far asthe early Upani~ads and the beginnings of Buddhism in the sixthcentury B.C.

The first Western philosophers and scholars outside the Christiantradition who recognized the importance of ritual continued to place itunquestioningly within the domain of religion. For Hegel, ritualstands at the center of the religious process, where the subject"participates in the absolute and is united with it."2 E. O. James(1917,215) expressed his views in less pompous but equally vacuousterms: "Generally speaking ritual evolved long before belief, sinceprimitive man is wont to 'dance out his religion'." The first seriousscholar who demonstrated the primacy of ritual over belief was W.Robertson Smith, author of a nineteenth century classic, the Leetureson the Religion 0/ the Semites of 1889. This view was incorporated inhis philosophy by Ernst Cassirer, who regarded man primarily as a"symbolizing animaI" but accepted at the same time that ritual wasprior to "dogma," both in a historical and in a psychological sense(Cassirer 1925, 11, 270-285). For Cassirer, therefore, ritual is to beinterpreted in symbolic terms, but since the symbols cannot refer tofeatures of belief, the question arises what they do refer to.

Doubts were cast on the idea that ritual is part of religion and onthe symbolic character of ritual by the founders of the "sociology ofreligion," Emile Durkheim and Max Weber. Durkheim was clearerand more methodical than Weber, his slightly younger contemporary,but he did not go as far. Though he saw clearly that religion is related,through ritual among other things, to social facts and institutions, hedid not question the view that ritual is part of religion. On thecontrary, he formulated that view with classic succinctness at theoutset of his book Les/ormes elementaires de la vie religieuse of 1912:

Religious phenomena are naturally arranged in two fundamentalcategories: beliefs and rites. The first are states of opinion, andconsist in representations; the second are determined modes ofaction. Between these two classes of facts there is all thedifference which separates thought from action (Durkheim 1912;English translation of 1915, 36).

4 FRITS STAAL

Following this statement of principle, which he adopted in theorganization of his book, Durkheim briefly and tentatively discussedthe two categories, but did not question their relationship: "It ispossible to define the rite only after we have defined the belief."

Durkheim's view of the primacy of belief over ritual, which was astep back from the position that had already been reached byRobertson Smith and others, has remained the preponderant view thatunderlies most Western studies of ritual. One reason for thispreponderance is that this view combines more easily with the beliefthat ritual is symbolic than that it is not: for it can then be simplymaintained that ritual is a symbolic representation of what peoplebelieve. In his discussions of ritual, Durkheim did not nlake much useof the category of "symbol,"3 but he referred throughout his book torites in terms of the human mind, e.g.: "Rites are a manner of actingwhich take rise in the midst of the assembled groups and which aredestined to excite, maintain or recreate certain mental states in thesegroups" (page 10), or: "At bottom, all these different practices areonly variations of one and the same theme: everywhere their basis isthe same state of mind, interpreted differently according to thesituations, the moments of history and the dispositions of theworshippers" (page 388).

There is a curious consequence of this approach to human ritual.Basing hirnself upon earlier ethnographie and ethnological investiga-tions, Durkheim paid much attention to the toternie cult. Of his ninechapters on "elementary beliefs," seven deal with "toternie beliefs."Toternie cults involve a close union between men and an animal species.If anthropologists had tried to interpret this phenomenon in the lightof the natural relatedness that exists between the human animal andother animals, they would have welcomed the facts about animal ritu-alization when these became known. But since they emphasized sym-bols and the human mind, anthropologists have been resistant to theidea that animal ritualization has anything to do with human rituals:for this would then involve the assumption that animals also have hu-man minds and beliefs. To a logician,.a different conclusion followsalmost immediately through contraposition: since animals have ritual,but do not have human minds or beliefs, ritual cannot be symbolic.

Durkheim's own analysis of rites throws doubts on his theoriesabout ritual. Discussing data from the Australian tribe of the Aruntamade available by Spencer and Gillen, he focussed on a significantfeature that the authors themselves did not seem to have noticed.


their first book, these ethnographers had analyzed a ceremony calledintichiuma, which was "destined exclusively for the assurance of thereproduction of the totemic species, and it seemed as though it oughtto lose all meaning, if this unique function were set aside" (Durkheim1915, 383). But in a later work by the same authors, the sameceremony was discussed as part of the initiation ritual, in whichfunction it was called by a different name: mbatjalkatiuma (page 384).Durkheim concluded that "according to the circumstances, one andthe same ceremony serves two distinct functions" (page 385). Hereferred to Hubert and Mauss, who had already pointed out afunctional ambiguity of the same sort in the "Hindu sacrifice," andthen expanded his conclusion as folIows:

This ambiguity shows that the real function of a rite does notconsist in the particular and definite effects which it seems to aimat and by which it is ordinarily characterized, but rather in ageneral action which, though always and everywhere the same, isnevertheless capable of taking on different forms according to thecircumstances. (page 386)

The idea that a single rite serves different ends would seem to suggestthat ritual is to some extent independent of the ends it is supposed toserve; but Durkheim did not draw this conclusion or even considersuch a possibility. Neither did van Gennep, who had made the samediscovery two years earlier, when he observed that: "the same rite,remaining absolutely the same, can change its meaning depending onthe position it is given in a ceremony, or on whether it is part of oneceremony or another. The aspersion rite ... is a fecundity rite in-marriage ceremonies, but an expulsion rite in separation ceremonies"(Van Gennep 1910, in: Waardenburg I, 1973, 299).

Van Gennep's observation remained virtually unknown, since itoccurred in a lecture delivered at the University of Brussels, which waspublished in French and Dutch in 1911, and in English translationonly in 1973. An English translation of Durkheim's work, on theother hand, was published in 1915, three years after the original hadappeared. Durkheim's work was very influential in France, andbecame widely known in the United States after the Second WorldWar. But Durkheim's observations on the functional an1biguity ofrites have not attracted any attention, and nobody has detected theirimportant theoretical implications.

6 FRITS STAAL

Weber studied religion within the context of society and in asimilar spirit as Durkheim had done. However, opposing currenttheories, he did not take it for granted that symbolization was one ofits important features. At the outset of his book on the sociology ofreligion,4 he interpreted magie, which is closely related to rites, as adirect manipulation of forces, which at first refleets some kind ofnaturalism, and is subsequently transformed into a symbolic activity:

Various consequences of significance to magical art emergedfrom the development of arealm of souls, demons, and gods.These beings cannot be grasped or perceived in any concrete sensebut manifest a type of transcendental being which normally isaccessible only through the mediation of symbols andsignificances, and which consequently is represented as shadowyand even unreal. Since it is assumed that behind real things andevents there is something else, distinctive and spiritual, of whichreal events are only the symptoms or indeed the symbols, aneffort must be made to influence, not the concrete things, but thespiritual powers that express themselves through concrete things.This is done through actions that address themselves to a spirit orsoul, hence done by instrumentalities that 'mean' something, Le.,symbols. Thereafter, naturalism may be swept away by a flood ofsymbolic actions. (Weber 1922; English translation, 1963, 6-7)

Waardenburg (1973, I, 49) has correctly emphasized that Weber's was"a new view of religion which worked against a German traditionstressing the mythological and symbolic aspects of religion." Animportant implication of this view is that ritual has to be primarilyunderstood without reference to the symbolization which wasattached to it only afterwards. Weber himself, however, wavered, anddid not draw any such conclusion. Both he and Talcott Parsons in hisinfluential Introduction to the 1963 American edition of the SociologyofReligion were more interested in the later symbolic derivations thanin the original "pre-animistic naturalism" somewhat murkilypostulated by the theory. Weber had become famous on account ofhis ideas about the relatedness between Protestantism and Capitalism,welcomed especially in the United States where they were interpretedas an endorsement of both. He came to issue pontifical statements nolonger consistent with his original insights, e.g.: "Events are not justthere and happen, but they have a meaning and happen because of

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that meaning." Such statements have become part of the credo ofcontemporary anthropology in the United States, where they arehighlighted in popular readers on cultural anthropology withsentimental titles such as Man Makes Sense. 5

The fashionableness of such views should not obscure the factthat they are wholly atavistic and metaphysical. No scholar or scientisthas adequate grounds for assuming that the data he seeks to interpretand explain are meaningful to begin with. Nature and culture aregoverned by chance, for example, as much as by necessity.Openmindedness with regard to such questions is required as a matterof course in the natural sciences. In the human sciences, suchopenmindedness cannot be circumvented by defining man apriori anddogmaticallyas "the animal that makes sense. " The unproductivenessof such an approach is particularly clear in biology, where many of themost interesting problems, which also involve the human animal,revolve around the question whether some of the phenomena can beshown to "make sense," or are merely due to chance (see, e.g.,Monod 1970).

