Sanskrit prosody

"Chanda" redirects here. For other uses, see Chanda (disambiguation).
"Chandas" redirects here. For the Telegu poetry, see Chandas (poetry). For the typeface, see Chandas (typeface).

Sanskrit prosody or Chandas refer to one of the six Vedangas, or limbs of Vedic studies.[1] It is the study of poetic metres and verse in Sanskrit.[1] This field of study was central to the composition of the Vedas, the scriptural canons of Hinduism, so central that some later Hindu and Buddhist texts refer to the Vedas as Chandas.[1][2]

The Chandas, as developed by the Vedic schools, were notable for including both linear and non-linear systems.[3] The system was organized around seven major meters, state Annette Wilke and Oliver Moebus, called the "seven birds" or "seven mouths of Brihaspati", and each had its own rhythm, movements and aesthetics wherein a non-linear structure (aperiodicity) was mapped into a four verse polymorphic linear sequence.[3] The structure of meters in Sanskrit prosody include those based on fixed number of syllables per verse, and those based on fixed number of morae per verse.[4]

The Gayatri meter was structured with 3 verses of 8 syllables (6x4), the Usnih with 2 verses of 8 and 1 of 12 syllables (7x4), the Anustubh with 4 verses of 8 syllables (8x4), Brihati with 2 verses of 8 followed by 1 each of 12 and 8 syllables (9x4), the Pankti with 5 verses of 8 syllables (10x4), the Tristubh with 4 verses of 11 syllables (11x4), and the Jagati meter with 4 verses of 12 syllables each (12x4).[5] In Vedic culture, the Chandas were revered for their perfection and resonance, with Gayatri meter treated as the most refined and sacred, and one that continues to be part of modern Hindu culture as part of Yoga and hymns of meditation at sunrise.[6]

Extant ancient manuscript on Chandas include Pingala's Chandah Sutra, while an example of Middle Ages Sanskrit prosody manuscript is Kedara Bhatta's Vrittaratnakara.[7][note 1] The most exhaustive compilations of Sanskrit prosody contain over 600 meters.[10] This is a substantially larger repertoire than in any other metrical tradition.[11]

Etymology

The term Chanda (Sanskrit: छन्द) means "pleasing, alluring, lovely, delightful or charming", and is based on the root chad which means "esteemed to please, to seem good, feel pleasant and/or something that nourishes, gratifies or is celebrated".[12] The term also refers to "any metrical part of the Vedas or other composition".[12]

History

Ancient Sanskrit on Hemp based Paper. Hemp Fiber was commonly used in the production of paper from 200 BCE to the Late 1800's.

The hymns of Rigveda include the names of meters which, states Peter Scharf, implies that the discipline of Chandas (Sanskrit prosody) emerged in the 2nd-millennium BCE.[4][note 2] The Brahmanas layer of Vedic literature, composed between 900 BCE and 700 BCE, contain a complete expression of the Chandas.[15] Panini's treatise on Sanskrit grammar distinguishes Chandas as verses that compose the Vedas, and Bhasya (Sanskrit: भाष्य) to be the speech language used for learned discourse and scholastic discussion of the Vedas.[16]

The Vedic Sanskrit texts employ fifteen meters, of which seven are common, and the most frequent are three (8-, 11- and 12-syllable lines).[17] The post-Vedic texts, such as the epics as well as other classical literature of Hinduism, deploy both linear and non-linear meters, many of which are based on syllables and others based on diligently crafted verses based on repeating numbers of morae (matra per foot).[17] About 150 treatises on Sanskrit prosody from classical era are known, in which some 850 meters were defined and studied by the ancient and medieval Hindu scholars.[17]

The ancient Chandahsutra of Pingala, also called Pingala Sutras, is the oldest Sanskrit prosody text that has survived into the modern age, and it is dated to between 600 and 200 BCE.[18][19] Like all Sutras, the Pingala text is distilled information in the form of aphorisms, and these were widely commented on through the bhasya tradition of Hinduism. Of the various commentaries, those widely studied are the three 6th century texts - Jayadevacchandas, Janasrayi Chandoviciti and Ratnamanjusa,[20] the 10th century commentary by Karnataka prosody scholar Halayudha, who also authored the grammatical Sastrakavya and Kavirahasya (literally, The Poet's Secret).[18] Other important historical commentaries include those by 11th-century Yadavaprakasha and 12th-century Bhaskaracharya, as well as Jayakriti's Chandonusasana, and Chandomanjari by Gangadasa.[18][20]

There is no word without meter,
nor is there any meter without words.

