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Sanskrit prosody

From Wikipedia, the free encyclopedia
Aspect of Vedic studies
"Chanda" redirects here. For other uses, seeChanda (disambiguation).
"Chandas" redirects here. For Vedic poetry, seeVedic metre. For the Kannada and Telugu poetry, seeChandas (poetry). For the quatrain poetic form of North India and Pakistan, seeChhand. For the typeface, seeChandas (typeface).

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Sanskrit prosody orChandas (छंद) refers to one of the sixVedangas, or limbs of Vedic studies.[1] It is the study ofpoetic metres and verse inSanskrit.[1] This field of study was central to the composition of theVedas, the scriptural canons ofHinduism; in fact, so central that some later Hindu and Buddhist texts refer to the Vedas asChandas.[1][2]

The Chandas, as developed by the Vedic schools, were organized around seven major metres, each with its own rhythm, movements and aesthetics. Sanskrit metres include those based on a fixed number of syllables per verse, and those based on fixed number ofmorae per verse.[3]

Extant ancient manuals on Chandas includePingala'sChandah Sutra, while an example of a medieval Sanskrit prosody manual is Kedara Bhatta'sVrittaratnakara.[4][note 1] The most exhaustive compilations of Sanskrit prosody describe over 600 metres.[7] This is a substantially larger repertoire than in any other metrical tradition.[8]

Etymology

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The termChandas (Sanskrit: छन्दः/छन्दस् chandaḥ/chandas (singular)) means "pleasing, alluring, lovely, delightful or charming", and is based on the rootchad which means "esteemed to please, to seem good, feel pleasant and/or something that nourishes, gratifies or is celebrated".[9] The term also refers to "any metrical part of theVedas or other composition".[9]

History

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The hymns ofRigveda include the names of metres, which implies that the discipline ofChandas (Sanskrit prosody) emerged in the 2nd-millennium BCE.[3][note 2] TheBrahmanas layer of Vedic literature, composed between 900 BCE and 700 BCE, contains a complete expression of theChandas.[12] Panini's treatise on Sanskrit grammar distinguishesChandas as the verses that compose the Vedas, fromBhāṣā (Sanskrit: भाषा), the language spoken by people for everyday communication.[13]

Vedic Sanskrit texts employ fifteen metres. Seven are common, and the most frequent three are 8-, 11- and 12-syllable lines.[14] Post-Vedic texts, such as the epics as well as other classical literature of Hinduism, deploy both linear and non-linear metres, many of which are based on syllables and others based on repeating numbers of morae (matra per foot).[14] About 150 treatises on Sanskrit prosody from the classical era are known, in which some 850 metres were defined and studied by the ancient and medieval Hindu scholars.[14]

The ancientChandahsutra ofPingala, also calledPingala Sutras, is the oldest Sanskrit prosody text that has survived into the modern age, and it is dated to between 600 and 200 BCE.[15][16] Like allSutras, the Pingala text is distilled information in the form of aphorisms, and these were widely commented on through thebhashya tradition of Hinduism. Of the various commentaries, those widely studied are the three 6th century texts -Jayadevacchandas,Janashrayi-Chhandovichiti andRatnamanjusha,[17] the 10th century commentary byKarnataka prosody scholar Halayudha, who also authored the grammaticalShastrakavya andKavirahasya (literally,The Poet's Secret).[15] Other important historical commentaries include those by the 11th-century Yadavaprakasha and 12th-century Bhaskaracharya, as well as Jayakriti'sChandonushasana, andChandomanjari by Gangadasa.[15][17]

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

Natya Shastra[18]

Major encyclopedic and arts-related Hindu texts from the 1st and 2nd millennium CE contain sections onChandas. For example, the chapters 328 to 335 of theAgni Purana,[19][20] chapter 15 of theNatya Shastra, chapter 104 of theBrihat Samhita, the Pramodajanaka section of theManasollasa contain embedded treatises onChandas.[21][22][23]

Elements

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Classification

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The metres found in classicalSanskrit poetry are classified into three kinds.[24]

  1. Syllabic verse (akṣaravṛtta or aksharavritta): metres 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, theMahabharata and theRamayana.
  2. Syllabo-quantitative verse (varṇavṛtta or varnavritta): metres depend on syllable count, but the light-heavy patterns are fixed.
  3. Quantitative verse (mātrāvṛtta or matravritta): metres depend on duration, where each verse-line has a fixed number ofmorae, usually grouped in sets of four.

