Skip to content

Latest commit

 

History

History
975 lines (690 loc) · 69.1 KB

File metadata and controls

975 lines (690 loc) · 69.1 KB

Hindu Ārṣa Chronometry: Complete Reference

Scope

This document presents a complete synthesis of Hindu temporal metrology from primary sources. Multiple texts use the same unit-names with different magnitudes — the most important case being the Bhāgavata chain versus the Manu and Viṣṇu chains. In addition, some texts explicitly present multiple coexisting "measures" (māna) for different applications (astronomy, ritual, lunar observances, etc.), and those must not be forced into a single unit-ladder.

Synthesis Rules

  1. Bhāgavata Purāṇa 3.11 is the only continuous atomic-to-year ladder among the primary sources.
  2. Manusmṛti 1.64-67 and Viṣṇu Purāṇa I.3.8-10 are parallel ritual/calendrical ladders, not identical to Bhāgavata below the muhūrta.
  3. Same-name units are kept separate when their magnitudes differ.
  4. Modern seconds, minutes, and microseconds are derived values only. The classical verses give ratios, not SI units.
  5. Multi-framework presentations (distinct māna systems) are handled as their own analytical layer, because they are not a single micro-to-macro metrology chain.

Source Families

1. Bhāgavata Atomic-Biological Chain

BhP 3.11.1, 3.11.5-12

  • paramāṇu -> aṇu -> trasareṇu
  • truṭi -> vedha -> lava -> nimeṣa -> kṣaṇa -> kāṣṭhā -> laghu -> nāḍikā -> muhūrta -> yāma -> ahorātra -> pakṣa -> māsa -> ṛtu -> ayana -> saṃvatsara

2. Manu Ritual Chain

Manusmṛti 1.64-67

  • 18 nimeṣas = 1 kāṣṭhā
  • 30 kāṣṭhās = 1 kalā
  • 30 kalās = 1 muhūrta
  • 30 muhūrtas = 1 ahorātra
  • then month, pitṛ-day, deva-day, year

3. Viṣṇu Ritual Chain

Viṣṇu Purāṇa I.3.8-10

  • 15 nimeṣas = 1 kāṣṭhā
  • 30 kāṣṭhās = 1 kalā
  • 30 kalās = 1 muhūrta
  • 30 muhūrtas = 1 ahorātra
  • then month, ayana, year

4. Sūrya Siddhānta Astronomical Chain

SS 1.11-13

  • prāṇa -> vināḍī -> nāḍikā -> ahorātra -> māsa -> varṣa
  • this is a separate astronomical line, not forced into the Bhāgavata / Manu / Viṣṇu ladder

5. Exact Corroborative Layer

  • Mahābhārata 12.224.12-15
  • Vāyu Purāṇa 50.168
  • Matsya Purāṇa 141.4, 142.5-6
  • Kūrma Purāṇa 5.4-6
  • Mārkaṇḍeya Purāṇa 46.23-25
  • Padma Purāṇa 1.3.4-6
  • Bhaviṣya Purāṇa 1.2.86-91
  • Brahmāṇḍa Purāṇa 1.13.16-18
  • Śatapatha Brāhmaṇa 10.4.2.18
  • Ṛgveda 1.164.11
  • Ṛgveda 1.164.48
  • Atharvaveda 19.53.1
  • Kauṭilīya Arthaśāstra time-ladder prose
  • Taittirīya Brāhmaṇa 3.10.1.1-4 (Muhūrta qualitative names: 15 daytime + 15 nighttime + 15 prati-muhūrtas for bright/dark fortnights)

5a. Vedic-Ritual Akṣara (Syllable) Time System

This is a distinct metrological framework where time is measured by performative action (recitation) rather than atomic or calendrical division.

  • akṣara (syllable) = base unit, time to pronounce one short vowel
  • 7200 akṣaras = 1 muhūrta → derived: 1 akṣara ≈ 0.4 s
  • 1000 bṛhatī verses = 1 year33,000 akṣaras = 1 saṃvatsara
  • this system is rooted in Vedic recitation practice and bridges ritual performance with temporal measurement
  • phonetic calibration: 60 Gurvakṣaras (long syllables) recited in exactly 24 seconds, used to regulate the Ghaṭī Yantra (water clock)

5b. Ayurvedic Time Chains (Sage-Attributed Medical Texts)

Two additional sage-attributed sources define time units for medical and physiological timing, providing alternative starting points below the nimeṣa.