—Natya Shastra[21]

Major encyclopedic and arts-related Hindu texts from the 1st and 2nd millennium CE contain sections on Chandas. For example, the chapters 328 to 335 of the Agni Purana,[22][23] chapter 15 of the Natya Shastra, chapter 104 of the Brihat Samhita, the Pramodajanaka section of the Manasollasa contain embedded treatises on Chandas.[24][25][26]

Elements of Sanskrit prosody

Nomenclature

A syllable (Akshara, अक्षर), in Sanskrit prosody, is a vowel with one or more consonants, or a vowel without any.[27] The short syllable is one with short (hrasva) vowels, which are a (अ), i (इ), u (उ), ṛ (ऋ) and ḷ (ऌ). The long syllable is defined as one with long (dirgha) vowels, which are ā (आ), ī (ई), ū (ऊ), ṝ (ॠ), e (ए), ai (ऐ), o (ओ) and au (औ).[27]

A stanza (pāda) is defined in Sanskrit prosody as a group of four verses, also called as four quarters.[27] Indian prosody studies developed two types of stanzas. Vritta stanza are those that are crafted with precise number syllables, while Jati stanza are those that are designed based on syllabic instants (morae, matra).[27]

The Vritta[note 3] stanza are further recognized in three forms, with Samavritta where the four quarters are similar in its embedded mathematical pattern, Ardhasamavritta where alternate verses keep similar syllabic structure, and Vishamavritta where all four quarters are different.[27] A regular Vritta is defined as that where the total number of syllables in each verse is less than or equal to 26 syllables, while irregulars contain more.[27] When syllabic instants (matra) is the foundation of the Sanskrit prosody, a short syllable is counted as one instant, and a long syllable is counted as two instants.[27]

Classification

The metres found in classical Sanskrit poetry are sometimes alternatively classified into three kinds.[29]

  1. Syllabic verse (akṣaravṛtta or aksharavritta): meters depend on the number of syllables in a verse, with relative freedom in the distribution of light and heavy syllables. This style is derived from older Vedic forms, and found in the great epics, the Mahabharata and the Ramayana.
  2. Syllabo-quantitative verse (varṇavṛtta or varnavritta): meters depend on syllable count, but the light-heavy patterns are fixed.
  3. Quantitative verse (mātrāvṛtta or matravritta): meters depend on duration, where each verse-line has a fixed number of morae, usually grouped in sets of four.

Light and heavy syllables

In most of Sanskrit poetry the primary determinant of a meter is the number of syllables in a unit of verse, called the pāda ("foot" or "quarter"). Meters of the same length are distinguished by the pattern of laghu ("light") and guru ("heavy") syllables in the pāda. The rules distinguishing laghu and guru syllables are the same as those for non-metric prose, and these are specified in Vedic Shiksha texts that study the principles and structure of sound, such as the Pratisakhyas. Some of the significant rules are:[30][31]

Metre is a veritable ship,
for those who want to go,
across the vast ocean of poetry.

—Dandin, 7th century[32]

  1. A syllable is laghu only if its vowel is hrasva ("short") and followed by at most one consonant before another vowel is encountered.
  2. A syllable with an anusvara ('ṃ') or a visarga ('ḥ') is always guru.
  3. All other syllables are guru, either because the vowel is dīrgha ("long"), or because the hrasva vowel is followed by a consonant cluster.
  4. The hrasva vowels are the short monophthongs: 'a', 'i', 'u', 'ṛ' and 'ḷ'
  5. All other vowels are dirgha: 'ā', 'ī', 'ū', 'ṝ', 'e', 'ai', 'o' and 'au'. (Note that, morphologically, the last four vowels are actually the diphthongs 'ai', 'āi', 'au' and 'āu', as the rules of sandhi in Sanskrit make clear.)[33]
  6. Gangadasa Pandita states that the last syllable in each pāda may be considered guru, but a guru at the end of a pāda is never counted as laghu.[note 4]

For measurement by mātrā (morae), laghu syllables count as one unit, and guru syllables as two units.[34]

Exceptions

The Hindu prosody treatises crafted exceptions to these rules based on their study of sound, which apply in Sanskrit and Prakrit prosody. For example, the last vowel of a verse, regardless of its natural length, may be considered short or long according to the requirement of the meter.[27] Exceptions also apply to special sounds, of the type प्र, ह्र, ब्र and क्र.[27]

Gaṇa

Gaṇa (Sanskrit, "group") is the technical term for the pattern of light and heavy syllables in a sequence of three. It is used in treatises on Sanskrit prosody to describe meters, according to a method first propounded in Pingala's chandahsutra. Pingala organizes the meters using two units:[35]

  • l: a "light" syllable (L), called laghu
  • g: a "heavy" syllable (H), called guru
Metrical feet
Disyllables
˘ ˘ pyrrhus, dibrach
˘ ¯ iamb
¯ ˘ trochee, choree
¯ ¯ spondee
Trisyllables
˘ ˘ ˘ tribrach
¯ ˘ ˘ dactyl
˘ ¯ ˘ amphibrach
˘ ˘ ¯ anapaest, antidactylus
˘ ¯ ¯ bacchius
¯ ¯ ˘ antibacchius
¯ ˘ ¯ cretic, amphimacer
¯ ¯ ¯ molossus
See main article for tetrasyllables.