Durkheim and Weber created the sociology of religion, and it islargely due to them that religion and ritual are nowadays studied notonly by scholars of religion and religious scholars, but also byanthropologists and sociologists, who should have less of an axe togrind. This development constitutes a significant and valuablewidening of perspective. However, Durkheim's return to a view thathad already been abandoned by others for good reasons, and Weber'sinconsistencies have also created a great deal of confusion. In thestudy of ritual, in particular, it is not possible to derive much helpfrom their insights. The real issues continue to be obscured by thecontinuation of syrrlbolic interpretations, due not only to the factsthat Durkheim and Weber had wavered, and that the break withthe past had not been radical, but also because of the general searchfor meaning as a substitute for religion that characterizes Westernman in the twentieth century.

The only scholars who freed themselves from these overbearingpreoccupations of their own culture were fieldworkers who immersedthemselves for extended periods of time in a foreign culture withoutlosing their rationaloutlook and common sense. Malinowski, forexample, originally a physicist and accordingly equipped with a goodmeasure of reason and rational training, spent several years with theTrobriand Islanders and in other parts of the Pacific. He recognized

8 FRITS STAAL

some of the functions of ceremonies in terms that are reminiscent ofDurkheim but that are much clearer than anything either Durkheim orWeber had written about ritual:

We may, therefore, lay down the main function of initiationceremonies: they are a ritual and dramatic expression of thesupreme power and value of tradition in primitive societies; theyalso serve to impress this power and value upon the minds of eachgeneration, and they are at the same time an extremely efficientmeans of transmitting tribai lore, of insuring continuity intradition and of maintaining tribai cohesion. (Malinowski 1948,in Waardenburg 1973, I, 555)

This statement rings true, but though it makes use of the notion of"expression," it has nothing to do with symbols or meaning. It ispartly applicable to other animals than men, and is moreover not onlytrue of other rites, but applies to many human institutions(universities, for example).

All these different unsuccessful attempts at characterizing ritualteach a lesson that is already known to many philosophers:symbolization requires n1inds and beliefs. Therefore, to grant thatritual is prior to belief, but to persist in trying to interpret it in terms ofsymbols is a hopeless task. If ritual is prior to belief, as it happens tobe in the scheme of evolution, it must be interpreted in differentterms.

2. NEW PERSPECTIVES ON RITUAL

How, then, is it possible to understand ritual without interpretingit in terms of symbols, meaning, or sense? In order to achieve such anunderstanding we have to do three things, more or less at the sametime: first we must have an open mind with regard to the conceptualquestion where ritual "belongs." We should detach it in particularfrom those domains where our culture and history have beenpredisposed to place it: in the realms of religion and society. Second,we must study ritual in much greater depth than is done by theprofessional students of religion and society. And third, we shouldconceive of ritual in more general and abstract perspectives than hasever been attempted. I shall take up these three topics one by one, and


then concentrate on the third, which is the subject proper of thisessay.

Detaching ritual from religion, anthropology and sociology is notmerelya mental exercise, but a necessary methodological prerequisite.Since it amounts to a basic change of perspective, it requires specialeffort. Fortunately there are two kinds of circumstantial evidence thatcome to our assistance in attempting to achieve such a turn of mind.The first consists in the realization that the interpretation of particularrites by scholars of religion and anthropologists are often inconsistentwith each other, and are sometimes different within each of thesefields. This holds for the opinions reviewed in the first section, andalso for the Indian BrhmaI).a literature, which is replete with fancifuland incompatible interpretations of ritual (for an example, see belowpage 42). The "functional ambiguities" detected by Van Gennepand Durkheim provide even more explicit illustrations of thesedifficulties. Once such inconsistencies of interpretation are met with,we should be prepared to accept that we may be barking up the wrongtree.

The second kind of circumstantial evidence that may help us todetach ritual from religion and anthropology comes from the conceptof ritualization that has been adopted in the description of animalbehavior. This has led to a new science, ethology, whose roots He inanother nineteenth century classic: Darwin's Expression 01 theEmotions in Men and Animals of 1872. Contemporary zoologistshave interpreted ritualization as a change in the function of a patternof behavior, often serving the purpose of communication. We shouldbe careful, however, that we study the parallels between human ritualand animal ritualization without necessarily adopting the interpreta-tions of the scholars and scientists who provide us with the data. Justas the rites of men may have nothing to do with religion or socialstructure, the rites of animals may have nothing to do with emotionsor communication. What is uncontroversial is only that the detailedformal paralleis between human and animal rites and rituals castdoubt on all religious, anthropological and sociological interpreta-tions, since for any of these to be true it would be necessary to assumethat animals that perform similar rites as men have similar religious orsocial characteristics. Such assumptions are, of course, far-fetchedoutside the realms of mythology and the fairy tale. Animals do haveaspersion rites, for example, but these express neither fecundity inmarriage ceremonies, nor expulsion in separation ceremonies.

10 FRITS STAAL

The second prerequisite for an openminded and non-symbolicunderstanding of ritual is that we should study rites and rituals ingreater depth. This may seem obvious; yet, it is rarely done in thedisciplines 1 have so far considered. Since the most sophisticated ofthese, in matters of ritual, is anthropology, 1 shall illustrate my claimwith the help of the work of the anthropologist Raymond Firth, pupiland successor of Malinowski at the London School 0/ Economics,who wrote several books and articles on Tikopia, a small Polynesianisland with a population of little more than 1,200 and comparativelyisolated from Western influence. It is not my aim to criticize Firth,whose data on ritual are among the best in contemporaryanthropology, but to illustrate from his work the inherent limitationsof the anthropological approach to the study of ritual.

Among the ceremonies the people of Tikopia perform forchildren there is a "fire formula" recited to a new born baby by aneIder while an assistant lights a torch so that the light falls on the faceof the child. The reciter then addresses the man who holds the child,and his principal deity as weIl:

Pa Fetauta! Assist me at the fire of Pa Tafua which is being set up.Unfold welfare here.

This is followed by a long recitation in which there is some variation,and which Firth has therefore described as a "free formula":

Thy fire Pa Tafua has been announced to theeUnfold welfareThat the child may sleep weIl.Thy fire Pa Saukirima O!Recite hither for welfare for herTo sleep weIl.My own fire Pa KorokoroLight be your eyesUnfold welfare for herPerfume a thing for her to eatThat the child may sleep weIl.From its recitation that has been performedClear be its eyes for the work.Wake up you for the taroTo be industrious in the clearing of the taro

11I THE SEARCH FOR MEANINGTo be healthy for your work.Wake you up to go and clear for taroThe taro which stands overgrownTo be cleared on the moment and finishedWake you up and the seedlings that I filled tie up completely to be

carried on your backHasten you and when your parents are hungry go to the woods to

gather food for your parents to come and cook it in the ovento be done quickly for your parents who hunger to be filled.

To go and get foodTo go to the waterTo carry a water-bottleFor your parents to drink.Be fit in your water-carryingStride off, stride backWe who are thirstyNow have become filled.Climb up there to the mountain standing thereThat you may be fit simply to get food.Cut the leaves of giant taro which stands, to lever it out and

proceed hither.Light the ovenCook it till it is doneGo and fetch the food-kits of your parents to put it inThen we are filled.Go and fetch the water-bottleThen we have drunkThen we are filled.Indeed you are industrious.Stand at the oven-border to uncover the oven at once to fill the

food basketsGo and give them to your parentsFHI the baskets of the relativesClear be your eyes for the fishingThe fish goes to a distance but bar it to dash hither to rest in your

netWe have eaten of your nettingThe fish that goes to a distance be turned by you to enter the netWhen your parents are hungry, go and catch fishTake your torch, go and take your net to go and fish.

12 FRITS STAAL

Go and parcel up; parcel up a package for your parents and givethem to eat

Parcel up a package for us relatives to carryParcel up a package for your brothersParcel up a package for your sistersThere they have eaten completelyThere have eaten completely the relatives, and I have eaten of the

packageGo and roast, there it is cookedGive to eat, there I am filledAnd distribute then to the relativesThere they have eaten completelyGo and give to your grand-parents; go and give to your fathers;

go give a package to your mother; go and give a package toyour brothers.

Then if there is one left, go and give a package to your brotherThere we have eaten of your food-procuring.

(Firth 1967, 53-55)

Firth observed these ceremonies in 1928-29. By 1952-53, when hevisited Tikopia again, he found that they had been much abbreviated.The question which naturally arises is whether the 1928-29performances themselves were abbreviations of earlier forms. Firthhas not raised this question, but he says in general about the historicaldepth of his data: "For about two centuries back from the presenttime the data are fairly clear, but beyond this they become veryimperfect and soon can be regarded only as myth" (page 28).