Caraka Saṃhitā (traditionally Agniveśa, revised by Caraka; Ṛṣi Punarvasu Ātreya lineage)

  • Sūtrasthāna 4/5: gives akṣi-nimeṣa (mātra) → kāṣṭhā → kalā → nāḍikā → muhūrta → yāma → ahorātra → pakṣa → māsa → ṛtu → ayana → varṣa
  • akṣi-nimeṣa = time to blink the eyelids, identified as the smallest unit in this system
  • 15 mātras = 1 kāṣṭhā; 30 kāṣṭhās = 1 kalā; 20 + 1/10 kalās = 1 nāḍikā; 2 nāḍikās = 1 muhūrta

Suśruta Saṃhitā (traditionally taught by Dhanvantari, an avatāra, to Suśruta)

  • Sūtrasthāna 6/4: defines akṣi-nimeṣa → kāṣṭhā → muhūrta → ahorātra → pakṣa → māsa → ṛtu → ayana → saṃvatsara
  • akṣi-nimeṣa = time taken to articulate a short vowel
  • 15 akṣi-nimeṣas = 1 kāṣṭhā; 30 kāṣṭhās = 1 kalā; 30 kalās = 1 muhūrta; 30 muhūrtas = 1 ahorātra

5c. Atharvaveda Kālasūkta (Time as Cosmological Principle)

The Atharvaveda establishes time (Kāla) as the supreme organizing principle of the cosmos, providing the philosophical foundation within which all Purāṇic time units operate.

  • Atharvaveda 19.53.1: Kāla described as a primordial horse with seven reins (rays) and a thousand eyes
  • Atharvaveda 19.53-54: Kālasūkta — earliest Vedic treatment of eternal time as the supreme principle
  • this does not define sub-units but establishes the cosmological framework for all later metrology

6. Nārada Purāṇa Multi-Māna Framework (Five Practical Reckonings)

This layer is not a replacement for the unit ladders above; it is a taxonomy of distinct time-reckonings and their use-cases.

Nārada Purāṇa (Pūrvārdha) 1.56.109-135


Metrological Synthesis

A. Bhāgavata Purāṇa Chain

This is the only full micro-to-macro chain among the primary sources.

Seq Unit Composition Derived Value Primary Verse
0 Paramāṇu ultimate indivisible particle 26.3374 us BhP 3.11.1
1 Aṇu 2 paramāṇus 52.6749 us BhP 3.11.5
2 Trasareṇu 3 aṇus 158.0247 us BhP 3.11.5
3 Truṭi 3 trasareṇus 474.0741 us BhP 3.11.6
4 Vedha 100 truṭis 47.4074 ms BhP 3.11.6
5 Lava 3 vedhas 142.2222 ms BhP 3.11.6
6 Nimeṣa (BhP) 3 lavas 426.6667 ms BhP 3.11.7
7 Kṣaṇa 3 nimeṣas 1.2800 s BhP 3.11.7
8 Kāṣṭhā (BhP) 5 kṣaṇas 6.4000 s BhP 3.11.7
9 Laghu 15 kāṣṭhās 96.0000 s BhP 3.11.7
10 Nāḍikā / Daṇḍa 15 laghus 24.0000 min BhP 3.11.8
11 Muhūrta 2 nāḍikās 48.0000 min BhP 3.11.8
12 Yāma / Prahara 1/8 of ahorātra 3.0000 hr BhP 3.11.8, 3.11.10
13 Ahorātra 30 muhūrtas 24.0000 hr BhP 3.11.10
14 Pakṣa 15 ahorātras 15 days BhP 3.11.10
15 Māsa 2 pakṣas 30 days BhP 3.11.11
16 Ṛtu 2 māsas 60 days BhP 3.11.11
17 Ayana 6 months 180 days BhP 3.11.11
18 Saṃvatsara 2 ayanas 360 days BhP 3.11.12

B. Manu and Viṣṇu Parallel Chains

These converge at muhūrta, but they do not match the Bhāgavata values below that point.

Unit Manusmṛti Viṣṇu Purāṇa Derived Value
Nimeṣa 1/18 kāṣṭhā 1/15 kāṣṭhā Manu: 177.7778 ms, VP: 213.3333 ms
Kāṣṭhā 18 nimeṣas 15 nimeṣas 3.2000 s
Kalā 30 kāṣṭhās 30 kāṣṭhās 96.0000 s
Muhūrta 30 kalās 30 kalās 48.0000 min
Ahorātra 30 muhūrtas 30 muhūrtas 24.0000 hr

C. Shared Higher Calendar Structure

Above the muhūrta, the three traditions are compatible enough to synthesize at the calendrical level.

