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The Navel of the Hymn: How to Read a Rigvedic Poem From the Middle

· By Sigmoid Vedanta· 23 min read· 18 views
Rigvedaring compositionomphalosVedic poeticshymn structureStephanie JamisonCalvert WatkinsJoel BreretonRV 10.27Vedic meterIndo-European poeticsSanskrit philology

The Last Verse Was Already in the First

RV 4.51 is eleven verses long and addressed to the Dawns. It opens with light standing up out of the darkness in the east, and then calls on the goddesses by a title the hymn will not let go of:

nūnaṃ divo duhitaro vibhātīr gātuṃ kṛṇavann uṣaso janāya

“Now let the Daughters of Heaven, the Dawns shining out, make a path for the people.”

Rigveda 4.51, verse 1. My rendering, checked against Griffith (1896).

Ten verses later the hymn stops. Here is how:

tad vo divo duhitaro vibhātīr upa bruva uṣaso yajñaketuḥ

“This I say to you, Daughters of Heaven, Dawns shining out, I whose banner is the sacrifice.”

Rigveda 4.51, verse 11. My rendering, checked against Griffith (1896).

Four words come back in the same order, divo duhitaro vibhātīr uṣasaḥ, though in the first verse they are not adjacent and in the last they are. A reader can treat that as formula, the way a letter begins “Dear” and ends “Yours”. But then you notice RV 10.26, nine verses to Pūṣan, whose first verse ends pūṣā aviṣṭu māhinaḥ, “may majestic Pūṣan help”, and whose ninth verse ends pūṣā aviṣṭu māhinaḥ, the identical half-line, with nothing in between to prepare you for the return. And then RV 1.48, sixteen verses to Dawn, which asks in verse 1 for dyumnena bṛhatā rāyā, “splendour, abundant wealth”, and in verse 16 for rāyā bṛhatā and dyumnena again, as though the poet had kept the opening line on a slip of bark and reached for it when he needed to land.

Something is being closed, deliberately, from the outside. For most of the history of Rigvedic scholarship this went mostly unanalysed, partly because the hymns were mined for mythology and grammar rather than read as made objects, and partly because nobody had a name for the thing. The name arrived from an unexpected direction. In 2002 the Indo-Europeanist Calvert Watkins published a short note in the Journal of the American Oriental Society called “Pindar’s Rigveda,” and carried a technical term out of Greek lyric criticism into Vedic studies: the omphalos, the navel.[2] The claim attached to that term is considerably more interesting than the observation that hymns have tidy endings. It is that a Rigvedic hymn can be built as a ring, and that the thing the poem is actually about may be sitting not at the end but in the middle, surrounded and protected by what frames it.

1,028hymns in the Śākala Rigveda
~10,500verses, every one in a fixed meter
30%of hymns naming a god in verse 1 name the same god in their last verse
24verses of RV 10.27, with its riddles in the middle
2002the year the omphalos crossed from Pindar to the Rigveda

A Hundred Years of Calling It a Heap

The older verdict on Rigvedic hymn construction was not that it was subtle. It was that there was not much of it. A hymn invokes a god, praises him in loosely connected stanzas that could often be reordered without loss, alludes to a myth or two, and asks for cattle. Translators noted that stanzas sometimes seemed transposed; editors argued about which verses were late additions; the arrangement of the collection itself turned out to be the work of redactors sorting by deity, meter and hymn length rather than by anything the poets intended, which is the subject of the companion piece on how the Rigveda was sorted. Abel Bergaigne’s work on the history of the Saṃhitā, published in 1887, put the editorial machinery on display and in doing so made the individual hymn look even more like raw material.[12] Hermann Oldenberg, the following year, separated the transmitted text from the composed one and treated the end of Maṇḍala 10 as an appendix.[13] Both were right, and the combined effect was to discourage anyone from asking whether a single hymn was shaped.