Using data such as these, Firth has formulated his views on ritualin tentative terms in his Introduction:

The notions of ritual and its close analogue ceremonial havebeen much debated in social anthropology. My own view is thatthe most convenient way to look at ritual is to consider it as aformal set of procedures of a symbolic kind, involving a code forsocial communication, and believed to possess a special efficacyin affecting technical and social conditions of the performers orother participants. The forn1ality of these procedures lies in thefact that they are directed not simply to the solution of animmediate technical problem by the most economical means, butare regarded as having in then1selves a certain validity irrespective


of their technical concomitants. Because of their general validity,apart from the individual situation, they tend to be given arepetitive routinized character which in itself is regarded asstrengthening their significance. This significance is basicallysymbolic in that the physical behaviour of the participants 'standsfor' relations of another kind, as between man and an aspect ofNature or man and putative spirits. Many rituals are performedto maintain an existing situation from degeneration; others tochange the situation, if only to restore it to an original state ofwell-being. Ceremonial (ceremony) I regard as a species of ritualin which, however, the emphasis is more upon symbolicacknowledgement and demonstration of a social situation thanupon the efficacy of the procedures in modifying that situation.Whereas other ritual procedures are believed to have a validity oftheir own, ceremonial procedures, while formal in character, arenot believed in themselves to sustain the situation or effect achange in i1.

(pages 12-13)

In the ancient Indian Vedic ritual several rites and recitations occurthat are to some extent similar to the Tikopia ceremonies. When fire(Agni) is to be generated by rubbing two pieces of wood together, theAdhvaryu, chief priest of the Yajurveda, says to the Hot, chief priestof the ~gveda:

Address Agni who is to be churned!

The Hot now recites three verses from the ~gveda, the first one threetimes:

We implore you for our share, god Savitr,owner of all that is worthwhile, always assisting!

(~gveda 1.24.3)

Great heaven and earth must mix this ritual for us;assist us with their support!

(RV 1.22.13)

Atharvan churched you, Agni, from the lotus;priests from the head of the universe.

(RV 6.16.13)

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When fire flares up, the Adhvaryu speaks to the Hot again:

Address Agni who is born!

The Hot recites:

And people will say: Agni, killer of the demon, has arisen,who in each fight wins booty. (RV 1.74.3)

When fire is about to be installed on the altar, the Adhvaryu says tothe Hota:

Address Agni who is thrust forward!

and the Hot recites:

Agni whom they carry like a ring on their hand,like a new born baby; who performs successfullyrites for the clans! (RV 6.16.40)

Next the Adhvaryu says to the Hot:

Address Agni who is kindled!

and the Hot recites a number of verses while the Adhvaryu putssticks of firewood on the fire (see Staal 1983a, which will be referredto as Agni, 1,307-311). The number of verses and sticks of firewooddepends on the ritual in which this rite is embedded.

On a later occasion, when fire is about to be transported from thefirst altar to another, placed further east, the Adhvaryu addresses theHota as weIl as a second Hot, and all , including the Adhvaryuhirnself, accompany the fire on its journey east with long recitationsfrom ~gveda and Yajurveda (Agni I, 551-555).

In describing these Vedic rites and recitations I have not specifiedcontexts in the manner in which this was done by Firth with regard tothe Tikopia rites. I have not specified, for example, whether these ritesare connected with new born babies, initiations, marriages, funerals,or other events. The reason for this omission is that rites such as thesemay be inserted or embedded in numerous ritual contexts. Thiscorroborates van Gennep's and Durkheim's observations referred t


before, and is a significant circumstance to which I shall return. Thiscircumstance is also related to the question whether these Vedicformulas may be regarded as "free formulas" in Firth's sense. Theseare not, though others are. However, this is a matter too complex tobe discussed in the present context (cf. Renou 1954, s.v. ha; Gonda1977,565-567; Agni, 1,310-311,532-533,683-685, etc.).

I have described these Vedic rites in some detail (omitting manyfurther details, for example those that pertain to the technique ofrecitation) not because they are so similar to the Tikopia ceremoniesrecorded by Firth, but in order to illustrate the difference in kindbetween the data we are dealing with. The anthropologist recordswhat he finds on his island or in his village or tribe; with luck, he is ina position to revisit the area of his earlier fieldwork, and find outwhether there have been changes. The student of Vedic ritual, on theother hand, deals with a very extensive ancient literature on ritual,which includes a complete inventory of all the recitations and chantsaccompanying rites that have been performed more or lesscontinuously in different parts of the Indian subcontinent for aboutthree millenia. The formulas I quoted with which the Adhvaryuaddresses the Hot are in fact about 2,700 years old, and therecitations by the Hota are even older.

How can we be certain about such unbelievably remote dates?Because of the structure and continuity of the Indian tradition. Theserecitations and the rites that they accompany have been the subject ofa continuous tradition of commentaries and subcommentaries fromshortly after the time of their first composition to the present day.While the works of this tradition have been largely committed towriting, there are also extensive oral traditions that supplement them.The rites themselves continue to be performed as a function of theseoral traditions, which have recently become the object of what hasbeen called "Vedic fieldwork" (a term introduced by C. G. Kashikar1968). A comparison of the oral traditions with each other and withthe texts shows that many of the original compositions survive in theirpristine form. Cross-references, quotations, and inscriptions, togetherwith their historieal, linguistic, philological and literary analysis,enable scholars to check and countercheck the authenticity of textsand traditions, establish their approximate date and origin, anddiscover what changes they have undergone.

In India, the Vedic rituals have not only been described inpainstaking detail, and subjected to careful discussions and

16 FRITS STAAL

commentaries by Indian scholars from about the eighth century B.C.,but all these ritual texts and their accessories have been studied andmade accessible by several generations of modern Sanskritists fromabout the middle of the nineteenth century. Albrecht (not Max)Weber, Hillebrandt, and Schwab were the founders, and Caland wasthe grand master of this branch of Sanskrit scholarship. Abibliography of works and publications on Vedic ritual (includingsurveys, manuals, dictionaries, etc.) by these savants and bycontemporary scholars from Europe, An1erica, Japan, and India itselfwould constitute a sizable volume. 6 The only social scientists whorecognized the importance of some of this work were Hubert andMauss, who published in 1899 in the Annee sociologique their article"Essai sur la nature et la fonction du sacrifice." This essay, whichmade ample use of Schwab's monograph on the Vedic animal sacrificeof 1886, provided an excellent starting point from which sophisticatedand possibly adequate theories of ritual could have been derived.Unfortunately, it has not induced other anthropologists orsociologists to consult the ongoing literature on Vedic ritual.Durkheim referred to Hubert and Mauss' article, as we have seen, inthe eontext of observations that he himself failed to interpret and thatwere generally ignored elsewhere. The only scholar who has beeninspired by the "Essai" is the Indologist J. C. Heesterman, whointroduced a soeiological perspeetive into the classical Indologicalstudies on ritual in his book The Ancient Indian Royal Consecrationof 1957 and in numerous articles.

What is true of India is also true of China, though the .ritualtradition is not equally ancient and contemporary scholars are onlybeginning to tap its resources (see, e.g., Schipper 1975). There is avoluminous literature in Japanese on ritual, Buddhist and Shinto, byancient ritualists as weIl as contemporary social scientists. In contrastto the veritable oceans of data and evidence that the classicalcivilizations of Asia provide and that modern scholars continue tomake accessible, the data brought back by contemporary anthropolo-gists, interesting and varied as they are, must strike any unbiasedobserver as meager. No wonder that the conclusions derived fromthese data are tentative and unsteady. Firth in his observations onritual, quoted above (pp. 12-13), refers on the one hand to the symbo-lie interpretations that reflect the traditional Western perspectivereinforced by German philosophers, and recognizes on the other handthat rites and rituals have a certain validity of thei!__?~~,-_~!!~Ql.l!_ _


however explaining in what this validity consists or where it resides.The cause for such wavering indecision, which is not very differentfrom the inconclusive views espoused by Durkheim, Weber, and evenMalinowski, lies to a large extent in the limited and inadequate natureof the source data. The first conclusion that may be inferred from thisstate of affairs is that no theory of ritual can be taken seriously unlessit comes to terms with the data provided by the classical civilizationsof Asia, in particular India and China.

A similar situation as we still find in the social sciences existed notlong aga in Western linguistics. At first it was thought that thestructure of human language could be studied adequately by collectingdata from so-called primitive and exotic languages. Wilhelm vonHumboldt in ber die Verschiedenheit des menschlichen Sprachbauesof 1836 used Javanese, Burmese, Chinese, Sanskrit, and "Delaware"in this spirit, though he also made some use of concepts thatoriginated with the Sanskrit grammarians. This is reminiscent of thoseearly ethnologists who adopted terms such as totem or mana from thecultures they had studied, the only difference being that the terms ofthe Sanskrit grammarians are technical terms with very precisemeanings, whereas totem and mana are hazy notions. The next step ofdevelopment of Western linguistics is represented by Whitney, whoprovided in his grammar of Sanskrit a virtually complete inventory ofthe language, but who still regarded Pl)ini, the greatest Indiangrammarian, as an object of Indological investigation, at best aninformant, and did not recognize what he was in fact: a deceasedcolleague of genius. This was not merely an oversight; it went hand inhand with profound misapprehensions that Whitney entertained withregard to the nature of human language (see Chomsky 1964, 22; Staal1972, 139-141). The final stage was initiated by Leonard Bloomfieldand has culminated in the work of Paul Kiparsky, in whichcontemporary linguistics comes to terms with the insights and resultsof the Sanskrit grammarians.