Pingala's method described any meter as a sequence of gaṇas, or triplets of syllables (trisyllabic feet), plus the excess, if any, as single units. There being eight possible patterns of light and heavy syllables in a sequence of three, Pingala associated a letter, allowing the meter to be described compactly as an acronym.[36] Each of these has its Greek prosody equivalent as listed below.

The Ganas (गण, class)[37][38]
Sanskrit
prosody 		Weight Symbol Style Greek
equivalent
Na-gaṇa L-L-L u u u
da da da
 Tribrach
Ma-gaṇa H-H-H — — —
DUM DUM DUM
 Molossus
Ja-gaṇa L-H-L u — u
da DUM da
 Amphibrach
Ra-gaṇa H-L-H — u —
DUM da DUM
 Cretic
Bha-gaṇa H-L-L — u u
DUM da da
 Dactyl
Sa-gaṇa L-L-H u u —
da da DUM
 Anapaest
Ya-gaṇa L-H-H u — —
da DUM DUM
 Bacchius
Ta-gaṇa H-H-L — — u
DUM DUM da
 Antibacchius

Pingala's order of the gaṇas, viz. m-y-r-s-t-j-bh-n, corresponds to a standard enumeration in binary, when the three syllables in each gaṇa are read right-to-left with H=0 and L=1.

A mnemonic

The word yamātārājabhānasalagāḥ (or yamātārājabhānasalagaṃ) is a mnemonic for Pingala's gaṇas, developed by ancient commentators, using the vowels "a" and "ā" for light and heavy syllables respectively with the letters of his scheme. In the form without a grammatical ending, yamātārājabhānasalagā is self-descriptive, where the structure of each gaṇa is shown by its own syllable and the two following it:[39]

The mnemonic also encodes the light "la" and heavy "gā" unit syllables of the full scheme.

The truncated version obtained by dropping the last two syllables, viz. yamātārājabhānasa, can be read cyclically (i.e., wrapping around to the front). It is an example of a De Bruijn sequence.[40]

Comparison with Greek and Latin prosody

Sanskrit prosody shares similarities with Greek and Latin prosody. For example, in all three, rhythm is determined from the amount of time needed to pronounce a syllable, and not on stress (quantitative meter).[41][42] Each eight syllable line, for instance in the Rigveda, is almost exactly equivalent to the Greek iambic dimeter.[28] The sacred Gayatri meter of the Hindus consists of three of such iambic dimeter lines, and this embedded meter alone is at the heart of about 25% of the entire Rigveda.[28]

The gaṇas are, however, not the same as the foot in Greek prosody. The metrical unit in Sanskrit prosody is the verse (line, pada), while in Greek prosody it is the foot.[43] The Sanskrit prosody allows elasticity similar to Latin Saturnian verse, uncustomary in Greek prosody.[43] The roots of the Sanskrit and Greek prosody likely are in Proto-Indo-European times, because the Vedic and Greek metrical principles are found in ancient Persian, Italian, Celtic, Slavonic, Graeco-Aryan and most of the European languages.[44]

The seven birds: major Sanskrit meters

The Vedic Sanskrit prosody included both linear and non-linear systems.[3] The field of Chandas was organized around seven major meters, state Annette Wilke and Oliver Moebus, called the "seven birds" or "seven mouths of Brihaspati",[note 5] and each had its own rhythm, movements and aesthetics. The system mapped a non-linear structure (aperiodicity) into a four verse polymorphic linear sequence.[3]

गायत्रेण प्रति मिमीते अर्कमर्केण साम त्रैष्टुभेन वाकम् ।
वाकेन वाकं द्विपदा चतुष्पदाक्षरेण मिमते सप्त वाणीः ॥२४॥

With the Gayatri, he measures a song; with the song – a chant, with the Tristubh – a recited stanza,
With the stanza of two feet and four feet – a hymn; with the syllable they measure the seven voices. ॥24॥

— Rigveda 1.164.24, Translated by Tatyana J. Elizarenkova[46]

The seven major ancient Sanskrit meters are the three 8-syllable Gayatri, the four 8-syllable Anustubh, the four 11-syllable Tristubh, the four 12-syllable Jagati, and the mixed padas meters named Ushnih, Brihati and Pankti.