The counter-tradition is quieter and mostly Dutch, Russian and American. Jan Gonda’s Stylistic Repetition in the Veda, a forty-three page monograph for the Dutch Academy in 1959, took the repetitions seriously as technique rather than as padding.[7] Tatyana Elizarenkova’s Language and Style of the Vedic Ṛṣis treated the hymn as an act of communication with a grammar of its own, which reframes repetition as addressed speech rather than ornament.[9] Jared Klein, in the same 2002 volume of JAOS that carried Watkins’s note, laid out the phenomenon he calls responsion: the deliberate answering of one verse by another across a hymn, in word, form and position.[8]

What made the difference, in the end, was comparison. Ring composition had been a working concept in Homeric studies since the 1940s, when the Dutch classicist W. A. A. van Otterlo gave the device its modern name; Mary Douglas’s late essay Thinking in Circles traces the idea through the Iliad, the Book of Numbers and Tristram Shandy, and defines it simply as a construction that opens a theme, develops it, and rounds it off by bringing the conclusion back to the beginning.[10] Watkins had spent a career showing that Vedic and Greek poets inherited not just words but formulas and techniques.[11] Pindar’s victory odes were the obvious bridge: in Pindaric criticism the omphalos is the central mythic block of the ode, the part the frame exists to deliver. Watkins put the two traditions side by side, and Stephanie Jamison then worked the device out for the Rigveda in a 2004 paper on structuring enigmas and in the four lectures she gave at the Collège de France that same year.[2][3][4] By the time Joel Brereton and Jamison published their guide to the Rigveda in 2020, “Ring composition and the omphalos” was a section heading in the chapter on poetics.[1]

Marble portrait bust of the Greek lyric poet Pindar, Roman copy after a Greek original
Figure 1. Pindar, in a Roman copy after a fifth-century BCE Greek original (Capitoline Museums). The analytic vocabulary now used for Rigvedic hymn architecture came out of criticism of Pindar's victory odes, where the "omphalos" is the central block the rest of the ode exists to frame. Image from Wikimedia Commons, File:Pindar Musei Capitolini MC586.jpg; see the file page for the licence terms.

What a Frame Looks Like

Start with the easy part of the claim, the part you can check in an afternoon. Rigvedic poets mark the edges of a hymn. The marking can be a repeated phrase, a repeated epithet, a metrical change, or the sudden dropping of a refrain, and the following table lists six hymns where the first verse and the last verse hold hands. Every row here was checked against the romanised Saṃhitā text rather than taken from a secondary source.

Hymn Verses Words shared by the first and last verse Sense
RV 3.28 6 agne … puroḷāśaṃ … jātavedaḥ … juṣasva “Agni, Jātavedas, enjoy the cake”
RV 4.51 11 divo duhitaro vibhātīr uṣasaḥ “Daughters of Heaven, Dawns shining out”
RV 10.26 9 pūṣā aviṣṭu māhinaḥ “may majestic Pūṣan help”
RV 1.48 16 rāyā bṛhatā, dyumnena “with abundant wealth, with splendour”
RV 1.39 10 marutaḥ, dhūtayaḥ “Maruts, you shakers”
RV 8.85 9 nāsatyā aśvinā … yuvam “you two, Nāsatyas, Aśvins”

The tightest of these is worth opening properly. RV 3.28 is six verses about a rice-cake. Verse 1:

agne juṣasva no haviḥ puroḷāśaṃ jātavedaḥ | prātaḥsāve dhiyāvaso

“Agni, enjoy our oblation, the cake, O Jātavedas, at the morning pressing, you whose wealth is insight.”

Rigveda 3.28, verse 1. My rendering, checked against Griffith (1896).

Verse 6:

agne vṛdhāna āhutiṃ puroḷāśaṃ jātavedaḥ | juṣasva tiroahnyam

“Agni, as you grow, the offering, the cake, O Jātavedas: enjoy it, the one kept since yesterday.”

Rigveda 3.28, verse 6. My rendering, checked against Griffith (1896).

Same god, same epithet, same cake, same verb. If that were all, it would be a bracket. It is not all, because the hymn also changes shape between the brackets. Counting syllables in the romanised text gives the profile below, and the profile is the argument.