Light and heavy syllables

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Most of Sanskrit poetry is composed in verses of four lines each. Each quarter-verse is called apāda (literally, "foot"). Meters of the same length are distinguished by the pattern oflaghu ("light") andguru ("heavy") syllables in thepāda. The rules distinguishinglaghu andguru syllables are the same as those for non-metric prose, and these are specified in VedicShiksha texts that study the principles and structure of sound, such as thePratishakhyas. Some of the significant rules are:[25][26]

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

Dandin, 7th century[27]
  1. A syllable islaghu only if its vowel ishrasva ("short") and followed by at most one consonant before another vowel is encountered.
  2. A syllable with ananusvara ('ṃ') or avisarga ('ḥ') is alwaysguru.
  3. All other syllables areguru, either because the vowel isdīrgha ("long"), or because thehrasva vowel is followed by a consonant cluster.
  4. Thehrasva vowels are the short monophthongs: 'a', 'i', 'u', 'ṛ' and 'ḷ'
  5. All other vowels aredirgha: '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 ofsandhi in Sanskrit make clear.)[28]
  6. Gangadasa Pandita states that the last syllable in each pāda may be consideredguru, but aguru at the end of a pāda is never counted aslaghu.[note 3][better source needed]

For measurement by mātrā (morae), laghu syllables count as one unit, and guru syllables as two units.[29]

Exceptions

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The Indian 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 metre.[30] Exceptions also apply to special sounds, of the type प्र, ह्र, ब्र and क्र.[30]

Stanzas

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A stanza (śloka) is defined in Sanskrit prosody as a group of four quarters (pādas).[30] Indian prosody studies recognise two types of stanzas.Vritta stanzas are those that have a precise number of syllables, whilejati stanzas are those that are based on syllabic time-lengths (morae,matra) and can contain varying numbers of syllables.[30]

Thevritta[note 4] stanzas have three forms:Samavritta, where the four quarters are similar in pattern,Ardhasamavritta, where alternate verses have a similar syllabic structure, andVishamavritta where all four quarters are different.[30] A regularVritta is defined as that where the total number of syllables in each line is less than or equal to 26 syllables, while irregulars contain more.[30] When the metre is based onmorae (matra), a short syllable is counted as one mora, and a long syllable is counted as two morae.[30]

Gaṇa

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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 metres, according to a method first propounded inPingala'schandahsutra. Pingala organizes the metres using two units:[32]

  • l: a "light" syllable (L), calledlaghu
  • g: a "heavy" syllable (H), calledguru
Metrical feet andaccents
Disyllables
◡ ◡pyrrhic, dibrach
◡ –iamb
– ◡trochee, choree
– –spondee
Trisyllables
◡ ◡ ◡tribrach
– ◡ ◡dactyl
◡ – ◡amphibrach
◡ ◡ –anapaest, antidactylus
◡ – –bacchius
– ◡ –cretic, amphimacer
– – ◡antibacchius
– – –molossus
Seemain article for tetrasyllables.

Pingala's method described any metre 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 metre to be described compactly as anacronym.[33] Each of these has itsGreek prosody equivalent as listed below.