The major ancient meters in Sanskrit prosody[5][47]
Meter Structure Mapped
Sequence[5] 		Varieties[48] Usage[49]
Gayatri 24 syllables;
3 verses of 8 syllables 		6x4 11 Common in Vedic texts
Example: Rigveda 7.1.1-30, 8.2.14[50]
Ushnih 28 syllables;
2 verses of 8;
1 of 12 syllables 		7x4 8 Vedas, not common
Example: Rigveda 1.8.23-26[51]
Anushtubh 32 syllables;
4 verses of 8 syllables 		8x4 12 Most frequent in post-Vedic Sanskrit metrical literature; embedded in the Bhagavad Gita, the Mahabharata, the Ramayana, the Puranas, Smritis and scientific treatises
Example: Rigveda 8.69.7-16, 10.136.7[52]
Brihati 36 syllables;
2 verses of 8;
1 verse of 12;
1 verse of 8 syllables 		9x4 12 Vedas, rare
Example: Rigveda 5.1.36, 3.9.1-8[53]
Pankti 40 syllables;
5 verses of 8 syllables 		10x4 14 Uncommon, found with Tristubh
Example: Rigveda 1.191.10-12[54]
Tristubh 44 syllables;
4 verses of 11 syllables 		11x4 22 Second in frequency in post-Vedic Sanskrit metric literature, dramas, plays, parts of the Mahabharata, major 1st-millennium Kavyas
Example: Rigveda 4.50.4, 7.3.1-12[55]
Jagati 48 syllables;
4 verses of 12 syllables 		12x4 30 Third most common, typically alternates with Tristubh in the same text, also found in separate cantos.
Example: Rigveda 1.51.13, 9.110.4-12[56]

Other syllable-based meters

Beyond these seven meters, ancient and medieval era Sanskrit scholars developed numerous other syllable-based meters (Akshara-chandas). Examples include Atijagati (13x4, in 16 varieties), Sakkari (14x4, in 20 varieties), Atisakkari (15x4, in 18 varieties), Ashti (16x4, in 12 varieties), Atyashti (17x4, in 17 varieties), Dhriti (18x4, in 17 varieties), Atidhriti (19x4, in 13 varieties), Kriti (20x4, in 4 varieties) and so on.[57][58]

Morae-based meters

See also: Mātrika metre

In addition to the syllable-based meters, Hindu scholars in their prosody studies, developed Gana-chandas or Gana-vritta, that is meters based on mātrās (morae, instants).[59][58][60] The metric foot in these are designed from laghu (short) morae or their equivalents. Sixteen classes of these instants-based meters are enumerated in Sanskrit prosody, each class has sixteen sub-species. Examples include Arya, Udgiti, Upagiti, Giti and Aryagiti.[61] This style of composition is less common than syllable-based metric texts, but found in important texts of Hindu philosophy, drama, lyrical works and Prakrit poetry.[17][62] The entire Samkhyakarika text of the Samkhya school of Hindu philosophy is composed in Arya meter, as are many chapters in the mathematical treatises of Aryabhata, and some texts of Kalidasa.[61][63]

Hybrid meters

Hindu scholars developed hybrid class of Sanskrit meters, which combined features of the syllable-based meters and morae-based meters.[64][58] These were called Matra-chandas. Examples of this group of meters include Vaitaliya, Matrasamaka and Gityarya.[65] The Hindu texts Kirātārjunīya and Naishadha Charita, for instance, feature complete cantos that are entirely crafted in the Vaitaliya meter.[64][66] The Hanuman Chalisa, a 40-verse hymn of praise to Hanuman, is composed in Matra-chanda.[67]

Meters as tools for literary architecture

The Vedic texts, and later Sanskrit literature, were composed in a manner where a change in meters was an embedded code to inform the reciter and audience that it marks the end of a section or chapter.[47] A stanza in these texts feature identical meters within, rhythmically presenting their ideas through common rules of composition.[47]

Similarly, the authors of Sanskrit hymns, used meters as tools of literary architecture, wherein they coded a hymn's end by frequently using a verse of a meter different than that used in the hymn's body.[47] However, they never used Gayatri meter to end a hymn or composition, possibly because it enjoyed a special level of reverence in Hindu texts.[47] In general, all meters were sacred and the Vedic chants and hymns attribute the perfection and beauty of the meters to divine origins, referring them as mythological characters or equivalent to gods.[47]

Screen to identify corrupt texts, correct texts

The verse perfection in the Vedic texts, verse Upanishads[note 6] and Smriti texts have led some Indologists from the 19th century onwards to identify suspect portions of texts where a line or sections are off the expected meter.[68][69]

Some manuscripts editors have controversially used this "metri causa" principle to emend Sanskrit verses, with similar-sounding words, assuming that their creative conjectural rewriting will restore the meter.[68] This practice has been criticized, states Patrick Olivelle, because such modern corrections may be changing the meaning, adding to corruption, and imposing modern pronunciation of words or prejudice to ancient times when the same syllable or morae may have been pronounced differently.[68][69]