Verse Syllables (counted) Meter implied Moment in the ritual day
1 25 gāyatrī, 3 x 8 morning pressing (prātaḥsava)
2 24 gāyatrī morning, the cake prepared
3 27 gāyatrī (irregular) the day-old cake
4 45 triṣṭubh, 4 x 11 midday pressing (mādhyandina savana)
5 48 jagatī, 4 x 12 third pressing (tṛtīya savana)
6 24 gāyatrī close, the day-old cake again

Three short verses, two long ones, one short one. The hymn physically swells at verses 4 and 5, and what sits in the swelling is the progress of the sacrificial day from midday to the evening pressing, with the heavier material, the rite carried to the gods and placed among the immortals, handled in the longer line. Then the meter contracts back to the opening shape and the cake comes round again. Anyone who has watched a piece of music return to its first theme after a modulation knows exactly what this is. It is not a string of praises. It is a designed object with a front, a back, and a middle that carries more weight than either.

Aside. A warning about the English in the data behind this site. Griffith printed the eleven Vālakhilya hymns of Maṇḍala 8 separately, so from 8.49 onward his hymn numbers run eleven below the standard text, and a careless lookup gives you the wrong hymn entirely. The renderings of 8.85 here are my own from the Sanskrit for that reason. Translation history has its own hazards, surveyed in the piece on Griffith and his Latin verses.

The Thing in the Middle

A frame is a modest claim. The omphalos is the ambitious one.

Delphi kept a stone called the navel of the world, a marked lump of rock that claimed to be the centre of the earth, and Greek critics borrowed the word for the centre of a Pindaric ode: the mythic narrative that the opening praise leads into and the closing praise leads out of. The ode’s architecture exists to put the myth in the middle. Jamison’s proposal, as a classicist summarising her scheme describes it, is that Rigvedic hymns can be laid out as A1, B1, X, B2, A2, where the matched outer elements frame a central X that is either a riddle or the conceptual key to the whole poem.[5] The frame is not decoration around the message. The frame is how you find the message.

Carved stone omphalos from Delphi displayed in the Delphi Archaeological Museum
Figure 2. The omphalos from Delphi, the stone that claimed to mark the navel of the world, now in the Delphi Archaeological Museum. The term it gave to Greek literary criticism was carried into Vedic studies in 2002. Image from Wikimedia Commons, File:Delphi omphalos.jpg; see the file page for the licence terms.
graph TD
    A1[A1: opening address] --> B1[B1: praise and myth]
    B1 --> X["X: riddle or key"]
    X --> B2[B2: praise resumed]
    B2 --> A2[A2: closing address]
    A1 -.->|echo| A2
    B1 -.->|echo| B2
    X -.->|carries the point| A2

This matters for a practical reason. If a hymn’s payload sits at the end, obscurity in the middle is a defect, and nineteenth-century readers duly marked Rigvedic middles as corrupt, interpolated or hopeless.[13] If the payload sits in the middle, obscurity there is the point: the poet has put the hard thing where the hard thing belongs, and the audience that solves it has earned something. Brereton argued exactly this for the most famous dark hymn in the collection, the creation hymn RV 10.129, in a paper whose title says it plainly: the enigma is edifying, a device with work to do rather than a failure of clarity.[6] Read the Nāsadīya with that in mind and its unanswered questions stop looking like modesty and start looking like a method.

Twenty-four Verses With a Riddle in the Middle

The hymn I would put in front of a sceptic is RV 10.27, twenty-four verses in Indra’s own voice, and one of the least quoted hymns in the collection, for the excellent reason that large stretches of it cannot be construed with confidence.

It begins as a contract. Indra states his terms: he will help the man who presses soma, and he will deal with the man who does not.

anāśīrdām aham asmi prahantā satyadhvṛtaṃ vṛjināyantam ābhum

“I am the one who strikes down the man who offers the unmixed drink, the twister of truth, the crooked, the good-for-nothing.”

Rigveda 10.27, verse 1. My rendering; Griffith’s English text for this verse is missing from the edition used here.