Unit Composition Documented Here Main Verse Set
Ahorātra 30 muhūrtas full day and night Manu 1.64, VP I.3.9, BhP 3.11.10
Pakṣa 15 days fortnight BhP 3.11.10, Manu 1.66
Māsa 2 pakṣas month of 30 days BhP 3.11.11, VP I.3.9
Ṛtu 2 māsas season BhP 3.11.11
Ayana 6 months half-year BhP 3.11.11, Manu 1.67, VP I.3.10
Saṃvatsara 2 ayanas 360-day year BhP 3.11.12, Manu 1.67, VP I.3.10

D. Distinct Māna Systems (Not One Ladder): Nārada Purāṇa 1.56.109-135

Multiple legitimate time-reckonings (māna) coexist, each chosen by function. This is the kind of layer that becomes confused if we force "time" into a single chain.

D.1 The nine māna (measures) and the practical subset

The text lists nine kinds of measure (māna): brahma, deva, manu, pitṛ, saura, sāvana, cāndra, ārkṣa, and guru (Bṛhaspati/Jupiter-based) (Nārada Purāṇa 1.56.109). Immediately after, it states that practical worldly "business" (vyavahāra) proceeds through five of these, and then promises a per-measure account of their distinct tasks (Nārada Purāṇa 1.56.110).

"Time" is not only a ladder of unit-multipliers, but also a selection of a reckoning framework suited to the question being asked.

D.2 Assigned use-cases: why different reckonings are not interchangeable

The chapter assigns use-cases:

  • Solar measure (saura) for the total motion/going of the planets (Nārada Purāṇa 1.56.111).
  • Civil measure (sāvana) for the rule of rains and pregnancy (Nārada Purāṇa 1.56.111).
  • Nakṣatra-based determination is explicitly invoked in the same practical domain (rainfall/pregnancy timing), while tithi-based decision-making is invoked for journeys, marriage, vows, shaving rites, and “year-lord” decisions (Nārada Purāṇa 1.56.112).
  • Lunar measure (cāndra) governs parva, vāstu, upavāsa, and the general class of lunar observances (Nārada Purāṇa 1.56.112).
  • Jupiter-based measure (guru-māna) governs the year-character beginning with Prabhava etc. (Nārada Purāṇa 1.56.113).

Once a text says "these nine exist, but practice uses five, and each has its own work", then "same month name" or "same year word" does not automatically mean "same calendar basis".

D.3 Bārhaspatya (Jovian) year-cycle: the 60 named saṃvatsara

The chapter explicitly defines a 60-year cycle of named years beginning with Prabhava (Nārada Purāṇa 1.56.114) and then lists the 60 names across Nārada Purāṇa 1.56.115-120. It then states that all sixty years are to be understood as having results corresponding to their names, and that a "yuga" is five years and there are twelve such yugas within the sixty-year cycle, along with enumerated "lords" (īśa) for those yugas (Nārada Purāṇa 1.56.121-123).

This section is calendrical (classification of year-names and their lords), not metrological (truṭi-to-day), so it belongs to a separate layer alongside the ladders above.

D.4 Ayanas, seasons, month-taxonomy, month names, and pakṣa semantics

The chapter states the six-month northern course (saumya-ayana) and the southern course beginning with karka (Nārada Purāṇa 1.56.125), and links them to the gods’ day and night (Nārada Purāṇa 1.56.125). It specifies that auspicious rites are performed in uttarāyaṇa, while dakṣiṇāyaṇa is treated oppositely in ritual valuation (Nārada Purāṇa 1.56.126-127).

It also defines the six ṛtu as two-month pairs starting with Māgha and groups them into the uttarāyaṇa and dakṣiṇāyaṇa halves (Nārada Purāṇa 1.56.127-128).

Then it distinguishes month-bases: the lunar month bounded by new moon, the solar month beginning from saṅkrānti, and the nakṣatra month (Nārada Purāṇa 1.56.129). It lists the 12 month-names from Madhu onward (Nārada Purāṇa 1.56.130) and gives the month naming principle: the month is named after the nakṣatra with which the full moon is conjoined in that month (Nārada Purāṇa 1.56.131). Finally, it defines the two pakṣa (śukla/kṛṣṇa) as "daiva" and "pitṛ" and links them to auspicious vs inauspicious ritual usage (Nārada Purāṇa 1.56.132).

D.5 Taittirīya Brāhmaṇa Time-Segment Qualitative Taxonomy

The Taittirīya Brāhmaṇa (3.10) goes beyond the quantitative definition of time units and assigns qualitative names to day-times, night-times, and muhūrtas. The text provides multiple naming systems (TB 3.10.1.1-3 for day-times/night-times, TB 3.10.1.1-4 for muhūrtas), establishing that time segments carry distinct energetic signatures.