The Ganas (गण, class)[34][35]
Sanskrit
prosody
WeightSymbolStyleGreek
equivalent
Na-gaṇaL-L-Lu u u
dadada
Tribrach
Ma-gaṇaH-H-H— — —
DUMDUMDUM
Molossus
Ja-gaṇaL-H-Lu — u
daDUMda
Amphibrach
Ra-gaṇaH-L-H— u —
DUMdaDUM
Cretic
Bha-gaṇaH-L-L— u u
DUMdada
Dactyl
Sa-gaṇaL-L-Hu u —
dadaDUM
Anapaest
Ya-gaṇaL-H-Hu — —
daDUMDUM
Bacchius
Ta-gaṇaH-H-L— — u
DUMDUMda
Antibacchius

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

A mnemonic

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The wordyamātārājabhānasalagāḥ (oryamātārājabhānasalagaṃ) is amnemonic 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 eachgaṇa is shown by its own syllable and the two following it:[36]

  • ya-gaṇa: ya-mā-tā = L-H-H
  • ma-gaṇa: mā-tā-rā = H-H-H
  • ta-gaṇa: tā-rā-ja = H-H-L
  • ra-gaṇa: rā-ja-bhā = H-L-H
  • ja-gaṇa: ja-bhā-na = L-H-L
  • bha-gaṇa: bhā-na-sa = H-L-L
  • na-gaṇa: na-sa-la = L-L-L
  • sa-gaṇa: sa-la-gā = L-L-H

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 aDe Bruijn sequence.[37]

Comparison with Greek and Latin prosody

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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 metre).[38][39] Each eight-syllable line, for instance in the Rigveda, is approximately equivalent to the Greek iambic dimeter.[31] The sacred Gayatri metre of the Hindus consists of three of such iambic dimeter lines, and this embedded metre alone is at the heart of about 25% of the entire Rigveda.[31]

The gaṇas are, however, not the same as thefoot in Greek prosody. The metrical unit in Sanskrit prosody is the verse (line,pada), while in Greek prosody it is the foot.[40] Sanskrit prosody allows elasticity similar to LatinSaturnian verse, uncustomary in Greek prosody.[40] The principles of both Sanskrit and Greek prosody probably go back to Proto-Indo-European times, because similar principles are found in ancient Persian, Italian, Celtic, and Slavonic branches of Indo-European.[41]

The seven birds: major Sanskrit metres

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The Vedic Sanskrit prosody included both linear and non-linear systems.[42] The field of Chandas was organized around seven major metres, 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.[42]

The seven major ancient Sanskrit metres are the three 8-syllable Gāyatrī, the four 8-syllable Anustubh, the four 11-syllable Tristubh, the four 12-syllable Jagati, and the mixedpāda metres named Ushnih, Brihati and Pankti.

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

gāyatréṇa práti mimīte arkám
arkéṇa sā́ma traíṣṭubhena vākám
vākéna vākáṃ dvipádā cátuṣpadā
akṣáreṇa mimate saptá vā́ṇīḥ

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[44]

The major ancient metres in Sanskrit prosody[45][46]
MeterStructureMapped
Sequence[45]
Varieties[47]Usage[48]
Gayatri24 syllables;
3 verses of 8 syllables
6x411Common in Vedic texts
Example: Rigveda 7.1.1-30, 8.2.14[49]
Ushnih28 syllables;
2 verses of 8;
1 of 12 syllables
7x48Vedas, not common
Example: Rigveda 1.8.23-26[50]
Anushtubh32 syllables;
4 verses of 8 syllables
8x412Most frequent in post-Vedic Sanskrit metrical literature; embedded in theBhagavad Gita, theMahabharata, theRamayana, thePuranas,Smritis and scientific treatises
Example: Rigveda 8.69.7-16, 10.136.7[51]
Brihati36 syllables;
2 verses of 8;
1 verse of 12;
1 verse of 8 syllables
9x412Vedas, rare
Example: Rigveda 5.1.36, 3.9.1-8[52]
Pankti40 syllables;
5 verses of 8 syllables
10x414Uncommon, found with Tristubh
Example: Rigveda 1.191.10-12[53]
Tristubh44 syllables;
4 verses of 11 syllables
11x422Second 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[54]
Jagati48 syllables;
4 verses of 12 syllables
12x430Third most common, typically alternates with Tristubh in the same text, also found in separate cantos.
Example: Rigveda 1.51.13, 9.110.4-12[55]

Other syllable-based metres

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Beyond these seven metres, ancient and medieval era Sanskrit scholars developed numerous other syllable-based metres (Akshara-chandas). Examples includeAtijagati (13x4, in 16 varieties),Shakvari (14x4, in 20 varieties),Atishakvari (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.[56][57]