The next six verses stay in that register: nobody obstructs him, the mountains do not, the deaf (so Griffith reads an obscure word) will shake at his roar, the wheel-rims of his chariot will run over those who slandered his friend. Then, at verse 8, the voice stops arguing and starts posing. Cattle have got loose and eaten another man’s barley. A daughter has been eyeless since birth, and who, knowing that, would be angry with her for blindness, and which of the two will turn his anger on him, the man who takes her home or the man who courts her (the syntax here is genuinely ambiguous, and translators split over who is angry with whom)? How many a girl pleases a suitor for her wealth? And then this, at the exact middle of the hymn:

“His feet have grasped: he eats the man who meets him. Around his head he sets the head for shelter. Sitting anear and right above he smites us, and follows earth that lies spread out beneath him.”

(RV 10.27, verse 13, trans. Griffith 1896)

Nobody knows what that is. It is a riddle with a missing answer, of the kind collected in the piece on verses nobody can translate, and it sits in the thirteenth of twenty-four verses, with eleven riddles before it and ten after. Seven heroes come up from below, eight from above, nine from behind with winnowing baskets, ten over the ridge. A cow lows, bound to every tree. A troop advances without wheels. Half of them will cook and half will not. The hymn’s own last verse then steps back out of the riddling and addresses someone directly:

sā te jīvātur uta tasya viddhi mā smaitādṛg apa gūhaḥ samarye

“That is your livelihood: know it, and know that. Do not hide yourself like that in the contest.”

Rigveda 10.27, verse 24. My rendering, checked against Griffith (1896).

Read linearly, the hymn is a mess: a boast, then sixteen verses of non sequitur, then an instruction. Read as a ring, it has a shape you could diagram on a napkin.

Verses What happens Function in the ring
1 to 7 Indra states his terms, names the sacrificer he backs and the miser he destroys A1: the frame, in direct speech
8 to 12 cattle, barley, the eyeless daughter, the suitor and the bride B1: riddles about ownership and exchange
13 the unnamed thing that eats whoever meets it X: the unsolved centre
14 to 23 leafless heaven, counted heroes, dice, the wheelless troop, the thunderbolt B2: riddles about counting and cosmos
24 “know it; do not hide yourself in the contest” A2: the frame closes, in direct speech

Two observations about that table. The first is that the frame verses are the only ones in the hymn whose addressee is unambiguous, which is what frames are for: they tell you who is talking to whom, so the centre is free to be strange. The second is that the last verse tells its addressee not to hide, in a hymn whose middle has spent sixteen verses hiding, and then adds that he makes the light manifest and hides the busa, a word rendered as chaff by some and as mist by others. The Rigveda does this sort of thing on purpose often enough that there is a whole essay in this series on its vocabulary of concealment.

I want to be careful here. The division above is my reading of the hymn, not a scholarly consensus, and a competing account is available: the end of Maṇḍala 10 carries compiled material, and a run of riddles can be an anthology rather than an argument.[13][19] Most of the riddles in this hymn have no agreed solution, and anyone claiming to know what verse 13 describes is guessing. What the ring hypothesis buys is not certainty. It is a reason to look at verse 13 at all.

I Tried to Count It, and Counting Failed

If hymns are rings, a computer should see the rings. This site ships the complete romanised Saṃhitā, so the test is cheap: measure how much vocabulary a hymn’s first and last verse share, and compare that with what the same hymn shares elsewhere. For two verses with word sets $T_i$ and $T_j$, take

$$\mathrm{ov}(i,j) = \frac{|T_i \cap T_j|}{\min(|T_i|, |T_j|)}$$

and compute it on five-character stems of every word longer than three characters, which is a crude way of surviving Sanskrit inflection. The results were not what I expected.

Test Measure Result What it says
First verse against last 589 hymns of 8 or more verses 0.0357 the raw echo is small
Matched control, verses (1, n-1) and (2, n) same hymns 0.0350 the echo is not larger than its neighbours
Hymns beating their own control 107 of 589 18% the device is a minority practice, not a default
Similarity of a verse to the rest of its hymn, by position opening verse 0.0452 openings restate the hymn’s own vocabulary
Same, final verse final verse 0.0337 endings are the most lexically foreign position
Metrically odd verse in mixed hymns 271 hymns 77 at the opening, 42 at the close, fewer in the middle meter marks the edges, not the centre