Large and significant changes in meter, wherein the meter of succeeding sections return to earlier sections, is an indication of likely later interpolations and insertion of text into a Sanskrit manuscript, or that the text is a compilation of works of different authors and time periods.[70][71][72] However, some meters are easy to preserve and consistent meter does not mean an authentic manuscript. This practice has also been questioned when applied to certain texts such as ancient and medieval era Buddhist manuscripts, with the assertion that this may reflect versatility of the author or changing styles over author's life time.[73]

Texts

Chandah Sutra

When halved, (record) two.
When unity (is subtracted, record) sunya.
When sunya, (multiply by) two.
When halved, multiply (by) itself (squared).

—Chandah Sutra 8.28-31
6th-2nd century BCE[74][75]

The Chandah Sutra is also known as Chandah sastra, or Pingala Sutras after its author Pingala. It is the oldest Hindu treatise on prosody to have survived into the modern era.[18][19] This text is structured in 8 books, with a cumulative total of 310 sutras.[76] It is a collection of aphorisms predominantly focussed on the art of poetic meters, and presents some mathematics in the service of music.[74][77]

Bhasyas

The 11th-century bhasya on Pingala's Chandah Sutra by Ratnakarashanti, called Chandoratnakara, added new ideas to Prakrit poetry, and this was influential to prosody in Nepal, and to the Buddhist prosody culture in Tibet where the field was also known as chandas or sdeb sbyor.[45]

Usage

Post-vedic poetry, epics

The Anushtubh Vedic meter has been the most popular in classical and post-classical Sanskrit works.[49] It is also octosyllabic, next harmonic to Gayatri meter that is sacred to the Hindus, and it appears either in free verse or fixed syllabic form (shloka). It has a rhythm, offers flexibility and creative space, but has embedded rules such as its sixth syllable is always long, the fifth syllable is always short; often, the seventh syllable in even numbered lines of a stanza is short (iambic) as well.[49] The Anushtubh is present in Vedic texts, but its presence is minor, and Trishtubh and Gayatri meters dominate in the Rigveda for example.[78] A dominating presence of the Anushtubh meter in a text is a marker that the text is likely post-Vedic.[79]

The Mahabharata, for example, features many verse meters in its chapters, but an overwhelming proportion of the stanzas, 95% are shlokas of the anustubh type, and most of the rest are tristubhs.[80]

The Hindu epics and the post-Vedic classical Sanskrit poetry is typically structured as quatrains of four pādas (verses), with the metrical structure of each pāda completely specified. In some cases, pairs of pādas may be scanned together as the hemistichs of a couplet.[81] It is then normal for the pādas comprising a pair to have different structures, to complement each other aesthetically. Otherwise the four pādas of a stanza have the same structure.

Chandas and mathematics

The attempt to identify the most pleasing sounds and perfect compositions led ancient Indian scholars to study permutations and combinatorial methods of enumerating musical meters.[82] The Pingala Sutras includes a discussion of binary system rules to calculate permutations of Vedic meters.[77][83][84] Pingala, and more particularly the classical Sanskrit prosody period scholars, developed the art of Matrameru, which is the field of counting sequences such as 0, 1, 1, 2, 3, 5, 8 and so on (Fibonacci numbers), in their prosody studies.[77][83][85]

The first five rows of the Pascal's triangle, also called the Halayudha's triangle.[86] Halayudha discusses this and more in his Sanskrit prosody bhasya on Pingala.

The 10th-century Halāyudha's commentary on Pingala Sutras, developed meruprastāra, which mirrors the Pascal's triangle in the west, and now also called as the Halayudha's triangle in books on mathematics.[77][86] The 11th-century Ratnakarashanti's Chandoratnakara describes algorithms to enumerate binomial combinations of meters through pratyaya. For a given class (length), the six pratyaya were:[87]

Some authors also considered, for a given metre, (A) the number of guru syllables, (B) the number of laghu syllables, (C) the total number of syllables, and (D) the total number of mātras, giving expressions for each of these in terms of any two of the other three. (The basic relations being that C=A+B and D=2A+B.)[88]

Influence

In India

Song and language

Children understand song,
beasts do too, and even snakes.
But the sweetness of literature,
does the Great God himself truly understand.