Morae-based metres

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See also:Arya metre andMātrika metre

In addition to the syllable-based metres, Hindu scholars in their prosody studies, developedGana-chandas orGana-vritta, that is metres based onmātrās (morae, instants).[58][57][59] The metric foot in these are designed fromlaghu (short) morae or their equivalents. Sixteen classes of these instants-based metres are enumerated in Sanskrit prosody, each class has sixteen sub-species. Examples includeArya,Udgiti,Upagiti,Giti andAryagiti.[60] This style of composition is less common than syllable-based metric texts, but found in important texts ofHindu philosophy, drama, lyrical works and Prakrit poetry.[14][61] The entireSamkhyakarika text of theSamkhya school of Hindu philosophy is composed in Arya metre, as are many chapters in the mathematical treatises ofAryabhata, and some texts ofKalidasa.[60][62]

Hybrid metres

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Indian scholars also developed a hybrid class of Sanskrit metres, which combined features of the syllable-based metres and morae-based metres.[63][57] These were calledMatra-chandas. Examples of this group of metres includeVaitaliya,Matrasamaka andGityarya.[64] The Hindu textsKirātārjunīya andNaishadha Charita, for instance, feature complete cantos that are entirely crafted in theVaitaliya metre.[63][65]

Metres as tools for literary architecture

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The Vedic texts, and later Sanskrit literature, were composed in a manner where a change in metres was an embedded code to inform the reciter and audience that it marks the end of a section or chapter.[46] Each section or chapter of these texts uses identical metres, rhythmically presenting their ideas and making it easier to remember, recall and check for accuracy.[46]

Similarly, the authors of Sanskrit hymns used metres as tools of literary architecture, wherein they coded a hymn's end by frequently using a verse of a metre different from that used in the hymn's body.[46] However, they never used Gayatri metre to end a hymn or composition, possibly because it enjoyed a special level of reverence in Hindu texts.[46] In general, all metres were sacred and the Vedic chants and hymns attribute the perfection and beauty of the metres to divine origins, referring to them as mythological characters or equivalent to gods.[46]

Use of metre to identify corrupt texts

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The verse perfection in the Vedic texts, verse Upanishads[note 6] and Smriti texts has led some Indologists from the 19th century onwards to identify suspected portions of texts where a line or sections are off the expected metre.[66][67]

Some editors have controversially used thismetri causa principle to emend Sanskrit verses, assuming that their creative conjectural rewriting with similar-sounding words will restore the metre.[66] This practice has been criticized, statesPatrick Olivelle, because such modern corrections may be changing the meaning, adding to corruption, and imposing the modern pronunciation of words on ancient times when the same syllable or morae may have been pronounced differently.[66][67]

Large and significant changes in metre, wherein the metre of succeeding sections return to earlier sections, are sometimes thought to be an indication of 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.[68][69][70] However, some metres are easy to preserve and a consistent metre 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, as this may reflect versatility of the author or changing styles over author's lifetime.[71]

Texts

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Chandah Sutra

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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[72][73]

TheChandah Sutra is also known asChandah sastra, orPingala Sutras after its authorPingala. It is the oldest Hindu treatise on prosody to have survived into the modern era.[15][16] This text is structured in 8 books, with a cumulative total of 310 sutras.[74] It is a collection of aphorisms predominantly focused on the art of poetic metres, and presents some mathematics in the service of music.[72][75]

Bhashyas

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There have been numerous Bhashyas (commentaries) of the Chanda sastra over centuries. These are:

Chandoratnakara: The 11th-centurybhashya on Pingala'sChandah Sutra byRatnakarashanti, calledChandoratnakara, added new ideas to Prakrit poetry, and this was influential to prosody inNepal, and to the Buddhist prosody culture inTibet where the field was also known aschandas orsdeb sbyor.[43]

Chandahsutrabhasyaraja: The 18th century commentary of the Chandra Sastra byBhaskararaya.