In the West, linguistics is now considerably ahead of the study ofritual, which has not even reached astate of development where it canbe regarded as a scientific discipline. If any progress is to be made,these studies will first have to incorporate the ritual evidence fromIndia, China, and Japan. Next they must take account of the Indianscience of ritual. Given further incentives and new creative insights,what has long been a grab-bag of metaphysical and other speculationsmay then finally turn into a science. 7

18 FRITS STAAL

3. MATHEMATICS

The preceding sections have demonstrated that aIl is not weIl withthe study of ritual. If the situation is as unsatisfactory as it appears tobe, it can do no harm to look in entirely different directions. Fromnow on let us assume, not only for the sake of argument, but also onmethodological grounds, that ritual is not part of religion and that it isnot symbolic. Then, let us try to conceive of it in more general andabstract terms. It stands to reason to begin by invoking the assistanceof the most general science of symbols, viz., mathematics.

One difficulty that schoolchildren often experience when they areintroduced to algebra is that its letter symbols are devoid of specificmeaning. They are "abstract." This applies not only to the x, whichstands for the unknown answer of a problem, and to other so-caIled"variables," but also to "constants," such as a and b, in terms ofwhich the problems themselves are formulated. For example, theexpression:

(1)

applies to many values and interpretations given to a and b, and tooperators other than (, = ," "+," and ".". The constants may beinterpreted as integers, e.g.:

or also:

but the expression (1) also applies to real numbers, imaginarynumbers, or even geometrical configurations, as in:

b

a

ab

ab

a b


In this figure, the total area of the square is (a + b)2, which consists,as mere visual inspection shows, of four areas: a2, b2, and twice ab.Such wide and flexible applications of the symbols of algebra arecharacteristic of all of mathematics, and explain why it is at the sametime abstract and powerful.

Now let us consider a general symbolic expression, not confiningourselves to algebra, for example:

ABC B A. (2)

There are two different ways of looking at this: the semantic and thesyntactic. In the semantic approach, the symbols A, B, and C areinterpreted as meaning something or referring to something. In thesyntactic approach we pay no attention to such possible meanings orinterpretations, but study the configurations of the letter symbolsonly.

Adopting first the semantic approach, (2) may be understood inmany different ways, for example:

I. referring to numbers, e.g.: 3 8 7 8 3.11. referring to segments, e.g.:

I I I I I111. referring to algebraic symbols, e.g.: (a + a).8IV. referring to words, e.g.: found sleepy on sleepy found.V. referring to tones, e.g.:

VI. referring to movements, e.g.: three steps up a staircase andthen down again; or: making a pirouette, jumping up, kneeling,jumping up, making a pirouette again.

VII. referring to activities, e.g.: unlocking a box, opening it, puttingsomething inside, closing it, locking it. 8

VIII. referring to rites, e.g.: making fire, pouring Soma, chanting ahymn, pouring Soma, making fire.

There is literally no end to the possible interpretations of (2).

20 FRITS STAAL

Adopting the syntactic approach, there are also indefinitely manypossibilities. For example, (2) is part of:I. M N ABC BAN M, but also of:11. M N ABC B A M N.111. it is a mirror image of itself.IV. it consists of five units, just as: P Q R S T.V. it has specific instances, such as: A B B C C C B B A,

but also:VI. ABC B A - BeB - C - BeB - ABC B A.VII. it is interspersed through: P A Q B R eRB Q A P,

but also through:VIII. P A B Q R SeT B U V W A.And so on. The expression (2) may be looked upon as a specificinstance of a more general expression, viz.:

Al ... An-I An An-l ... Al

where "n" is a natural number. In the case of (2), nbe rewritten as:

(3)

3, for (2) can

It is relevant in the present context that the elementary units ofmathematical theories, and anything that can be stated in terms ofsuch units, may be of any size or kind: these structures operate onmany levels. Mathematics applies accordingly to the inside of theatom as weil as to the universe.

What then is the meaning of mathematics? From what we havejust seen, it makes no sense to ask for "the" meaning of mathematicalsymbols, expressions, statements, or theories, because they can beinterpreted in indefinitely many ways, and this is precisely what makesthem so interesting and universal. And yet, the meaning ofmathematics has exercised the minds not only of philosophers but alsoof mathematicians. According to Pythagoras or Kepler, for example,mathematics applies to the universe because there are deep and realconnections between the two. These views have also led to numbersymbolism and other allegorical interpretations, but neitherPythagoras nor Kepler are remembered on those accounts. Newtonalso is only remembered because of his contributions to physics, _


though he hirnself thought much more highly of his discoveries intheology.

The problem of meaning came up within mathematics itselfaround the turn of the century, when its foundations were shaken byparadoxes. Many ofthese paradoxes had been known for a long time,and it was thought at first that they could be solved. Here is anexample of a related puzzle in a less weIl known form that shouldappeal to fieldworkers: "A traveler has fallen among cannibals. Theyoffer hirn the opportunity to make astatement, attaching theconditions that if his statement be true, he will be boiled, and if it befalse, he will be roasted. What statement should he make?" (Kleene1952, 40). The answer is that he should say: "I shall be roasted." If itis true, it is false, and vice versa. It is hoped that the resultingconfusion may cause the cannibal hosts to pause.

How can such contradictions be eliminated? There have beenthree famous attempts: Logicism, developed by Bertrand Russell andA. N. Whitehead in England; Intuitionism, developed by L. E. J.Brouwer in Holland; and Formalism, developed by David Hilbert inGermany. All present difficulties.

According to Logicism, mathematics is a branch of logic. Theactual program of deriving mathematics from logic was carried out toa large extent in the Principia Mathematica of 1910-1913, anddeveloped further in numerous other publications. The questionarises, however, whether logic itself does not presuppose mathematicalideas (e.g., iteration) in its own foundation. It is not at all obvious thatlogic is more fundamental than mathematics. Moreover, even if it is,we have only shifted the problem. The question which then arises is,what is "the meaning" of logic.

Intuitionism accepts a direct meaning for mathematicalstatements because it holds the view that such statements refer toconstructions that the mathematician carries out in his mind. Amongthese constructions are finite objects and indefinitely proceedingsequences of such objects. According to Brouwer, logic is abstractedfrom finite mathematics, and cannot be applied to the mathematics ofinfinite sequences, or indeed to the infinite series of natural numbers.One logical principle that does not apply to infinite mathematics is theprinciple of the excluded third or middle, which declares that for anystatement A, it is either true or false. Brouwer and othersreconstructed apart of classical mathematics without making use ofthis principle, and showed thereby incidentally that it was free of

22 FRITS STAAL

contradiction. But other parts could not be derived in this rigorousfashion, and since mathematicians continued to develop them freelyregardless of these criticisms, it is clear that the Intuitionistic programhas not been widely accepted.

According to Formalism, mathematics is a kind of game. Itproposes to derive all of mathematics from formal axiomatic theories,in which the symbols are uninterpreted. Hilbert accepted certainsimple mathematical statements as meaningful, and proposed to showthe consistency of others by using methods of a higher order, called"metamathematical. " Formalism agrees with Intuitionism that it isdifficult to explain the meaning of certain nonintuitionistic parts ofclassical mathematics. But Hilbert wrote: "It is by no meansreasonable to set up in general the requirement that each separateformula should be interpretable taken by itself .... " In theoreticalphysics, "only certain combinations and consequences of the physicallaws can be checked experimentally-likewise in my proof theory onlythe real statements are immediately capable of a verification" (quotedin Kleene 1956, 57). Though Gdel and others have demonstrated thatit is impossible in principle to carry out the program of Formalism, itsoutlook is in accordance with the practice of most mathematicians,for it put no stop to the continuing creation and development ofabstract symbols and theories that are uninterpreted and perhapsuninterpretable.

Other theories have been proposed to provide a foundation formathematics or throw light on its nature. In combinatory logic, forexample, (developed largely by H. B. Curry since 1929) logical andmathematical proofs are analyzed into snlall steps which arenumerous but intuitively meaningful. Variables have been eliminated.It takes longer to reach results, and many fornlulas are so abstract andgeneral that they are not intuitively perspicious. The language ofcombinatory logic is very flexible, and has not led to anycontradictions.

More recently, Saunders Mac Lane has suggested an interpreta-tion of mathematics as a formal and abstract development of notionsunderlying various ordinary activities, such as counting, measuring,moving, proving, calculating, and collecting. The actual structure ofmathematical ideas is an incredibly elaborate development throughcomplex interactions between the general notions abstracted fromthese activities. In the course of this development, it becomes less andless easy to assign meaning to the forms by simple appeals to the real


world. It is important, therefore, that the resulting nonobviousabstractions are developed rigorously and perspicuously.