Read those rows together and they say two things. A blunt word-matching instrument does not find ring composition, which is a fact about the instrument as much as about the poetry: the echo between boundary verses is often a matter of syntax, grammatical form and theme rather than identical strings, which is precisely the kind of answering that Klein’s work on responsion was built to describe.[8] And in the places where a crude test does see structure, it sees it at the edges. The final verse of a Rigvedic hymn is the single most lexically distinctive position in the whole poem, because that is where the formulaic closers live: the benediction, the gift-list, the family signature studied in the piece on Rigvedic sign-offs. In the eleven hymns where the identical three-word ending survives in at least sixty per cent of the verses, the verses that break the refrain cluster at the beginning and the end rather than in the middle. RV 1.105 carries vittaṃ me asya rodasī, “take note of this trouble of mine, Heaven and Earth”, through eighteen consecutive verses and then drops it in verse 19 for a standard closing formula naming Mitra, Varuṇa, Aditi, Sindhu, Earth and Heaven. The refrain is the body; dropping it is the door.

Methods note. Three cautions about the table. The counts come from the romanised Saṃhitā in this repository, which derives from the Sanskrit text at sacred-texts.com; verse division differs slightly between editions, so the totals here are not identical to the standard 10,552. Stem truncation at five characters is a hack, not morphology, and it both merges words it should not and splits words it should not. And the measure is symmetric and bag-of-words, so it is blind to word order, to position within the verse, and to the grammatical responsion that carries much of the real work. The deity-name figure in the stat grid counts hymns of six verses or more whose first verse contains the name of one of fifteen major gods, then asks whether the final verse contains the same name: 107 of 354, or 30.2 per cent. The refrain tally undercounts, because the source edition abbreviates repeated refrains in some hymns, RV 1.105 among them, where the refrain is printed in full once and then cut short. A negative result from a blunt instrument is evidence about the instrument.

Where the Poets Put Their Own Navel

The Greek word for the centre of a poem is the word for the centre of a body. So is the Sanskrit one.

Nābhi (नाभि) in the Rigveda is the navel, the hub of a wheel, the kinship-centre of a family, and by extension the point at which a structure holds. Agni Vaiśvānara is called nābhir asi kṣitīnām, “you are the navel of the settlements”, in RV 1.59, and in the next verse the image is pushed to cosmic scale:

mūrdhā divo nābhir agniḥ pṛthivyā

“Agni is the head of heaven, the navel of the earth.”

Rigveda 1.59, verse 2. My rendering, checked against Griffith (1896).

The riddle hymn calls the year’s wheel trinābhi, three-naved, and insists that its nave has not broken since ancient times (RV 1.164, verses 2 and 13). Fire at the centre of a settlement, the hub at the centre of a wheel, the navel at the centre of a body and a lineage: the Vedic poets had one word for the place where a thing is held together from inside, and they used it constantly. The essay on the poet as carpenter documents how thoroughly these poets thought of a hymn as something built, measured and fitted. A builder who has a word for a hub is not unlikely to have put one in his poem.

That paragraph is the most seductive thing in this article and should be taken with the most salt. No Rigvedic poet calls the middle of his own hymn a nābhi. There is no Vedic treatise on hymn structure; the ancillary literature is interested in meter, phonetics and ritual application, not in composition. The convergence of omphalos and nābhi is a resonance a modern reader notices, not evidence of a native theory.

Aside. Structure-hunting has a known failure mode. Hymns are short, formulaic and full of divine names, so a determined reader can find a ring in almost any of them, and a published ring analysis is unfalsifiable if the analyst is free to choose which elements count as matched. The honest form of the claim is comparative and probabilistic: this hymn, measured against the way other hymns in its own book handle their edges and their middles, is doing something unusual. RV 1.105 is a good test of one’s own discipline. Its central verses say madhye tasthur maho divaḥ, “they stood in the middle of great heaven”, and madhya ārodhane divaḥ, “in the middle of heaven’s ascent”, and the verse just before them has the poet’s own nābhir ātatā, “my navel stretched out”. A hymn’s middle that keeps saying “middle” is either a wink or a coincidence, and I cannot prove it is a wink.

