The fourth Vedanga. Chhandasmeans “that which covers, conceals, protects” - the metres cover the Vedic meaning in beautiful form and protect the mantra from corruption (a missing syllable breaks the metre and is immediately detected). Pingala’s Chhandahshastra(~3rd c BCE) is the foundational text. It catalogues guru (long) and laghu (short) syllable patterns, the eight ganas (tri-syllabic feet), and - most remarkably - introduces binary arithmetic and the meru-prastara triangle (identical to Pascal’s Triangle, which Pascal “discovered” in 1654 - Pingala had it 1,900 years earlier).
Pingala (~3rd c BCE) - possibly the younger brother of Panini in some traditions - composed the Chhandahshastra(also called Chhandasutra) in 8 chapters totalling 310 sutras. The text catalogues every Vedic and classical metre, defines the marking of guru/laghu, names the 8 ganas, and presents six sub-disciplines for analysing any verse.
Halayudha’s 10th-c CE commentary Mritasanjivani(“the reviver of the dead”) is the standard companion to Pingala. It is from Halayudha that we have the full elaboration of Pingala’s six pratyayas (procedures): prastara (enumeration of patterns), nashta (find pattern from index), uddishta (find index from pattern), eka-dvi-laghu-kriya (count of binary digits), sankhya (total count), and adhvayoga (sum-of-arrangements).
Pingala writes the binary digits as laghu (˘, weight 1) and guru (-, weight 2). His sutra 8.23 - “dvikau glau” - states explicitly the binary doubling rule. Sutras 8.24-8.32 develop the algorithms for enumeration that are now recognised as the first formal treatment of binary arithmetic in history.
The Vedic Samhitas use 7 principal metres (named by syllable count). Pingala enumerates 26 in total but the seven below account for ~99% of Vedic verses.
3 padas × 8 syllables each
Most famous of all Vedic metres. The Gayatri mantra (RV 3.62.10 - "tat savitur varenyam…") is its archetypal use. Symbolises Vak (speech-goddess). Said to "save" (gayantam trayate) the one who chants it.
tát savitúr váreṇyaṃ | bhárgo devásya dhīmahi | dhíyo yó naḥ pracodáyāt (8+8+8 = 24)
4 padas: 8+8+8+4 OR 3 padas: 8+8+12
Less common than Gayatri. Used in several Rig Vedic hymns to Agni (RV 1.8) and Indra. Considered a transitional metre between Gayatri and Anushtubh.
4 padas × 8 syllables each
The metre of the Bhagavad Gita and Mahabharata. Also the primary shloka metre of classical Sanskrit. Most flexible - only the 5th, 6th, 7th syllables of each pada have strict rules.
dhŕ̥tarāṣṭra uvāca: dharmakṣetre kurukṣetre | samavetā yuyutsavaḥ (Gita 1.1 - 8+8+8+8 = 32)
4 padas: 8+8+12+8 OR 9+9+9+9
Vedic metre, common in Atharva Veda. The name means "great, expanded". Less common in classical poetry.
5 padas × 8 syllables each
Vedic metre. The name refers to the "row of five" - five 8-syllable padas in a verse. Less frequent.
4 padas × 11 syllables each
Most common metre in the Rig Veda - about 40% of all Rig Vedic verses are in Tristubh. Heroic, formal tone. Common in hymns to Indra. (Note: RV 1.1.1 - "agním īḷe" - is in Gāyatrī, not Tristubh; the first verse of the Rig Veda was composed to Agni in the Gayatri metre.)
indrasya nu vīryāṇi pra vocam | yāni cakāra prathamāni vajrī (RV 1.32.1 - Vritra-slaying hymn, a classic Tristubh, 4×11 syllables).
4 padas × 12 syllables each
Frequent in the Rig Veda after Tristubh. Long, sustained tone - well-suited to cosmic or descriptive hymns. The Purusha Sukta (RV 10.90) uses Jagati for some of its verses.
To describe any classical metre concisely, Pingala uses 8 named tri-syllabic units called ganas. Each gana is one of the 2³ = 8 possible combinations of guru (G) and laghu (L). The mnemonic “yamātārājabhānasalagāḥ” encodes all 8 patterns: each successive triplet within this string is a gana.
| Gana | Pattern (L=˘ short, G=- long) | Mnemonic syllables | Source in yamatarajabhanasalaga |
|---|---|---|---|
| ya | L G G | la-tā-rā (-˘˘ no, ˘--) | Yamatārājabhānasalagāḥ - Yaśasāmkara |
| ma | G G G | mā-tā-rā (---) | Three gurus together |
| ta | G G L | tā-rā-ja (--˘) | Two gurus + laghu |
| ra | G L G | rā-ja-bhā (-˘-) | Guru-laghu-guru |
| ja | L G L | ja-bhā-na (˘-˘) | Laghu-guru-laghu |
| bha | G L L | bhā-na-sa (-˘˘) | Guru + two laghus |
| na | L L L | na-sa-la (˘˘˘) | Three laghus |
| sa | L L G | sa-la-gā (˘˘-) | Two laghus + guru |
Classical Sanskrit (Kalidasa, Bhartrihari, Shankara) uses fixed-syllable-count metres specified by a sequence of ganas plus optional final guru / laghu. Each metre has a distinctive emotional register.