Mac Lane has emphasized a property of mathematics that issimilar to the "functional ambiguity" we have signalIed in ritual.There are always several mathematical interpretations or models ofreality. Space is originally experienced as extensive and hollow, fixedand the locus of movement. With Euclidian geometry it is analyzed asa receptacle for things that can be pushed around within it. Itsdescription by means of Cartesian coordinates leads to an analysis ofmuch more general figures. In the study of spaces of more than threedimensions, space is apprehended partially in algebraic fashion.

Similarly, real numbers can be constructed from rationalnumbers in many ways: "A real number, for Dedekind, is a cut in therationals. For Cantor or Meray, it is an equivalence class of sets ofrational numbers. For Weierstrass, it is an equivalence class of sets ofrationals with a bounded sumo With any of these three constructionsone obtains a complete ordered field of real numbers, differentconstructions yielding isomorphie fields. There is no unique set-theoretical model for the reals" (Mac Lane 1981, 467).

It is not my purpose to advocate any of these various approaches.All such theories have exerted a positive influence oft mathematics. Itis clear that the interpretations of many theoreticians are largelyirrelevant to the practice of most mathematicians. All of mathematicswas at one time supposed to be derived from set theory, itself basedupon the Zermelo-Fraenkel axioms. But, says Mac Lane (1981, 468),"most professional mathematicians never have occasion to use theZermelo-Fraenkel axioms, while others do not even know them."Whether or not it can be interpreted meaningfully, mathematics goeson. The same holds for music and ritual.

4. MUSIC9

In medias res: without beating about the bush, I shall give sevenexamples of musical structures described in syntactic terms. All aretaken from classical Western music. The units range over a wide area,from single tones, motives, and phrases ("approximating to what onecould sing in a single breath": Schoenberg 1970, 3) to Sonatas orSymphonies. These examples are of different kinds also in otherrespects.

24 FRITS STAAL

I. REFRAIN. In poetry as weH as music, it is common to end each ofa sequence of structures with the same form, as in:

AR-BR-CR-DR- ... (4)

Music differs from poetry in that the refrain frequently occurs at thebeginning as weH as at the end. In Gregorian chant, the variableelements A, B, C, ... are often sung as a solo, and the refrain R by achorus. In church music, the refrain may be Amen or Alleluia, thelatter closing with the jubilus, a long vocalization on the final -a.Medieval and Renaissance music is known for its formes fixes such asrondeau, ballatta, and virelai. In the virelai, the refrain occurs at thebeginning and serves each time as the opening of the next unit, as in:

RAR B R C R. (5)

In aH these forms, the refrains are each time exactly the same. Afterthe Renaissance, refrains tend to be varied in many ways, makingthem musically more interesting. I shall express a variation of a form"R" as: "R'''. In the foHowing example, the second Nocturne forPiano by Erik Satie, the refrain consists of four measures. It occurs atthe beginning, and recurs twice in a varied form (where the score says:"Reprendre"):

,....' ..._..... ,1...


The structure is:

RAR' B R". (6)

11. CYCLE. I shall use this term, which is very general, to refer to astructural property that is equally general, viz., one that begins andends with the same element, as:

ABC D ... A. (7)

In musical phrases, it is extremely common to begin and end with thesame note, e.g., in Mozart's Nozze di Figaro, No. 3 ("Se vuolbaHare"):

Al1e~retto

Se vuol baI - IR. - re, si -gnor Con - ti - no,

Larger compositions often begin and end in the same key. Forcompositions to begin and end with exactly the same phrase is actuallyrather rare: the Harvard Dictionary 0/Music refers to two seventeenthcentury examples, from Giovanni Maria Trabaci and Steffano Landi(ApeI1970, 218a referring to Davison and Apel, 1974, Nos. 191 and208).

It is nearly universal, on the other hand, for musicalcompositions to return to their point of departure at the end by meansof a variation of the opening theme, viz., adopting a structure of theform:

ABC D ... A'. (8)

A very weH known example is the first movement of Beethoven'sSymphony No. 5, which begins as folIows:

An'Kro roD brlo.

26 FRITS STAAL

and ends:

A particularly important simple form of (8) is:

AB A'. (9)

This is the basic form of many types of composition, including theSonata and the Symphony to which I shall return. The musical termfor "A'" in such cases is recapitulation or restatement.

111. PALYNDROME. I shall use this term for a special type of cycle,also referred to as retrograde or mirror. It is a nlusical illustration ofthe structure discussed in the previous section:

ABC B A,

or its generalization:

Al ... An-l An A n-l ... Al.

(2)

(3)

The simplest example is ascending and descending a scale (or the otherway round). In a musical composition there is generally some kind ofvariation. In classical Indian music, when the scale is introduced by anascent (roha1)a) followed by adescent (avarohaf)a) , the latter uses


different notes and is therefore not a mirror of the former. Anidentical retrograde movement occurs in Debussy's Prelude No. 10("The Engulfed Cathedral"):

Retrograde structures are used in most canonical, fugal, and 12-tonecompositions. In the cancrizans (crab canon), the melody isaccompanied by itself played backwards, as in the following examplefrom Bach's Musical Ojjering:

.- -

~ - , I~" J I ~ -__1*'a_

__"1"'a_a- L .........

rW1 ..-Ie) - I .......... -

----- ---

l_--

----- -

_._-

IW ~ ......---

- - -

....

- -

,-

rJ -- .. "."..."", I I ~CoI I -

The palindrome occurs with variations in larger structures. Thestructure of Fugue No. 16 in Book I of Bach's WohltemperiertesClavier can be expressed by the following scheme of expositions(referred to by A's) and episodes (referred to by B's and C's):(cf. Green 1965, 265-267)

A B A C - A' B' A" - C' A'" B" A"" (10)

28 FRITS STAAL

Bach's motet Jesu, meine Freude consists of eleven parts: the music ofNo. 11 (a 4-part Chorale) is identical with that of No. 1, and No. 10(a 5-part Chorus) is a shortened version of No. 2 (Steinitz 1978, 34), sothat the structure is:

AB B' A. (11)

A similar pattern, ranging over longer stretches and closer to afull-fledged palindrome, occurs in Bach's Johannes Passion (Steinitz,ibid.). If we on1it the Evangelist recitatives from the section consistingof parts Nos. 27 through 52, and regard Nos. 31 and 32 as parallelinterpolations with No. 48, the structure may be described as follows(the numers of the parts are written below the correspondingstructural elements):

ABC D E D' C' B' A' (12)27 29,31-2,34 36 38 40 42 44 46,48,50 52.

IV. OVERLAPPING. This feature of structure applies only tosimultaneous occurrences, Le., two (or more) tones, motives, phrasesor melodies played or sung at the same time. It cannot therefore berepresented by linear sequences of symbols, such as I have used so far.Here is a simple example of overlapping motives from Mozart'sSonata for Violin and Piano, K.402:

Allegro moderato,r------........

Overlapping occurs frequently in counterpoint and polyphonic music,especially in fugues, canons, etc.

V. THREESOMES. Tripie repetitions are common on many levels,from simple triplets to the threesomes that were universal in churchmusic because of their symbolism (viz., the trinity). For compositionsto begin or end with a tripie repetition of a motive or theme is not verycommon, but occurs, e.g., in Mozart's Sonata for Violin and Piano,K.377-II:


or in Schubert's String Quartet, Op. 29-111:

Throughout classical Western music, the chief function of the number"three" is that it is the most common number of subdivisions of manylarger units. It is characteristic of the two following structures, Sonataand Symphony.

VI. SONATA. This form is characteristic of classical Western musicsince Haydn and Mozart. It has the following structure:

AB A',

which originated from the simpler form:

AB A,

(9)

(13)

which is found in the Rondo and Minuet. Often the elementsthemselves are again of the same form. In the paradigm, A is calledthe exposition, B the development (German: Durchfhrung which isbetter translated as "elaboration" : Schoenberg 1970, 200, note), andA' the recapitulation. A and A' are usually in the same key, while Buses various keys and therefore modulation.

The prehistory and history of the Sonata form exhibitextraordinary variety. Sometimes the structure is influenced by the useof various instruments, or varying numbers of players. At first theparts were numerous and brief, and followed each other without abreak. Later they became fewer, longer, and more separate from eachother. The solo parts were played by violins, flutes, oboes, etc.; theaccompaniment was often on the harpsichord. Before the eighteenth

30 FRITS STAAL

century, the principle was simple: if someone was around who wasable to play the part on his instrument, he was welcome to do it.