Naming Scheme A — Day-Portion Names (bright fortnight; TB 3.10.1.1-3): saṃjñānaṃ, vijñānaṃ, prajñānaṃ, jānad, abhijānad, saṃkalpamānaṃ, prakalpamānaṃ, upakalpamānaṃ, upakṛptamānaṃ, kṛpta, śreya, vaśiya, āyat, sambhūta, bhūta

Naming Scheme A — Night-Portion Names (bright fortnight; TB 3.10.1.1-3): darśa, dṛṣṭā, darśatā, viśvarūpa, sudarśanā, āpyāyamānā, pyāyamānā, pyāyā, sunṛtā, īrā, apūryamāṇā, pūryamāṇā, pūrayantī, pūrṇā, paurṇamāsī

Naming Scheme B — Daylight Muhūrta Names (bright fortnight; TB 3.10.1.1-4): citrā, ketuḥ, prabhā, nabhan, sambhan, jyotiṣmān, tejasvān, ātapan, tapan, abhitapan, rocanā, rocāmānaḥ, śobhanā, śobhamānaḥ, kalyāṇaḥ

Naming Scheme B — Night Muhūrta Names (bright fortnight; TB 3.10.1.1-4): savitā, prasavitā, diptā, dīpāyan, dīpyamānaḥ, jvalan, jvalitā, tapan, vitapan, śāntapan, rocanā, rocāmānaḥ, śumbhuḥ, śumbhamānaḥ, vāmaḥ

Naming Scheme A assigns names to the day-portion and night-portion of the bright fortnight; Naming Scheme B assigns names to each of the 15 individual muhūrtas within the daylight hours and the 15 individual muhūrtas within the night hours. The daylight muhūrtas progress through luminosity and radiant energy (Citrā → Kalyāṇaḥ); the night muhūrtas govern illumination, burning, and pacification (Savitā → Vāmaḥ). This qualitative mapping establishes that the 30 muhūrtas of a day are not interchangeable slots but carry distinct character and intent, aligning human action (karma) with appropriate temporal windows.


What Must Not Be Blurred

1. Different nimeṣa magnitudes

  • Nimeṣa (BhP) = 3 lavas = 426.6667 ms
  • Nimeṣa (Manu) = 1/18 kāṣṭhā = 177.7778 ms
  • Nimeṣa (VP) = 1/15 kāṣṭhā = 213.3333 ms

2. Different kāṣṭhā magnitudes

  • Kāṣṭhā (BhP) = 5 kṣaṇas = 6.4 s
  • Kāṣṭhā (Manu / VP) = 3.2 s

3. Equal magnitude, different name/path

  • Bhāgavata laghu = 96 s
  • Manu / VP kalā = 96 s
  • same derived magnitude, different chain position and different textual role

4. Sūrya Siddhānta is not the same ladder

  • SS 1.11-13 gives prāṇa, vināḍī, nāḍikā, ahorātra, māsa, varṣa
  • this document does not use it to overwrite Bhāgavata, Manu, or Viṣṇu values

5. Corroboration does not mean identical magnitude

  • a text may confirm a unit-name without matching another text's exact sub-chain
  • therefore corroboration is useful, but only after checking whether the unit is truly the same in magnitude and position

6. Different calendar-frameworks can coexist without contradiction

  • a text may discuss not just smaller and larger units, but distinct māna systems meant for different functions
  • separate calendar frameworks should not be merged into a single unit-ladder unless their exact verses are also reproduced and compared
  • Nārada Purāṇa 1.56.109-113 explicitly states multiple coexisting measures with assigned use-cases; treat it as a separate analytical layer, not as a "missing rung" in the ladder

7. The akṣara (syllable) system is not a sub-chain of the atomic ladder

  • akṣara = ~0.4 s derived from 7200 akṣaras per muhūrta
  • this is a performative unit based on Vedic recitation speed, not an atomic or physiological division
  • it belongs to the ritual-metrical framework, not the metrological chain
  • phonetic calibration (60 Gurvakṣaras = 24 s) was used to regulate water clocks independently of atomic or calendrical measures

8. Ayurvedic chains start at akṣi-nimeṣa, not paramāṇu

  • Caraka Saṃhitā Sū. 4/5 and Suśruta Saṃhitā Sū. 6/4 define time starting from the blink of the eye (akṣi-nimeṣa / mātra)
  • these are sage-attributed medical texts using physiological timing for clinical and pharmacological purposes
  • they do not include the paramāṇu → aṇu → trasareṇu → truṭi → vedha → lava sequence found in BhP 3.11
  • treat them as a separate analytical layer focused on human-scale temporal perception