—Rajatarangini[89]

Chandas have been one of the five categories of literary knowledge in Hindu traditions. The other four are, states Sheldon Pollock, Gunas or expression forms, Riti, Marga or the ways or styles of writing, Alankara or tropology, and Rasa, Bhava or aesthetic moods and feelings.[89]

The Chandas have been revered in Hindu texts for their perfection and resonance, with Gayatri meter treated as the most refined and sacred, and one that continues to be part of modern Hindu culture as part of Yoga and hymns of meditation at sunrise.[6]

Outside India

The influence of Sanskrit Chanda has been found in southeast Asian prosody and poetry, such as Thai Chan.[90] Its influence as evidenced in the 14th-century Thai texts such as the Mahachat kham luang, has been proposed to have come either through Cambodia or Sri Lanka.[90] Evidence of the influence of Sanskrit prosody in 6th-century Chinese literature is found in the works of Shen Yueh and his followers, likely introduced through Buddhist monks who visited India.[91]

See also

Notes

  1. ↑ For a review of other Sanskrit prosody texts, see Moriz Winternitz's History of Indian Literature,[8] and HD Velankar's Jayadaman.[9]
  2. ↑ See, for example, Rigveda hymns 1.164, 2.4, 4.58, 5.29, 8.38, 9.102 and 9.103;[13] and 10.130[14]
  3. ↑ Vritta, literally "turn", is rooted in vrit, Latin vert-ere, thereby etymologically to versus of Latin and "verse" of Indo-European languages.[28]
  4. ↑ सानुस्वारश्च दीर्घश्च विसर्गी च गुरुर्भवेत् । वर्णः संयोगपूर्वश्च तथा पादान्तगोऽपि वा ॥
  5. ↑ These seven meters are also the names of the seven horses of Hindu Sun god (Aditya or Surya), mythically symbolic for removing darkness and bringing the light of knowledge.[45] These are mentioned in Surya verses of the Ashvini Shastra portion of Aitareya Brahmana.
  6. ↑ Kena, Katha, Isha, Shvetashvatara and Mundaka Upanishads are examples of verse-style ancient Upanishads.