VII. SYMPHONY. The symphony started tripartite, in the Sonataform, with more instruments and performers: a Sonata for orchestra.Soon a fourth part was added, chiefly for entertainment: the Scherzo.The two middle movements, Andante and Scherzo, are frequently ofthe form (13), whereas the first and last movement are more often ofthe form (9). The form was perfected by Haydn and Mozart, andenlarged and extended by Beethoven. Beethoven lengthened the coda,a final piece following A', and the development, introducednumerous variations and added introductions to the various pieces.The increasing complexity of symphonies after Beethoven has fromtime to time been counterbalanced by simplification of the thematicstructure. In Berlioz' first two symphonies, for example, a singletheme (the "idee fixe") appears in each movement. The openingtheme of the first movement returns in the final movement in Brahms'Third Symphony (the same return is found in his Clarinet Quintet).The finale of Bruckner's Eighth Symphony includes a simultaneousstatement of the principal themes of the three preceding movements(Green 1965, 176). (Some recurrences are incidental, or have thecharacter of reminiscences or quotations, as in Beethoven's Fifth andNinth Symphonies, and in his Piano Sonata, Op. 101.)

To express these structures adequately more complex mathemati-cal expressions than the linear are required (for other formalizationssee Ruwet 1966, reprinted in Ruwet 1972, 100-134). Although theexpression A - B - A (13) is linear, the expression A - B - A' (9) is onlyapparently so: it has an inner or underlying structure that is not linear.The variation A' depends on the original statement A, and thereforeon the context. However, it does not depend on the immediatelypreceding context, in which case it would have been possible to expressit with the help of a context-sensitive rule of the form:

B A ~ BA'. (14)

The variation depends on a context that is further away, which canonly be expressed by using what linguists have called trans/ormationalrules-the kind of rules that are characteristic of human language.With the help of such rules, the variation A' can be introduced by rulestructures like the following:

THE SEARCH FR MEANING 31

S~

A B A

S=9 ~

A B A'

(15)

This expresses at the same time that the variation is a variation of thefirst movement, and that it occurs only in the finale.

1 have purposely provided a medley of musical forms in order toillustrate the considerable variety of possible musical structures.Whenever such a structure is given, it is possible to define a notion of"structural meaning" that depends entirely on structure. The"structural meaning" of the entire structure is that structure itself,and the "structural meaning" of an element within the structure isdefined in terms of the position the element occupies in that structure.For example, part of the structural meaning of a phrase may be that itis a refrain because it occurs as arefrain. The notion of structuralmeaning adds nothing to the existing structures themselves.

Another type of structural meaning that is typical of classicalWestern music may be defined in terms of the notions of consonantand dissonant intervals. Consonant intervals are intervals such as thefourth and fifth that "sound stable and complete" (Piston 1962, 6).Dissonant intervals deviate from these and require aresolution intoconsonant intervals. Such resolutions operate on the harmonie as weIlas on the melodie level. The musicologist Schenker and the composerHindemith have used the terms "tension" and "release" tocharacterize this fundamental opposition between the formation ofdissonance and its resolution into consonance.

The resolution is only rarely introduced by a single move. It ismore often reached through intermediate steps that introduce newdissonances and resQlutions. An example occurs at the end of the firstPrelude of Das Wohltemperierte Clavier:

Consonance and dissonance are to some extent relative concepts:their perception changes with history because ears get used todissonances. This was pointed out by the devil to the composer AdrianLeverkhn in Thomas Mann's Dr. Faustus (English translation, 1949,

32 FRITS STAAL

239): "The diminished seventh is right and fuH of expression at thebeginning of Op. 111. It corresponds to Beethoven's whole technicalniveau, doesn't it?-the tension between consonance and the harshestdissonance known to hirn. The principle of tonality and its dynamicslend to the chord its specific weight. It has lost it-by a historicalprocess which nobody reverses .... Every sound carries the whole,carries also the entire history in itself." 10

Notes possess structural meaning when their occurrence can beexplained because it contributes to the formation of dissonances ortheir resolution into consonances. Since some dissonant intervals havedifferent resolutions, notes may have multiple meaning. In otherwords, there is functional ambiguity. The diminished seventh cord,for example, may be interpreted in four different ways, each expectinga different resolution. The four interpretations can be distinguishedby sounding different notes (in the left hand) against the chord (in theright hand) in the following example constructed by Piston (1962,193):

Philosophers and musicologists have not been satisfied withstructural meaning alone, even with functional ambiguity added. Theyhave mused and written extensivelyon the meaning of music ingeneral. In simplified terms, there can be said to be two schools.According to the first, music is allegorical and expresses nonmusicalelements, e.g., features of the universe or of man, such as emotions,passions, or moods. According to the second, music is to beunderstood on its own terms. This somewhat academic distinctioncorresponds to a distinction made by some composers, musicians andmusic critics between "program music" and "absolute music."Program music is inspired by a nonmusical program, for example, apoem or picture, usuaHy indicated in its title (like Debussy's"Engulfed Cathedral"). Absolute music is not characterized innonmusical terms. The Harvard Dictionary (s.v. "program music")elaborates instructively:


Although examples of program music are found in nearly allperiods from at least the 14th century, it was not until the 19thcentury that it became a serious riyal of absolute music, to thepoint of ousting the latter-at least temporarily-from itsdominating position. About 1900, many persons, particularlywriters on music, believed that in order to be understandablemusic must 'express something' or 'tell a story.' ... Today suchviews are a thing of the past. .. " (Apel 1970, 696a).

Sometimes music actually imitates the sounds of nature orculture. Schoenberg (1970, 95-97) quotes examples from Beethovenand Smetana (the sound of a brook or river), Wagner (flickeringflames), Schubert (the weathervane) and Bach (the tearing of thetemple veil). The Harvard Dictionary refers to Beethoven's renderingsof the cries of the nightingale, cuckoo and quail, Wagner's imitationsof the toad and serpent, and Richard Strauss' of a flock of sheep."The climax of this trend (and, in asense, the reductio ad absurdumof program music) is Respighi's The Pines 0/ Rome, where theproblem of imitating the nightingale is solved by simply using arecording of an actual nightingale's song" (Apel 1970, 697a).

It is obvious that all such imitations are anecdotal and have littleor nothing to do with "the meaning of music." Musical compositionsmay be inspired or occasioned by nonmusical things such as acathedral, but no music conveys the meaning cathedral in thesystematic manner in which the word "cathedral" of a naturallanguage such as English refers to a cathedral. What such titlesindicate is that music may be composed or played on almost anyoccasion. These titles are mere names, and therefore arbitrary.Architectural monuments mayaIso be referred to by names (e.g.,"The Parthenon," "The White House"), but such names convey noarchitectural meaning. Similarly, Sonatas may be referred to by namessuch as "Spring," "Waldstein," "Moonlight," or "Appasionata,"but these convey no musical meaning. They give radio announcerssomething to talk about for the benefit of listeners in need ofnonmusical entertainment. If the expression "the meaning of music"must be used, it can only refer to the structure of music, that is, tosyntactic structures like the ones I have exemplified under theheadings I-VII, and expressed by formulas such as (2)-(15).

What is characteristic of music, viz., formal structures, is notequally characteristic of other arts. Schopenhauer expressed thisinsight in the following terms:

34 FRITS STAAL

Die Musik ist ... darin von allen andern Kunstenverschieden, dass sie nicht Abbild der Erscheinung, oderrichtiger, der adquaten Objektivitt des Willens, sondernunmittelbar Abbild des Willens selbst ist und also zum allenphysischen der Welt das Metaphysische, zu aller Erscheinung. dasDing an sich darstellt (Music differs from all the other arts in thatit is not representation of appearance, or rather, of the adequateobjectivity of the Will, but a direct representation of the Willitself, and therefore manifests the metaphysical in all that isphysical in the world, and the thing-in-itself in all appearance").

The idea is buried in metaphysical notions such as Kant's"thing-in-itself" and Schopenhauer's "Will" (with a capital "W").However, des Pudels Kern is straightforward: "music differs from allother arts in that it represents no appearance of anything else, but onlyitself." This passage occurs in Schopenhauer's Welt als Wille undVorstellung of 1818 and is quoted by Nietzsche in Die Geburt derTragdie aus dem Geiste der Musik of 1872. Schopenhauer clarifiedhis view later by adapting traditional scholastic terms: concepts are theuniversalia post rem, music provides the universalia ante rem, andreality the universalia in re.

5. RITUAL

I shall again begin with seven examples described in syntacticterms, this time of ritual structures. The first five correspond in astraightforward manner with the first five musical examples discussedin the preceding section. In the case of the latter two, thecorrespondence is equally significant but more roundabout. Thecorrespondences between musical and ritual structures will subse-quently be discussed and placed in a wider perspective.

All ritual structures to which I shall refer are taken from Vedicritual, and are described in greater detail and within a fuller context inAgni I. The structural elements range over units of different size, fromsmall elements of single rites that take less than aminute to perform,to larger rituals that take several days or more to execute. Theexamples are of different kinds also in other respects.