Gana pattern: ma bha na ta ta ga ga | ma=GGG bha=GLL na=LLL ta=GGL
Famous use - Kalidasa's Meghaduta - entirely in Mandakranta. The slow, lingering rhythm matches the cloud-messenger's journey from Ramagiri to Alaka.
kaścit kāntā-virahaguruṇā svādhikārāt pramattaḥ | śāpenāstaṃgamita-mahimā varṣa-bhogyena bhartuḥ (Meghaduta 1.1).
Gana pattern: ma sa ja sa ta ta ga | "tiger-play" - a tiger's leaping rhythm
Famous use - Bhartrihari's Niti Shataka, Vairagya Shataka, Shringara Shataka. Adi Shankara's Vivekachudamani uses it heavily. The most weighty, dignified classical metre.
kśantya prīti-paraṃ rta-pradāyakaṃ saṃ-bhāva-yat-saṅgataṃ | sevā-svādhyaya-tap-nirantara-rataṃ buddhyā svayaṃ paśyataḥ (typical pattern).
Gana pattern: ta bha ja ja ga ga | "ornament of spring"
Famous use - Kalidasa's Ritusamhara (cycle of seasons) - the primary example of Vasantatilaka in extended use. Soft, graceful - befits subjects of beauty + romance. (Note: the famous Devi Mahatmya refrain "yā devī sarva-bhūteṣu…" is in Anushtubh, not Vasantatilaka.)
Gana pattern: na na ma ya ya | "garland"
Famous use - Kalidasa's Kumara-sambhava. Bhavabhuti's Uttara-rama-charita. A flowing, lyrical metre - well-suited to descriptive passages.
aja-rāja-vimṛṣya-pratyāgataṃ siṃha-rāja-pradṛśyaṃ (typical 15-syllable pattern).
Gana pattern: ya ma na sa bha la ga | "she-of-the-summit"
Famous use - Soundarya Lahari (entirely in Shikharini). Many devotional stotras of Shankara. The metre’s alternating long-short pulse mirrors emotional crescendo.
śivaḥ śaktyā yukto yadi bhavati śaktaḥ prabhavituṃ | na cedevaṃ devo na khalu kuśalaḥ spanditum-api (Soundarya Lahari 1).
Gana pattern: ta ta ja ga ga (Indravajra) | mixed (Upajati)
Famous use - Bhagavad Gita Chapter 11 (Vishvarupa Darshana) uses Upajati extensively. Indravajra is the "thunderbolt of Indra" - a forceful metre. Upajati is a mixture of Indravajra + Upendravajra padas.
śrī-bhagavān uvāca: paśya me pārtha rūpāṇi śataśo 'tha sahasraśaḥ (Gita 11.5).
Gana pattern: ma ra bha na ya ya ya | "garland-bearer"
Famous use - Bhartrihari's Vairagya Shataka. Many classical sutra-commentaries open in Sragdhara because of its formal, weighty rhythm.
21 syllables × 4 padas = 84 syllables per verse - among the longest standard classical metres.
Gana pattern: ya ya ya ya | "serpent-glide"
Famous use - Shankara's Bhuj-anga-prayata Stotra to Subrahmanya. The metre’s undulating ya-ya-ya-ya pattern mimics a serpent’s motion.
mayūrādhirūḍhaṃ mahā-vākya-gūḍhaṃ | manohāri-dehaṃ mahaccitta-gehaṃ (Subrahmanya Bhujanga 1).
Pingala gives precise rules (sutras 1.1-1.10). A syllable is laghu (˘) if it contains a short vowel (a, i, u, ṛ, ḷ) that is not followed by a conjunct, anusvara, or visarga. Otherwise it is guru (-).
A syllable is guru if:
For an n-syllable metre, there are 2n possible guru/laghu arrangements. Pingala’s sutra dvikau glau (8.23) gives the rule: doubling. Two values (laghu = 0, guru = 1) combine binary-fashion. For a 24-syllable Gayatri, there are 224= 16,777,216 possible arrangements. Pingala’s algorithms enumerate them.
In sutra 8.34, Pingala arranges the count of arrangements by number of gurus in a triangular table. Row n, column k gives C(n,k) - the number of ways to place k gurus among n syllables. This is mathematically identical to Pascal’s Triangle. Halayudha’s commentary explicitly draws the meru (“mountain”) shape.
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1When counting matra-vrittas(metres by syllable-weight rather than syllable-count: laghu = 1 matra, guru = 2 matras), Pingala’s enumeration gives the sequence 1, 2, 3, 5, 8, 13, 21, 34, … - the Fibonacci numbers. Acharya Hemachandra (12th c) formalised this rule (“the count of n-matra metres = count of (n-1)-matra + (n-2)-matra metres”) - 50 years before Fibonacci’s 1202 CELiber Abaci.
Knuth’s The Art of Computer Programming(Vol 4A, 2011) credits Pingala explicitly for the first known treatment of binary numbers and Pascal’s triangle. Subhash Kak (Louisiana State University) and Manjul Bhargava (Princeton, Fields Medal 2014) have written extensively on the priority claims.