References

  1. 1 2 3 James Lochtefeld (2002), "Chandas" in The Illustrated Encyclopedia of Hinduism, Vol. 1: A-M, Rosen Publishing, ISBN 0-8239-2287-1, page 140
  2. ↑ Moriz Winternitz (1988). A History of Indian Literature: Buddhist literature and Jaina literature. Motilal Banarsidass. p. 577. ISBN 978-81-208-0265-0.
  3. 1 2 3 4 Annette Wilke & Oliver Moebus 2011, pp. 391-392 with footnotes.
  4. 1 2 Peter Scharf (2013). Keith Allan, ed. The Oxford Handbook of the History of Linguistics. Oxford University Press. pp. 228–234. ISBN 978-0-19-164344-6.
  5. 1 2 3 Annette Wilke & Oliver Moebus 2011, p. 392.
  6. 1 2 Annette Wilke & Oliver Moebus 2011, pp. 393-394.
  7. ↑ Deo 2007, pp. 6-7 section 2.2.
  8. ↑ Maurice Winternitz 1963, pp. 1-301, particularly 5-35.
  9. ↑ HD Velankar (1949), Jayadāman (a collection of ancient texts on Sanskrit prosody and a classified list of Sanskrit metres with an alphabetical index), OCLC 174178314, Haritosha;
    HD Velankar (1949), Prosodial practice of Sanskrit poets, Journal of Royal Asiatic Society, Volume 24-25, pages 49-92.
  10. ↑ Deo 2007, pp. 3, 6 section 2.2.
  11. ↑ Deo 2007, pp. 3-4 section 1.3.
  12. 1 2 Monier Monier-Williams (1923). A Sanskrit-English Dictionary. Oxford University Press. p. 332.
  13. ↑ Origin and Development of Sanskrit Metrics, Arati Mitra (1989), The Asiatic Society, pages 4-6 with footnotes
  14. ↑ William K. Mahony (1998). The Artful Universe: An Introduction to the Vedic Religious Imagination. State University of New York Press. pp. 110–111. ISBN 978-0-7914-3579-3.
  15. ↑ Guy L. Beck 1995, pp. 40-41.
  16. ↑ Sheldon Pollock 2006, pp. 46, 268-269.
  17. 1 2 3 4 Alex Preminger; Frank J. Warnke; O. B. Hardison Jr. (2015). Princeton Encyclopedia of Poetry and Poetics. Princeton University Press. pp. 394–395. ISBN 978-1-4008-7293-0.
  18. 1 2 3 4 Sheldon Pollock 2006, p. 370.
  19. 1 2 B.A. Pingle 1898, pp. 238-241.
  20. 1 2 Andrew Ollett (2013). Nina Mirnig; Peter-Daniel Szanto; Michael Williams, eds. Puspika: Tracing Ancient India Through Texts and Traditions. Oxbow Books. pp. 331–334. ISBN 978-1-84217-385-5.
  21. ↑ Har Dutt Sharma (1951). "Suvrttatilaka". Poona Orientalist: A Quarterly Journal Devoted to Oriental Studies. XVII: 84.
  22. ↑ Rocher 1986, p. 135.
  23. ↑ MN Dutt, Agni Purana Vol 2, pages 1219-1233 (Note: Dutt's manuscript has 365 chapters, and is numbered differently)
  24. ↑ Sheldon Pollock 2006, pp. 184-188.
  25. ↑ T. Nanjundaiya Sreekantaiya (2001). Indian Poetics. Sahitya Akademi. pp. 10–12. ISBN 978-81-260-0807-0.
  26. ↑ Maurice Winternitz 1963, pp. 8–9, 31–34.
  27. 1 2 3 4 5 6 7 8 9 Lakshman R Vaidya, Sanskrit Prosody - Appendix I, in Sanskrit-English Dictionary, Sagoon Press, Harvard University Archives, pages 843-856; Archive 2
  28. 1 2 3 A history of Sanskrit Literature, Arthur MacDonell, Oxford University Press/Appleton & Co, page 56
  29. ↑ Deo 2007, p. 5.
  30. ↑ Coulson, p.21
  31. ↑ Muller & Macdonell, Appendix II
  32. ↑ Maurice Winternitz 1963, p. 13.
  33. ↑ Coulson, p.6
  34. ↑ Muller and Macdonell, loc.cit.
  35. ↑ Pingala CS 1.9-10, in order
  36. ↑ Pingala, chandaḥśāstra, 1.1-10
  37. ↑ Horace Hayman Wilson 1841, pp. 415-416.
  38. ↑ Pingala CS, 1.1-8, in order
  39. ↑ Coulson, p.253ff
  40. ↑ Stein, Sherman K. (1963), "Yamátárájabhánasalagám", The Man-made Universe: An Introduction to the Spirit of Mathematics, pp. 110–118. Reprinted in Wardhaugh, Benjamin, ed. (2012), A Wealth of Numbers: An Anthology of 500 Years of Popular Mathematics Writing, Princeton Univ. Press, pp. 139–144.
  41. ↑ Barbara Stoler Miller (2013). Phantasies of a Love Thief: The Caurapancasika Attributed to Bilhana. Columbia University Press. pp. 2 footnote 2. ISBN 978-0-231-51544-3.
  42. ↑ Alex Preminger; Frank J. Warnke; O. B. Hardison Jr. (2015). Princeton Encyclopedia of Poetry and Poetics. Princeton University Press. p. 498. ISBN 978-1-4008-7293-0.
  43. 1 2 A history of Sanskrit Literature, Arthur MacDonell, Oxford University Press/Appleton & Co, page 55
  44. ↑ Stephen Dobyns (2011). Next Word, Better Word: The Craft of Writing Poetry. Macmillan. pp. 248–249. ISBN 978-0-230-62180-0.
  45. 1 2 Jamgon Kongtrul Lodro Taye; Koṅ-sprul Blo-gros-mthaʼ-yas; Gyurme Dorje (2012). The Treasury of Knowledge: Indo-Tibetan classical learning and Buddhist phenomenology. Book six, parts one and two. Shambhala Publications. pp. 26–28. ISBN 978-1-55939-389-8.
  46. ↑ Tatyana J. Elizarenkova (1995). Language and Style of the Vedic Rsis. State University of New York Press. pp. 113–114. ISBN 978-0-7914-1668-6.