9. Muhūrtas carry qualitative names, not only quantitative value

  • Taittirīya Brāhmaṇa 3.10.1.1-4 assigns distinct qualitative names to each of the 15 daytime muhūrtas (citrā → kalyāṇaḥ) and 15 nighttime muhūrtas (savitā → vāmaḥ)
  • TB 3.10.1.1-3 additionally assigns separate names to day-times (saṃjñānaṃ → bhūta) and night-times (darśa → paurṇamāsī) for the bright fortnight
  • this establishes that time segments are not interchangeable but carry distinct energetic character
  • the 30 muhūrtas of a day are qualitatively differentiated, affecting ritual suitability and action timing

Appendix A: Consolidated Concordance

Only exact additional loci cited in Appendix C are listed here.

Seq Unit Composition Derived Value Primary Source + Ślokas Also Found In (Exact Additional Loci)
0 Paramāṇu ultimate indivisible particle 26.3374 us BhP 3.11.1 BhP 3.11.4
1 Aṇu 2 paramāṇus 52.6749 us BhP 3.11.5
2 Trasareṇu 3 aṇus 158.0247 us BhP 3.11.5
3 Truṭi 3 trasareṇus 474.0741 us BhP 3.11.6
4 Vedha 100 truṭis 47.4074 ms BhP 3.11.6
5 Lava 3 vedhas 142.2222 ms BhP 3.11.6
6 Nimeṣa (BhP) 3 lavas 426.6667 ms BhP 3.11.7
7 Nimeṣa (Manu) 1/18 kāṣṭhā 177.7778 ms Manu 1.64 Bhaviṣya Purāṇa 1.2.86
8 Nimeṣa (Viṣṇu) 1/15 kāṣṭhā 213.3333 ms VP I.3.8 Vāyu Purāṇa 50.168; Matsya Purāṇa 141.4; Padma Purāṇa 1.3.4; Kūrma Purāṇa 5.4; Mārkaṇḍeya Purāṇa 46.23; MBh 12.224.12
9 Kṣaṇa 3 BhP nimeṣas 1.2800 s BhP 3.11.7
10 Kāṣṭhā (BhP) 5 kṣaṇas 6.4000 s BhP 3.11.7
11 Kāṣṭhā (Manu / Viṣṇu) 18 or 15 nimeṣas 3.2000 s Manu 1.64 / VP I.3.8 Vāyu Purāṇa 50.168; Matsya Purāṇa 141.4; Padma Purāṇa 1.3.4; Kūrma Purāṇa 5.4; Mārkaṇḍeya Purāṇa 46.23; MBh 12.224.12
12 Laghu 15 kāṣṭhās 96.0000 s BhP 3.11.7
13 Kalā 30 kāṣṭhās 96.0000 s Manu 1.64 / VP I.3.8 Bhaviṣya Purāṇa 1.2.87; MBh 12.224.12; Vāyu Purāṇa 50.168; Matsya Purāṇa 141.4; Padma Purāṇa 1.3.4; Kūrma Purāṇa 5.4; Mārkaṇḍeya Purāṇa 46.23
14 Nāḍikā / Daṇḍa 15 laghus 24.0000 min BhP 3.11.8 BhP 3.11.9; SS 1.11; Arthaśāstra time-ladder prose passage
15 Muhūrta 2 nāḍikās or 30 kalās 48.0000 min BhP 3.11.8 / Manu 1.64 VP I.3.8; Bhaviṣya Purāṇa 1.2.87-88; Vāyu Purāṇa 50.168; Matsya Purāṇa 141.4; Padma Purāṇa 1.3.4; Kūrma Purāṇa 5.4; Mārkaṇḍeya Purāṇa 46.23; ŚB 10.4.2.18; MBh 12.224.12
16 Yāma / Prahara 1/8 of ahorātra 3.0000 hr BhP 3.11.8, 3.11.10 Manu 1.65; MBh 12.224.13-15
17 Ahorātra 30 muhūrtas 24.0000 hr BhP 3.11.10 / Manu 1.64 VP I.3.9; SS 1.12; Bhaviṣya Purāṇa 1.2.88-90; Vāyu Purāṇa 50.168; Matsya Purāṇa 141.4, 142.5; Padma Purāṇa 1.3.5; Kūrma Purāṇa 5.5; Mārkaṇḍeya Purāṇa 46.24; Arthaśāstra time-ladder prose passage; MBh 12.224.13-14
18 Pakṣa 15 ahorātras 15 days BhP 3.11.10 Manu 1.66; VP I.3.9; Vāyu Purāṇa 50.168; Matsya Purāṇa 142.6; Padma Purāṇa 1.3.5; Kūrma Purāṇa 5.5; Mārkaṇḍeya Purāṇa 46.24; MBh 12.224.15
19 Māsa 2 pakṣas 30 days BhP 3.11.11 VP I.3.9; Manu 1.66; Vāyu Purāṇa 50.168; Matsya Purāṇa 142.6; Padma Purāṇa 1.3.5; Kūrma Purāṇa 5.5; Mārkaṇḍeya Purāṇa 46.24; MBh 12.224.13-15
20 Ṛtu 2 māsas 60 days BhP 3.11.11 Bhaviṣya Purāṇa 1.2.88-89
21 Ayana 6 months 180 days BhP 3.11.11 VP I.3.10; Manu 1.67; SS 1.13; Bhaviṣya Purāṇa 1.2.89-91; Padma Purāṇa 1.3.6; Kūrma Purāṇa 5.6; Mārkaṇḍeya Purāṇa 46.25
22 Saṃvatsara 2 ayanas 360 days BhP 3.11.12 RV 1.164.11; RV 1.164.48; VP I.3.10; Manu 1.67; AV 19.53.1; Bhaviṣya Purāṇa 1.2.88-91