Usage

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Post-vedic poetry, epics

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The Hindu epics and the post-Vedic classical Sanskrit poetry is typically structured asquatrains of fourpādas (lines), with the metrical structure of eachpāda completely specified. In some cases, pairs ofpādas may be scanned together as thehemistichs of acouplet.[76] This is typical for theshloka used in epic. It is then normal for thepādas comprising a pair to have different structures, to complement each other aesthetically. In other metres, the fourpādas of a stanza have the same structure.

TheAnushtubh Vedic metre became the most popular in classical and post-classical Sanskrit works.[48] It is octosyllabic, like the Gayatri metre that is sacred to the Hindus. The Anushtubh is present in Vedic texts, but its presence is minor, and Trishtubh and Gayatri metres dominate in the Rigveda for example.[77] A dominating presence of the Anushtubh metre in a text is a marker that the text is likely post-Vedic.[78]

TheMahabharata, for example, features many verse metres in its chapters, but an overwhelming proportion of the stanzas, 95% areshlokas of theanustubh type, and most of the rest aretristubhs.[79]

Chandas and mathematics

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The attempt to identify the most pleasing sounds and perfect compositions led ancient Indian scholars to study permutations and combinatorial methods of enumerating musical metres.[72] ThePingala Sutras includes a discussion of binary system rules to calculate permutations of Vedic metres.[75][80][81] Pingala, and more particularly the classical Sanskrit prosody period scholars, developed the art ofMatrameru, 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.[75][80][82]

The first five rows of the Pascal's triangle, also called the Halayudha's triangle.[83] Halayudha discusses this and more in his Sanskrit prosodybhashya on Pingala.

The 10th-century Halāyudha's commentary onPingala Sutras, developedmeruprastāra, which mirrors thePascal's triangle in the west, and now also called as the Halayudha's triangle in books on mathematics.[75][83] The 11th-century Ratnakarashanti'sChandoratnakara describes algorithms to enumerate binomial combinations of metres throughpratyaya. For a given class (length), the sixpratyaya were:[84]

  • prastāra, the "table of arrangement": a procedure for enumerating (arranging in a table) all metres of the given length,
  • naṣṭa: a procedure for finding a metre given its position in the table (without constructing the whole table),
  • uddiṣṭa: a procedure for finding the position in the table of a given metre (without constructing the whole table),
  • laghukriyā orlagakriyā: calculation of the number of metres in the table containing a given number oflaghu (orguru) syllables,
  • saṃkhyā: calculation of the total number of metres in the table,
  • adhvan: calculation of the space needed to write down theprastāra table of a given class (length).

Some authors also considered, for a given metre, (A) the number ofguru syllables, (B) the number oflaghu 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.)[85]

Influence

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In India

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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[86]

TheChandas are considered one of the five categories of literary knowledge in Hindu traditions. The other four, according to Sheldon Pollock, areGunas or expression forms,Riti, Marga or the ways or styles of writing,Alankara or tropology, andRasa, Bhava or aesthetic moods and feelings.[86]

TheChandas are revered in Hindu texts for their perfection and resonance, with the Gayatri metre treated as the most refined and sacred, and one that continues to be part of modern Hindu culture as part ofYoga and hymns of meditation at sunrise.[87]

Outside India

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The SanskritChanda has influenced southeast Asian prosody and poetry, such as ThaiChan (Thai:ฉันท์).[88] Its influence, as evidenced in the 14th-century Thai texts such as theMahachat kham luang, is thought to have come either throughCambodia orSri Lanka.[88] Evidence of the influence of Sanskrit prosody in 6th-century Chinese literature is found in the works of Shen Yueh and his followers, probably introduced through Buddhist monks who visited India.[89]