Why Anyone Would Build a Poem This Way

The Rigvedic poet worked in a competitive, paid, single-performance economy. A hymn was commissioned, performed once at a ritual before an audience of specialists who knew the repertoire, and judged against rival poets, who were paid by a patron for the result.[1] Its author needed to be recognised as doing something new within an inherited idiom, which is the subject of the piece on the cult of the new song. Three features of that situation favour rings.

First, orientation. A listener with no written text and no title page needs to know when a poem has started and when it has ended, and a repeated frame does that work audibly. The modern listener’s equivalent is the returning chorus.

Second, difficulty management. If the hard material sits at the end, a performance that loses its audience loses everything; if it sits in the middle, framed by material that tells you who is being addressed and what the transaction is, the obscurity is survivable and even enjoyable. The Rigveda contains outright riddle contests and the vocabulary of verbal competition; the riddle hymn of Dīrghatamas is fifty-two verses of this, and the dialogue hymns suggest performance conditions in which a listener was expected to follow sharp shifts without stage directions.

Third, concealment as value. This is the part modern readers find strangest. In a tradition where knowledge is a professional asset, and where the text itself keeps saying that the good things are guhā, in hiding, placing the key where it has to be looked for is not obstruction, it is pricing. The poet who buries the point in verse 13 is selling the audience a reason to come back, and selling the patron a poem that cannot be fully consumed on first hearing.

What Is Still Unsettled

Three open questions, in increasing order of how much they would change the picture.

Is the unit the hymn or something smaller? Jamison’s lectures are concerned with the internal unity of the hymn, but Rigvedic poets also worked in strophes and verse-groups, and the pragātha pairs of Maṇḍala 8 show that a two-verse strophe could be the compositional atom.[1] A frame around a three-verse strophe and a frame around a twenty-four verse hymn may not be the same technique scaled up.

Is the centre a key or a turn? Jamison’s formulation makes X the conceptual key or the riddle. Alexander Forte has argued that in a set of early Indo-European poems, including RV 10.129, Cato’s field lustration and a passage of Iliad 23, the centre works instead as a turning point, a hinge rather than a vault; he also raises the question of whether the technique is an inheritance from a common oral tradition or a convergent solution to the same performance problem.[5]

And how much of the shape belongs to editors? Rigvedic hymns passed through redactors who arranged the collection and, in places, appended verses; the gift-praises and benedictions that make hymn endings so lexically distinctive are exactly the material most suspected of being added.[12][13][19] A ring whose closing element is an editorial addition is a ring the poet did not make. For some hymns this is certainly the case. For RV 3.28, where the closing verse returns the opening meter as well as the opening words, it is hard to believe.

Read One From the Middle

Here is an experiment that takes ten minutes. Open RV 10.27 and read verse 13 first, cold, with no context: the thing that eats whoever meets it. Then read verse 1 and verse 24, the two frame verses, and notice that between them they tell you the entire transaction the hymn is about, a god and a sacrificer settling terms, with a warning against hiding at the end. Then read the riddles in between in the knowledge that they are the goods, not the packaging.

What this does, cumulatively, is change the Rigveda from an anthology of devotion into a corpus of designed objects, which is what its poets would have recognised. They were professionals who said they fashioned a hymn with the verb used for carpentry: at RV 1.130.6 men shape a speech for Indra rathaṃ na dhīraḥ svapā atakṣiṣuḥ, “as a skilled craftsman fashions a chariot”, and at RV 1.62.13 a poet of the Gotamas has atakṣad brahma navyam, “fashioned a new formulation”. These are people who had one word for the hub of a wheel and the navel of the earth. Ṛta, the order they believed the world ran on, was not a sentiment; it was fit, joint, the correct assembly of parts. A hymn with a frame and a loaded middle is that conviction rendered in syllables. It is also, incidentally, a reading instruction that the text has been issuing for three thousand years to anyone who started at verse 1 and stopped at the end.

Next time, start in the middle.

References

  1. Brereton, Joel P., and Stephanie W. Jamison. The Rigveda: A Guide. New York: Oxford University Press, 2020. Chapter 9, “Ṛgvedic Poetry and Poetics,” pp. 112-190, includes the section “Ring composition and the omphalos.” academic.oup.com.