Most of these ritual structures involve recitations or chants. Inthe discussion of Tikopia ceremonies (above pages 10-12) we have had

----------------------- - - - - - - - - - - - --


occasion to observe that recitations are often an important feature ofritual. To the extent that the ritual recitations and chants exhibitmusical features, the similarity between ritual and music isunsurprising. It will be found, however, that even if we disregardmusical features of rituals, the similarities remain. Those interested inthe purely musical structures that are also features of Vedic ritualshould turn to the chants of the Smaveda. Their internal structure istaken into account only occasionally in the present context, but isstudied elsewhere (see Staal 1961, chapter VII; 1968; 1983b and c;Howard 1977).

I. REFRAIN. There are several reasons for the frequency of ritualrefrains. The ritual acts often culminate in an offering or oblationmade by the Adhvaryu priest into the fire. These offerings andoblations are of several kinds, but they naturally come at the end ofacts which exhibit great variety themselves. The refrains consist of twoparts: an exclamation by the Adhvaryu (either svh! or vau~a!!) andthe "renunciation" (tyga) recited by the Yajamana or patron of theritual, for example: "This is for Agni, not for me!" (Agni 1,47). Thegeneral structure is therefore of the form:

APQ-BPQ-CPQ-DPQ (4')In long recitations from the ~gveda, such as the sastra recitations

to which I shall return, the verses are recited uninterruptedly, withouttaking breath at the end of each verse. Breath is taken at the caesurabetween the second and third quarter of each verse. At each caesura,the final vowel or nasal is lengthened. Each verse ends in a lengthenedOM-the famous mantra of later Hindu mysticism.

The bird shaped altar that is characteristic of the Agnicayana isconstructed from a thousand bricks, each consecrated with threemantras. Of these, the first is generally specific and described for eachbrick or group of bricks, but the second and third are always the same,so that the structure is again the same as (4') (see Agni I, 399).

The mantras recited before the final exclamations thataccompany offerings, have often a similar internal structure. Here aretwo examples. After the altar has been completed, there are sixoblations of curds mixed with honey. The accompanying mantrasdiffer in their first lines, but all end with:

36 FRITS STAAL

Hirn whom we hate and who hates usI place in your jaws!

which is followed by: sviih! (Agni I, 104, 381, 544-545).Not long after this rite, which takes place on the ninth day of the

Agnicayana performance, there is a long recitation called camakamafter ca me, "and for met"~ recited by the Adhvaryu after each word(Agni I, 563-574). This is immediately followed by seven butteroblations, made through a copper pipe attached to a small toy cart.Each mantra ends with the same refrain:

May he protect brahman, k~atram,may they protect brahman, k~atram!

followed by: svh! (Agni I, 574-575). Both rites have the samestructure, expressed by (4').

11. CYCLE. I shall use this term again for a structure of the form (7)(above, page 25). This is relatively rare in Vedic ritual, but aninteresting variant occurs in the Agnicayana just before the camakamrecitation. Seven oblations of cooked rice are made on potsherds forthe Maruts, storm gods and companions of Indra. Seven recitationsare involved that will be referred to as At, ... , A,. These mantras arerecited in low voice, cyclically, and in overlapping pairs, the firstmantra always ending in the long vocalic insertion -0, and the oblationmade with the last, as folIows:

Al - A 2 - svhii!A 2 - A 3 - sviih!A 3 - A 4 - svh!A 4 - A s - svh!A s - A 6 - svh!A6 - A, - svh!A, - Al - svhii!

(Agni I, 562-563). This kind of pairwise overlapping, but without thecycle, is also found in the kramap!ha mode of Veda recitation, usedin the traditional transmission of ~g- and Yajurveda (see Staal 1961,24, 44). ------------


111. PALINDROME. This is a very basic structure in Vedic ritual. Itranges, generally with variations, over small as weIl as large units. TheAgni~toma, a ritual performance that lasts five days, has such astructure, which is also found in the Darsaprl}amasa, or "Full andNew Moon Ceremonies." Many sastra recitals and stotra chants areembedded in similar portmanteau patterns. I shall not describe thesestructures in greater detail, since I have discussed them elsewhere(Staal 1980a, 133-136; and Agni 11, 127-134).

IV. OVERLAPPING. A variety of this structure was described inthe cycle discussed in 11. The basic structure is very common andreflects a general principle that is metaphysical as weIl as structural:horror vacui. There should be no gaps; accordingly, everything has tobe performed continuously (salfltatam). The next rite is thereforebegun before the previous one is over, and the same holds forrecitations, chants, and their similar units (e.g., bhakti, to be chantedwith one breath, from which the chants are constructed). Thepractice extends to forms of transmission of the ritual material. Forexample, some recitations are "prompted" by a helper, line for line,"before' , they are recited by the ritually chosen and qualifiedofficiating priest: but this priest starts each time before the promptingis over. It might be feIt that this kind of "overlapping" is a practicalmatter and not the outcome of a structural principle. However, it iswidespread and based upon principles. I have included it precisely inorder to show that we are not in a position to pass such kinds ofjudgment when we are only beginning to subject the data to astructural analysis.

V. THREESOMES. Triplets are everywhere. All longer recitationsfrom the Rgveda are subject to the rule: "Recite the first thrice, recitethe last thrice," resulting in the structure:

The Yajamana and some of the priests frequently begin their recita-tions with the so-called vyhrti: BHUR-BHUVAij-SVAR ("Earth-Sky-Heaven!"). Many larger units are subdivided into three, thoughfour is also met with (see the structure discussed below, VI and VII).Each of the bricks is consecrated with three mantras, as we haveseen. All these are structural threesomes and are different from

38 FRITS STAAL

unstructured groups such as the three fires or altars, the threeassistants of each chief priest, the three stotra chanters (see below,VII), the three Vedas, etc.

VI. I~TI. The i~ti is one of the basic structural units of Vedic ritual.It culminates in an offering of rice or barley cakes. The Yajamna andhis wife are assisted by four priests: the Adhvaryu of the Yajurvedawho performs the ritual acts; the Hot who recites from the ~gveda;the Brahman who supervises the rites without participating; and theAgnldhra or "kindler." An i~!i is preceded, accompanied andfollowed by numerous accessory rites, but its basic structure consistsin abrief series of acts that follow each other in rapid succession. Thesubdivision of these acts into elements is fixed, but their numberingand grouping together is to some extent arbitrary. In the followingdescription of the i~!i paradigm, six elements are grouped in threeepisodes of two elements each, which is a natural manner ofsubdivision:

EPISODE J.Element 1. The Adhvaryu commands the Hot to address the deity,

e.g., Agni, by saying: "Address Agni!"Element 2. The Hot addresses or invites Agni by reciting verses from

the ~gveda.

EPISODE 11.Element 3. The Adhvaryu exclaims to the Agnjdh: "Make (hirn)

hear!"Element 4. The Agnldh shouts: "Be it so! May he hear!"

EPISODE 111.Element 5. The Adhvaryu commands the Hot to recite his nlain

recitation, the yjy ("offering vetse") by saying: "Saythe yjy for Agni!"

Element 6. The Hot begins the yajy by murmuring: "Earth! Air!We who say the yjy ... " and then recites verses fromthe ~gveda, ending with the exclamation: "May (Agni)lead (the offerings to the gods)!" At the last syllable,which the Hot shouts at the top of his voice, theAdhvaryu makes the offering by throwing or pouring itinto the fire, and the Yajamna pronounces his"renunciation": "This i~_f~!_~~_I!t,_~Q!_f9J-m~J-'~_------------


Some of the elements or parts of elements in this structure are fixed(e.g., 3,4, and the exclamation in 6). Others contain variable units, orare themselves variable. In 1 and in the renunciation in 6, the nameAgni may be replaced by another, but in the exclamation in 6 it isalways Agni who is understood. The verses from the ~gveda in 2 and 6vary. As a result of these and other variations, there are manydifferent i~tis. All have the same structure, but they have differentnames and address different gods with different verses. The largerituals contain many i~!is, which occur either in sequence, or insideother units themselves inserted within the larger rituals. (Theseinsertions are described by transformational rules: see Staal 1980,125-133; Agni 11, 131-133).

The structural relations between the six elements in the threeepisodes can be described in various terms and from various points ofview. From the point of view of the Hot, who recites twice, thestructure is:

AR-BC-DR'. (18)

From the point of view of the Adhvaryu, who issues a command threetimes, it is:

R A - R' B - R" A' . (19)

The i~tis constitute the paradigm for one type of ritualperformance. Other forms are obtained by extending or modifying thebasic form. In the animal sacrifice, for example, there is an additionalofficiating priest, the MaitrvaruI)a, and Episode I of the basicstructure is extended with one element, as folIows:

Element 1. The Adhvaryu commands the MaitravaruQa to commandthe Hota to address the deity.

Element 1'. The MaitravaruQa commands the Hota to address thedeity.

The rest is the same.