Appendix A2: Non-Sage-Attributed / Syncretic & Macro Units

This appendix collects time units and subdivisions that appear in later pedagogical compilations, mathematical texts, and civil/astrological conventions. None of these belong to the sage-attributed metrological chains (BhP, Manu, VP, SS). They are documented here because they appear in modern charts and panchāṅga practice, and their presence in those contexts must be explicitly distinguished from the Ārṣa textual sources.

A2.1 Sidereal Units (Commentarial Tradition)

A 60-fold sexagesimal sub-muhūrta chain appears in later commentarial and pedagogical sources. This is not from Sūrya Siddhānta. The Sūrya Siddhānta (1.11) defines only Prāṇa → Vināḍī → Nāḍikā — it does not define this 60-fold ladder below the prāṇa. The units and multipliers below are reconstructed from later astronomical commentary:

Unit Definition Value in SI Units
Truṭi (त्रुटि) base unit ≈ 308.6 ns
Reṇu (रेणु) 60 Truṭi ≈ 18.5 μs
Lava (लव) 60 Reṇu ≈ 1,111 μs
Līkṣaka (लीक्षक) 60 Lava ≈ 66.66 ms
Liptā (लिप्ता) / Vipala (विपल) 6 Līkṣaka ≈ 0.4 s
Prāṇa (प्राण) 10 Liptā ≈ 4 s
Pala (पल) / Vighaṭi (विघटि) / Vināḍī (विनाडी) 60 Liptā or 6 Prāṇa ≈ 24 s
Ghaṭi (घटि) / Nāḍī (नाडी) / Daṇḍa (दण्ड) 60 Vighaṭi ≈ 1.44 ks (24 min)
Muhūrta (मुहूर्त) 2 Ghaṭi ≈ 2.88 ks (48 min)
Nakṣatra Ahorātram (नक्षत्र अहोरात्रम्; sidereal day) 60 Ghaṭī or 30 Muhūrta ≈ 86.4 ks (24 h)

Status: Textually unattested as a continuous ladder in any single canonical śāstra. The terms are drawn from disparate sources (Truṭi from SS, Reṇu from Jain/cosmological texts, Lava from Purāṇas, Līkṣaka from Bhāskarācārya's Līlāvatī as a distance unit, not a time unit) and harmonized into a uniform 60× chain by later commentators.

A2.2 Siddhānta Śiromaṇi — Mathematical Computation Chain

Bhāskarācārya's Siddhānta Śiromaṇi (12th century CE) provides a 30-fold mathematical hierarchy used in the Madhyamādhikāra (Chapter on Mean Longitudes) for astronomical computation. This chain uses different multipliers and values from the Purāṇic chains:

Unit Definition Value in SI Units
Truṭi base unit ≈ 29.6 μs
Tatpara 100 Truṭi ≈ 2.96 ms
Nimeṣa 30 Tatpara ≈ 88.9 ms
Kāṣṭhā (काष्ठा) 18 Nimeṣa ≈ 1.6 s
Kalā (कला) 30 Kāṣṭhā ≈ 48 s
Ghaṭikā 30 Kalā ≈ 1.44 ks (24 min)
Muhūrta (मुहूर्त) / Kṣaṇa (क्षण) 2 Ghaṭikā ≈ 2.88 ks (48 min)
Ahorātram (sidereal day) 30 Muhūrta ≈ 86.4 ks (24 h)

Source: Bhāskarācārya, Siddhānta Śiromaṇi, Madhyamādhikāra. This chain converges at the muhūrta (48 min) with the Purāṇic chains but diverges completely in the sub-nimeṣa range. It is a computational tool for planetary mean longitudes, not a biological or metrological ladder.