  47. 1 2 3 4 5 6 Tatyana J. Elizarenkova (1995). Language and Style of the Vedic Rsis. State University of New York Press. pp. 111–121. ISBN 978-0-7914-1668-6.
  48. ↑ Horace Hayman Wilson 1841, pp. 418-421.
  49. 1 2 3 Horace Hayman Wilson 1841, pp. 418-422.
  50. ↑ Arnold 1905, pp. 10, 48.
  51. ↑ Arnold 1905, p. 48.
  52. ↑ Arnold 1905, p. 11, 50 with note ii(a).
  53. ↑ Arnold 1905, p. 48, 66 with note 110(i).
  54. ↑ Arnold 1905, p. 55 with note iv, 172 with note viii.
  55. ↑ Arnold 1905, pp. 48 with table 91, 13 with note 48, 279 with Mandala VII table.
  56. ↑ Arnold 1905, pp. 12 with note 46, 13 with note 48, 241-242 with note 251.
  57. ↑ Horace Hayman Wilson 1841, pp. 422-426.
  58. 1 2 3 Hopkins 1901, p. 193.
  59. ↑ Horace Hayman Wilson 1841, p. 427.
  60. ↑ Andrew Ollett (2013). Nina Mirnig; Peter-Daniel Szanto; Michael Williams, eds. Puspika: Tracing Ancient India Through Texts and Traditions. Oxbow Books. pp. 331–358. ISBN 978-1-84217-385-5.
  61. 1 2 Horace Hayman Wilson 1841, pp. 427-428.
  62. ↑ Maurice Winternitz 1963, pp. 106-108, 135.
  63. ↑ Annette Wilke & Oliver Moebus 2011, pp. 230-232 with footnotes 472-473.
  64. 1 2 Horace Hayman Wilson 1841, pp. 429-430.
  65. ↑ Horace Hayman Wilson 1841, pp. 429-432.
  66. ↑ Kālidāsa; Hank Heifetz (1990). The Origin of the Young God: Kālidāsa's Kumārasaṃbhava. Motilal Banarsidass. pp. 153–154. ISBN 978-81-208-0754-9.
  67. ↑ Annette Wilke & Oliver Moebus 2011, p. 1044.
  68. 1 2 3 Patrick Olivelle (1998). The Early Upanisads : Annotated Text and Translation. Oxford University Press. pp. xvi–xviii, xxxvii. ISBN 978-0-19-535242-9.
  69. 1 2 Patrick Olivelle (2008). Collected Essays: Language, Texts and Society. Firenze University Press. pp. 293–295. ISBN 978-88-8453-729-4.
  70. ↑ Maurice Winternitz 1963, pp. 3-4 with footnotes.
  71. ↑ Patrick Olivelle (2008). Collected Essays: Language, Texts and Society. Firenze University Press. pp. 264–265. ISBN 978-88-8453-729-4.
  72. ↑ Alf Hiltebeitel (2000), Review: John Brockington, The Sanskrit Epics, Indo-Iranian Journal, Volume 43, Issue 2, pages 161-169
  73. ↑ John Brough (1954), The Language of the Buddhist Sanskrit Texts, Bulletin of the School of Oriental and African Studies, Volume 16, Number 2, pages 351-375
  74. 1 2 Kim Plofker (2009). Mathematics in India. Princeton University Press. pp. 55–57. ISBN 0-691-12067-6.
  75. ↑ Bettina Bäumer; Kapila Vatsyayan (January 1992). Kalātattvakośa: A Lexicon of Fundamental Concepts of the Indian Arts. Motilal Banarsidass. p. 401. ISBN 978-81-208-1044-0.
  76. ↑ Nooten, B. Van (1993). "Binary numbers in Indian antiquity". J Indian Philos. Springer Science $\mathplus$ Business Media. 21 (1): 31–32. doi:10.1007/bf01092744.
  77. 1 2 3 4 Nooten, B. Van (1993). "Binary numbers in Indian antiquity". J Indian Philos. Springer Science $\mathplus$ Business Media. 21 (1): 31–50. doi:10.1007/bf01092744.
  78. ↑ Kireet Joshi (1991). The Veda and Indian Culture: An Introductory Essay. Motilal Banarsidass. pp. 101–102. ISBN 978-81-208-0889-8.
  79. ↑ Friedrich Max Müller (1860). A History of Ancient Sanskrit Literature. Williams and Norgate. pp. 67–70.
  80. ↑ Hopkins, p.192
  81. ↑ Hopkins, p.194. (This is typical for the shloka).
  82. ↑ Kim Plofker (2009). Mathematics in India. Princeton University Press. pp. 53–57. ISBN 0-691-12067-6.
  83. 1 2 Susantha Goonatilake (1998). Toward a Global Science. Indiana University Press. p. 126. ISBN 978-0-253-33388-9.
  84. ↑ Alekseĭ Petrovich Stakhov (2009). The Mathematics of Harmony: From Euclid to Contemporary Mathematics and Computer Science. World Scientific. pp. 426–427. ISBN 978-981-277-583-2.
  85. ↑ Keith Devlin (2012). The Man of Numbers: Fibonacci's Arithmetic Revolution. Bloomsbury Academic. p. 145. ISBN 978-1-4088-2248-7.
  86. 1 2 Alexander Zawaira; Gavin Hitchcock (2008). A Primer for Mathematics Competitions. Oxford University Press. p. 237. ISBN 978-0-19-156170-2.
  87. ↑ Hahn, p. 4
  88. ↑ Hahn, pp. 15–18
  89. 1 2 Sheldon Pollock 2006, p. 188.
  90. 1 2 B.J. Terwiel (1996). Jan E. M. Houben, ed. Ideology and Status of Sanskrit: Contributions to the History of the Sanskrit Language. BRILL. pp. 307–323. ISBN 90-04-10613-8.
  91. ↑ B.J. Terwiel (1996). Jan E. M. Houben, ed. Ideology and Status of Sanskrit: Contributions to the History of the Sanskrit Language. BRILL. pp. 319–320 with footnotes. ISBN 90-04-10613-8.

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