VII. SOMA SEQUENCE. All the larger Soma rituals are character-ized by sequences of rites that I have called "Soma sequences" (AgniI, 49, 54, 599, 608, etc.). Each Soma ritual is defined by a specific

40 FRITS STAAL

number of these sequences. The Agni~toma consists of twelve Somasequences: five at the morning pressing, five at the midday pressing,and two at the third (or evening) pressing. The Atirtra consists of 29such sequences. The number is not symbolic, but arrived at bycomputation: the Atiratra is constructed from the Agni~toma by firstmodifying some of its twelve Soma sequences; and then adding tothem: three; one (the "sixteenth"); three nocturnal rounds of four;and one final sequence. Thus 12 + 3 + 1 + 12 + 1 = 29.

Each Soma sequence consists of a chant (stotra) from theSmaveda; a recitation (sastra) from the ~gveda; Soma offerings tothe deities; and Soma drinking by the Yajamna and some of hispriests. Each of these four episodes consist of several smaller rites andother elements, some of them fixed, and others variable. Here followsa simplified description of the four episodes and their constituentelements:

EPISODE I. CHANT (by three chanters)Element 1. The Adhvaryu (or his assistant, the Pratiprasthta,

depending on certain circumstances: see Agni I, 625)hands two blades of darbha grass to the Udgt, mainchanter of the Smaveda, while reciting: "You are thebed for the coupling of ~k and Sman-for the sake ofprocreation!' ,

Element 2. The Adhvaryu or Pratiprastht continues with arecitation in which the sound H~, certain gods andchanters occur, and which ends with: "OM! Chant!"

Element 3. The three chanters, facing west, north, and south, intonethe chant which begins with H~ and consists of threesequences in each of which are tripie repetitions ofcertain lines, depending on which chant it is. This complexpattern is marked with the help of sticks placed on a pieceof cloth. Each chant consists of an addition of five pieces,in some of which the original syllables of the verse are"hidden" by lengthened "0" 'Se Numerous other rules arefollowed (see Agni I, 602, etc.).

Element 4. Yajamna and Adhvaryu recite together a piece called"Chant Milking" (stutadoha).

EPISODE 11. RECITATION (by Hota, MaitravaruI.1a, Brahma-naccharpsin, or Acchavaka)


Element 1. The Hot (or one of the other priests) recites a piece called"prior light" (puroruc). Without making any pause, infact, without taking breath, this leads into:

Element 2. the main recitation. This is marked by tripie repetition ofthe first and last verse, taking breath only at certainjunctions, etc. There are other insertions by the reciter(e.g., "Let us both recite!") and by the Adhvaryu. Thelatter, called "salutation" (pratigara) are inserted whenthe reciter produces his lengthened "0" 'So - Caland andHenry (1906, I, 232, note 8), generally dauntless, referredto these as "bizarres contorsions liturgiques."

Element 3. The Hot adds a piece called "Recital Strength"(ukthavirya).

Element 4. Yajamna and Adhvaryu recite together a piece called"Recitation Milking" (sastradoha).

Element 5. The Yajamna adds another piece, which has no namebut which I shall translate for the sake of illustration:

The ritual has been, has been produced,it is born, it has grown,it has become king of the gods.May it turn us into kings,may we be masters of wealth!

EPISODE 111. SOMA OFFERING.This is in some respects like an i~ti. It involves an offering,an offering verse (yiijyii) , and ends in the exclamation:"May (Agni) lead (the offerings to the gods)!"

EPISODE IV. SOMA DRINKINGElement 1. Each priest who is about to drink addresses the Adhvaryu

with: "Adhvaryu, invite me"Element 2. The Adhvaryu replies: "You are invited!"Element 3. The priest drinks and recites from the ~gveda, touching

his face and heart at certain points.Element 4. The Adhvaryu recites a long piece from the Yajurveda,

called "Long Drink" (dfrghabhak~a).

This concludes the simplified description of a Soma sequence. Again,some elements are fixed, others are variable, and there is a certainamount of overall variation which it is not necessary to describe in the

42 FRITS STAAL

present context. Some Soma sequences are more complicated than thetype outlined here, others are simpler. Some deviate considerably,e.g., the sixteenth.

All such patterns and deviations are provided with fanciful andcontradictory explanations in the BrahmaJ)a literature. Oftenalternatives are given, thus indicating their arbitrariness. Here is atypical example. In the praga recitation or recitation "of the frontalpart of the chariot shafts," the "prior light" (puroruc) immediatelypreceeds each of its seven triplets, so that the reciter's insertions andAdhvaryu's "salutations" should come before the "prior light." The

Kau~rtaki BrhmaQa explains this in such slovenly terms, that I shallreproduce them not in my own translation, lest the reader suspectsthat I am tampering with the data: "Now, the puroruc is he yonderwho gives out light (viz., the sun); for he shines in (from the) front.Now, the puroruc is the vital breath, the hymn the body (tmii, theperson hirnself). (Or) the puroruc is the body, the hymn offspring andcattle" (Gonda 1981, 63, note 9 = Sreekrishna Sarma in: Agni 11,679).

Anyone who has spent any time with the Brhmal).a literature willagree that this passage is quite representative. The fact that suchinterpretations are arbitrary need not prevent them from constitutinga systenl within themselves. Mylius (1976) has shown that manyidentifications given in the same Kau~itaki BrhmaI].a can in fact besystematically interpreted in social, psychological, or ideologicalterms. But even if such interpretations refer to reality, they still faH toelucidate rites, and throw no light on the Vedic ritual.

So let us revert to structure. Some of the variations of Somasequences exhibit dependencies that may be described as thematic. Inmany Soma sequences, the chant of the first episode is composed byputting to music three verses fronl the ~gveda. The recitation of thesecond episode begins with the same three verses, the first repeatedthree times. In the nocturnal rounds of the Atirtra, there is anadditional refinement: in the first nocturnal round, the first quarterverse of each of these three verses (that occur both in the chant and inthe recitation) is repeated; in the second nocturnal round, the secondquarter verse of each of these three verses is repeated; and in the thirdnocturnal round, the third quarter verse is similarly repeated (see AgniI, 663-680).

Now let us return to our old question: what does all of this mean?I hope it has become clear by this time that this question, with respect


Ito the structures we have discussed, does not make sense. TheseIstructures do not mean anything apart from and beyond the structuralcomplexity they display. They do not "refer" to specific aims ordeities, and although their names (insofar as they have names) mayseem to hint at their longforgotten origins, these names do not evokeanything. The complexities inherent in these structures have to belearned and practised, and can be expressed with the help of preciserules-but they are not symbolizations of anything else and do notpoint to arealm beyond themselves.

In all these respects, there is considerable similarity between themusical and ritual categories we have considered. The similarities arenot only structural, but also circumstantial. Just like Sonatas andSymphonies, i~!is are performed on different occasions (providingample evidence in support of van Gennep;s and Durkheim'sobservations, quoted above, pages 3-5) and have different names (likethe intichiuma and mbatja/katiuma rites referred to by Durkheim).Even the fact that a Soma sequence ends with drinking Soma is remi-niscent of what may happen to music: smoking and drinking ofcoffee and beer was quite common during musical performancesthroughout the nineteenth century. In Amsterdam it took strongconductors like Willem Kes and Willem Mengelberg to get rid of thecups, glasses and ashtrays, and introduce the musical puritanism thatassimilated concert performances further to church services. 1 1

To dissociate rituals from religious services and group themtogether with music performances is only a small part of a generalreclassification of the ritual phenomena. This becomes clear only at alevel of abstraction sufficiently high to enable us to abstract from, ordisregard, certain dissimilarities in order to detect certain similarities.Of course, there are dissimilarities as weIl as similarities betweenSonatas, Symphonies, i~tis, and Soma sequences. But all fourstructures are also different from many other things, e.g., poems,epics, laws, theories, stories, cults, commercial transactions,educational projects, etc.-and similar to many others, e.g., dances,games, and certain sports.

There is a certain rigidity in ritual that is absent from many kindsof music. This is partly characteristic, 12 and partly due to the nature ofour evidence, as I shall show in the next section. Western classicalmusic is comparatively rigid in the sense that it shuns improvisation.The cadenzas in concertos are exceptional, and many are writtendown. A parallel occurs in the larger Soma rituals. A lecture in the

44 FRITS STAAL

local language, called prai~rtha, which was originally largelyin1provised, is addressed to the Yajan1na after his consecration by asenior member of the community (Agni I, 329-333, 698-702). Ofcourse, improvisation often stands at the beginning, and is in duecourse replaced by rigidity- but this is a diachronistic consideration.

The structural similarities between music and ritual discussedunder the heading I through V are more than mere similarities: theyare identities. However, the structures discussed under VI and VII arenot sufficiently similar for one to say more than: i~ti and Somasequence are to some extent to Vedic ritual what Sonata andSymphonyare to classical Western music. Why then compare themwith each other? The true significance of the comparison is this.Sonata and Symphony exhibit structural categories that characterizeclassical Western music, and do not refer to anything nonmusical.Similarly, i~ti and Soma sequence exhibit structural categories thatcharacterize Vedic ritual, and do not refer to anything nonritual. Noteven the defenders of program music

the search for meaning, mathematics, music, and ritual - frits staal

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