A2.3 Macro-Units (Civil & Astrological)

These are larger time units that appear in civil practice, panchāṅga tradition, and later astrological convention:

Unit Composition Derived Value Status
Coghadiyā (चोघडिया) 1.875 Muhūrta ≈ 1.5 hours 1.5 hr Later astrological construct — derived from "Chau-Ghaḍī" (4 Ghaṭikās, where 4 × 24m = 96m ≈ 1.5h). Used for auspicious timing (muhūrta-śāstra), not found in canonical Ārṣa metrology.
Saptāha (सप्ताह) 7 Ahorātra 7 days Historical/civil unit — the 7-day week (Vāra) is a historical and civil convention, not foundational to the Ārṣa atomic framework. The seven Vāras are named after the seven grahas (Sun, Moon, Mars, Mercury, Jupiter, Venus, Saturn).

Appendix A3: Nārada Purāṇa Māna Concordance (Non-Ladder Layer)

This concordance exists because these citations are about selecting a reckoning framework (māna) and its calendrical semantics, not about extending the truṭi-to-year ladder.

Topic Exact Locus
Nine measures (māna) named Nārada Purāṇa 1.56.109
Practical “vyavahāra” uses five; tasks differ by measure Nārada Purāṇa 1.56.110
Solar measure used for planet-motion Nārada Purāṇa 1.56.111
Civil measure used for rains and pregnancy Nārada Purāṇa 1.56.111
Nakṣatra- and tithi-based determinations invoked for specific acts Nārada Purāṇa 1.56.112
Lunar measure used for parva/vāstu/upavāsa, etc. Nārada Purāṇa 1.56.112
Jupiter-measure for Prabhava-type year-character Nārada Purāṇa 1.56.113
60-year cycle and its names Nārada Purāṇa 1.56.114-120
5-year yuga grouping; 12 yugas within the 60-year cycle; yuga lords Nārada Purāṇa 1.56.121-123
Ayanas; deva day/night Nārada Purāṇa 1.56.125
Ritual valuation of uttarāyaṇa vs dakṣiṇāyaṇa Nārada Purāṇa 1.56.126-127
Ṛtu grouping across uttarāyaṇa/dakṣiṇāyaṇa Nārada Purāṇa 1.56.127-128
Month-bases (cāndra/saurā/sāvana/nākṣatra) Nārada Purāṇa 1.56.129
12 month-names (Madhu etc.) Nārada Purāṇa 1.56.130
Month naming by full-moon nakṣatra Nārada Purāṇa 1.56.131
Pakṣa semantics (daiva/pitṛ) and auspiciousness pairing Nārada Purāṇa 1.56.132
Tithi-lord list begins Nārada Purāṇa 1.56.133-135

Appendix B: Sūrya Siddhānta, Kept Separate

Unit Composition Derived Value Exact Verse
Prāṇa base practical breath-unit 4.0000 s SS 1.11
Vināḍī 6 prāṇas 24.0000 s SS 1.11
Nāḍikā 60 vināḍīs 24.0000 min SS 1.11
Nākṣatra ahorātra 60 nāḍikās 24.0000 hr SS 1.12
Sāvana māsa 30 such days 30 days SS 1.12
Varṣa 12 months 360 days in this civil derivation SS 1.13

Appendix C: Sanskrit Verses Covering All Citations Used Above

I. Bhāgavata Purāṇa 3.11

BhP 3.11.1

मैत्रेय उवाच चरमः सद्विशेषाणामनेकोऽसंयुतः सदा । परमाणुः स विज्ञेयो नृणामैक्यभ्रमो यतः ॥ १ ॥

Translation: "Maitreya said: The ultimate particle of the material manifestation, which is indivisible and never combined, is called the atom (paramāṇu). It should be known as the source of people's confusion about unity."

BhP 3.11.4

स कालः परमाणुर्वै यो भुङ्क्ते परमाणुताम् । सतोऽविशेषभुग्यस्तु स कालः परमो महान् ॥ ४ ॥

Translation: "That time which consumes the atomic state is the supreme great time, which consumes the undifferentiated state of being."

BhP 3.11.5

अणुर्द्वौ परमाणु स्यात्त्रसरेणुस्त्रयः स्मृतः । जालार्करश्म्यवगतः खमेवानुपतन्नगात् ॥ ५ ॥

Translation: "Two atoms make one double atom, and three double atoms make one hexatom. This is observed in the sun's rays passing through the holes of a lattice, as they move through the sky."