See also

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Notes

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  1. ^For a review of other Sanskrit prosody texts, see Moriz Winternitz'sHistory of Indian Literature,[5] and HD Velankar'sJayadaman.[6]
  2. ^See, for example,Rigveda hymns 1.164, 2.4, 4.58, 5.29, 8.38, 9.102 and 9.103;[10] and 10.130[11]
  3. ^सानुस्वारश्च दीर्घश्च विसर्गी च गुरुर्भवेत् । वर्णः संयोगपूर्वश्च तथा पादान्तगोऽपि वा ॥
  4. ^Vritta, literally "turn", is rooted invrit, Latinvert-ere, thereby etymologically toversus of Latin and "verse" of Indo-European languages.[31]
  5. ^These seven metres are also the names of the seven horses of Hindu Sun god (Aditya orSurya), mythically symbolic for removing darkness and bringing the light of knowledge.[43] These are mentioned in Surya verses of theAshvini Shastra portion ofAitareya Brahmana.
  6. ^Kena, Katha, Isha, Shvetashvatara and Mundaka Upanishads are examples of verse-style ancient Upanishads.

References

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  1. ^abcJames 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. ^abPeter 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.
  4. ^Deo 2007, pp. 6-7 section 2.2.
  5. ^Maurice Winternitz 1963, pp. 1–301, particularly 5-35.
  6. ^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 the Royal Asiatic Society, Volume 24-25, pages 49-92.
  7. ^Deo 2007, pp. 3, 6 section 2.2.
  8. ^Deo 2007, pp. 3-4 section 1.3.
  9. ^abMonier Monier-Williams (1923).A Sanskrit-English Dictionary. Oxford University Press. p. 332.
  10. ^Origin and Development of Sanskrit Metrics, Arati Mitra (1989), The Asiatic Society, pages 4-6 with footnotes
  11. ^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.
  12. ^Guy L. Beck 1995, pp. 40–41.
  13. ^Sheldon Pollock 2006, pp. 46, 268–269.
  14. ^abcdAlex 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.
  15. ^abcdSheldon Pollock 2006, p. 370.
  16. ^abB.A. Pingle 1898, pp. 238–241.
  17. ^abAndrew 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.
  18. ^Har Dutt Sharma (1951)."Suvrttatilaka".Poona Orientalist.XVII: 84.
  19. ^Rocher 1986, p. 135.
  20. ^MN Dutt,Agni Purana Vol 2, pages 1219-1233 (Note: Dutt's manuscript has 365 chapters, and is numbered differently)
  21. ^Sheldon Pollock 2006, pp. 184–188.
  22. ^T. Nanjundaiya Sreekantaiya (2001).Indian Poetics. Sahitya Akademi. pp. 10–12.ISBN 978-81-260-0807-0.
  23. ^Maurice Winternitz 1963, pp. 8–9, 31–34.
  24. ^Deo 2007, p. 5.
  25. ^Coulson, p.21
  26. ^Muller & Macdonell, Appendix II
  27. ^Maurice Winternitz 1963, p. 13.
  28. ^Coulson, p.6
  29. ^Muller and Macdonell, loc.cit.
  30. ^abcdefgLakshman R Vaidya,Sanskrit Prosody - Appendix I, inSanskrit-English Dictionary, Sagoon Press, Harvard University Archives, pages 843-856;Archive 2
  31. ^abcA history of Sanskrit Literature, Arthur MacDonell, Oxford University Press/Appleton & Co, page 56
  32. ^Pingala CS 1.9-10, in order
  33. ^Pingala,chandaḥśāstra, 1.1-10
  34. ^Horace Hayman Wilson 1841, pp. 415–416.
  35. ^Pingala CS, 1.1-8, in order
  36. ^Coulson, p.253ff
  37. ^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.
  38. ^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.
  39. ^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.
  40. ^abA history of Sanskrit Literature, Arthur MacDonell, Oxford University Press/Appleton & Co, page 55
  41. ^Stephen Dobyns (2011).Next Word, Better Word: The Craft of Writing Poetry. Macmillan. pp. 248–249.ISBN 978-0-230-62180-0.
  42. ^abAnnette Wilke & Oliver Moebus 2011, pp. 391-392 with footnotes.