  2. Watkins, Calvert. “Pindar’s Rigveda.” Journal of the American Oriental Society 122, no. 2 (2002): 432-435.

  3. Jamison, Stephanie W. The Rig Veda between Two Worlds / Le Ṛgveda entre deux mondes: Quatre conférences au Collège de France en mai 2004. Publications de l’Institut de Civilisation Indienne 74. Paris: Édition-Diffusion de Boccard, 2007.

  4. Jamison, Stephanie W. “Poetry and Purpose in the Ṛgveda: Structuring Enigmas.” In The Vedas: Texts, Language and Ritual, edited by Arlo Griffiths and Jan E. M. Houben, Groningen Oriental Studies XX. Groningen: Egbert Forsten, 2004.

  5. Forte, Alexander S. W. “A New Type of Ring Composition? Towards a Technique of Inherited Poetics.” Abstract, Society for Classical Studies annual meeting. classicalstudies.org. Cited here for its statement of Jamison’s A1-B1-X-B2-A2 scheme and for the turning-point alternative.

  6. Brereton, Joel P. “Edifying Puzzlement: Ṛgveda 10.129 and the Uses of Enigma.” Journal of the American Oriental Society 119, no. 2 (1999): 248-260.

  7. Gonda, Jan. Stylistic Repetition in the Veda. Verhandelingen der Koninklijke Nederlandse Akademie van Wetenschappen, Afd. Letterkunde, Nieuwe Reeks 65:3. Amsterdam: Noord-Hollandsche Uitgevers Maatschappij, 1959.

  8. Klein, Jared S. “Responsion in the Rigveda.” Journal of the American Oriental Society 122, no. 2 (2002): 311-317.

  9. Elizarenkova, Tatyana J. Language and Style of the Vedic Ṛṣis. Edited with an introduction by Wendy Doniger. SUNY Series in Hindu Studies. Albany: State University of New York Press, 1995.

  10. Douglas, Mary. Thinking in Circles: An Essay on Ring Composition. The Terry Lectures. New Haven: Yale University Press, 2007. yalebooks.yale.edu.

  11. Watkins, Calvert. How to Kill a Dragon: Aspects of Indo-European Poetics. New York: Oxford University Press, 1995.

  12. Bergaigne, Abel. Recherches sur l’histoire de la Saṃhitā du Rig-Véda. Paris: Imprimerie Nationale, 1887. gallica.bnf.fr.

  13. Oldenberg, Hermann. Die Hymnen des Rigveda, Band I: Metrische und textgeschichtliche Prolegomena. Berlin: Wilhelm Hertz, 1888. archive.org.

  14. Jamison, Stephanie W., and Joel P. Brereton, trans. The Rigveda: The Earliest Religious Poetry of India. 3 vols. New York: Oxford University Press, 2014. global.oup.com. The standard modern English translation; used as a control on every rendering here.

  15. Jamison, Stephanie W., and Joel P. Brereton. Rigveda Translation: Commentary. Los Angeles: UCLA, ongoing. rigvedacommentary.alc.ucla.edu.

  16. Griffith, Ralph T. H. The Hymns of the Rigveda. 2 vols. Benares: E. J. Lazarus, 1896. archive.org. Used throughout as the check translation; renderings marked as mine are my own from the Sanskrit.

  17. Geldner, Karl Friedrich. Der Rig-Veda aus dem Sanskrit ins Deutsche übersetzt. 4 vols. Harvard Oriental Series 33-36. Cambridge, MA: Harvard University Press, 1951.

  18. Macdonell, Arthur A., and Arthur B. Keith. Vedic Index of Names and Subjects. 2 vols. London: John Murray, 1912. archive.org. Consulted for nābhi and for the Vālakhilya numbering.

  19. Witzel, Michael. “The Development of the Vedic Canon and its Schools: The Social and Political Milieu.” In Inside the Texts, Beyond the Texts: New Approaches to the Study of the Vedas, edited by Michael Witzel. Harvard Oriental Series, Opera Minora 2. Cambridge, MA, 1997, pp. 257-345.

  20. Renou, Louis. Études védiques et pāṇinéennes. 17 vols. Paris: de Boccard, 1955-1969.

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