  43. ^abJamgon 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.
  44. ^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.
  45. ^abAnnette Wilke & Oliver Moebus 2011, p. 392.
  46. ^abcdefTatyana 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.
  47. ^Horace Hayman Wilson 1841, pp. 418–421.
  48. ^abHorace Hayman Wilson 1841, pp. 418–422.
  49. ^Arnold 1905, pp. 10, 48.
  50. ^Arnold 1905, p. 48.
  51. ^Arnold 1905, p. 11, 50 with note ii(a).
  52. ^Arnold 1905, p. 48, 66 with note 110(i).
  53. ^Arnold 1905, p. 55 with note iv, 172 with note viii.
  54. ^Arnold 1905, pp. 48 with table 91, 13 with note 48, 279 with Mandala VII table.
  55. ^Arnold 1905, pp. 12 with note 46, 13 with note 48, 241-242 with note 251.
  56. ^Horace Hayman Wilson 1841, pp. 422–426.
  57. ^abcHopkins 1901, p. 193.
  58. ^Horace Hayman Wilson 1841, p. 427.
  59. ^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.
  60. ^abHorace Hayman Wilson 1841, pp. 427–428.
  61. ^Maurice Winternitz 1963, pp. 106–108, 135.
  62. ^Annette Wilke & Oliver Moebus 2011, pp. 230-232 with footnotes 472-473.
  63. ^abHorace Hayman Wilson 1841, pp. 429–430.
  64. ^Horace Hayman Wilson 1841, pp. 429–432.
  65. ^Kālidāsa; Hank Heifetz (1990).The Origin of the Young God: Kālidāsa's Kumārasaṃbhava. Motilal Banarsidass. pp. 153–154.ISBN 978-81-208-0754-9.
  66. ^abcPatrick Olivelle (1998).The Early Upanisads : Annotated Text and Translation. Oxford University Press. pp. xvi–xviii, xxxvii.ISBN 978-0-19-535242-9.
  67. ^abPatrick Olivelle (2008).Collected Essays: Language, Texts and Society. Firenze University Press. pp. 293–295.ISBN 978-88-8453-729-4.
  68. ^Maurice Winternitz 1963, pp. 3-4 with footnotes.
  69. ^Patrick Olivelle (2008).Collected Essays: Language, Texts and Society. Firenze University Press. pp. 264–265.ISBN 978-88-8453-729-4.
  70. ^Alf Hiltebeitel (2000), Review: John Brockington, The Sanskrit Epics, Indo-Iranian Journal, Volume 43, Issue 2, pages 161-169
  71. ^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
  72. ^abcKim Plofker (2009).Mathematics in India. Princeton University Press. pp. 53–57.ISBN 978-0-691-12067-6.
  73. ^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.
  74. ^Nooten, B. Van (1993). "Binary numbers in Indian antiquity".J Indian Philos.21 (1). Springer Science $\mathplus$ Business Media:31–32.doi:10.1007/bf01092744.S2CID 171039636.
  75. ^abcdNooten, B. Van (1993). "Binary numbers in Indian antiquity".J Indian Philos.21 (1). Springer Science $\mathplus$ Business Media:31–50.doi:10.1007/bf01092744.S2CID 171039636.
  76. ^Hopkins, p.194.
  77. ^Kireet Joshi (1991).The Veda and Indian Culture: An Introductory Essay. Motilal Banarsidass. pp. 101–102.ISBN 978-81-208-0889-8.
  78. ^Friedrich Max Müller (1860).A History of Ancient Sanskrit Literature. Williams and Norgate. pp. 67–70.
  79. ^Hopkins, p.192
  80. ^abSusantha Goonatilake (1998).Toward a Global Science. Indiana University Press. p. 126.ISBN 978-0-253-33388-9.
  81. ^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.
  82. ^Keith Devlin (2012).The Man of Numbers: Fibonacci's Arithmetic Revolution. Bloomsbury Academic. p. 145.ISBN 978-1-4088-2248-7.
  83. ^abAlexander Zawaira; Gavin Hitchcock (2008).A Primer for Mathematics Competitions. Oxford University Press. p. 237.ISBN 978-0-19-156170-2.
  84. ^Hahn, p. 4
  85. ^Hahn, pp. 15–18
  86. ^abSheldon Pollock 2006, p. 188.
  87. ^Annette Wilke & Oliver Moebus 2011, pp. 393–394.
  88. ^abB.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.
  89. ^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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