BhP 3.11.6

त्रसरेणुत्रिकं भुङ्क्ते यः कालः स त्रुटिः स्मृतः । शतभागस्तु वेधः स्यात्तैस्त्रिभिस्तु लवः स्मृतः ॥ ६ ॥

Translation: "The time that consumes three hexatoms is called one truṭi. One hundredth of that is called vedha, and three vedhas make one lava."

BhP 3.11.7

निमेषस्त्रिलवो ज्ञेय आम्नातस्ते त्रयः क्षणः । क्षणान्पञ्च विदुः काष्ठां लघु ता दश पञ्च च ॥ ७ ॥

Translation: "One nimeṣa should be known as three lavas. Three nimeṣas are called one kṣaṇa. Five kṣaṇas make one kāṣṭhā, and fifteen kāṣṭhās make one laghu."

BhP 3.11.8

लघूनि वै समाम्नाता दश पञ्च च नाडिका । ते द्वे मुहूर्तः प्रहरः षड्यामः सप्त वा नृणाम् ॥ ८ ॥

Translation: "Fifteen laghus make one nāḍikā. Two nāḍikās make one muhūrta. The day and night of mortals consists of six or seven praharas (yāmas)."

BhP 3.11.9

द्वादशार्धपलोन्मानं चतुर्भिश्चतुरङ्गुलैः । स्वर्णमाषैः कृतच्छिद्रं यावत्प्रस्थजलप्लुतम् ॥ ९ ॥

Translation: "A measure of twelve and a half palas, with a hole made by four fingers of gold māṣas, is filled up to one prastha of water." (This describes the water-clock mechanism for measuring one nāḍikā.)

BhP 3.11.10

यामाश्चत्वारश्चत्वारो मर्त्यानामहनी उभे । पक्षः पञ्चदशाहानि शुक्लः कृष्णश्च मानद ॥ १० ॥

Translation: "Four yāmas each make the two halves (day and night) of mortals. A pakṣa consists of fifteen days — the bright fortnight and the dark fortnight, O giver of measure."

BhP 3.11.11

तयोः समुच्चयो मासः पितॄणां तदहर्निशम् । द्वौ तावृतुः षडयनं दक्षिणं चोत्तरं दिवि ॥ ११ ॥

Translation: "The combination of those two (pakṣas) makes one month, which is one day and night of the pitṛs. Two months make one ṛtu; six ṛtus make one ayana — the southern and the northern, in the celestial sphere."

BhP 3.11.12

अयने चाहनी प्राहुर्वत्सरो द्वादश स्मृतः । संवत्सरशतं नृणां परमायुर्निरूपितम् ॥ १२ ॥

Translation: "The two ayanas make one day and night (of the gods). Twelve months are called one year. One hundred saṃvatsaras are established as the maximum lifespan of humans."

II. Manusmṛti 1.64-67

Manu 1.64

निमेषा दश चाष्टौ च काष्ठा त्रिंशत् तु ताः कला । त्रिंशत् कला मुहूर्तः स्यादहोरात्रं तु तावतः ॥ ६४ ॥

Translation: "Ten and eight nimeṣas make one kāṣṭhā; thirty kāṣṭhās make one kalā; thirty kalās make one muhūrta; and one day-and-night (ahorātra) consists of that many (thirty muhūrtas)."

Manu 1.65

अहोरात्रे विभजते सूर्यो मानुषदैविके । रात्रिः स्वप्नाय भूतानां चेष्टायै कर्मणामहः ॥ ६५ ॥

Translation: "The sun divides the day and night into human and divine. Night is for the sleep of beings; the day is for the performance of actions."

Manu 1.66

पित्र्ये रात्र्यहनी मासः प्रविभागस्तु पक्षयोः । कर्मचेष्टास्वहः कृष्णः शुक्लः स्वप्नाय शर्वरी ॥ ६६ ॥

Translation: "For the pitṛs (ancestors), a month is the division of their day and night, split between the two fortnights. The dark fortnight (kṛṣṇa pakṣa) is their day for activity; the bright night (śukla pakṣa) is for their sleep."

Manu 1.67

दैवे रात्र्यहनी वर्षं प्रविभागस्तयोः पुनः । अहस्तत्रोदगयनं रात्रिः स्याद् दक्षिणायनम् ॥ ६७ ॥

Translation: "For the gods, a year is the division of their day and night. There, the northern solstice (udagayana) is their day; the southern solstice (dakṣiṇāyana) is their night."

III. Viṣṇu Purāṇa I.3.8-10

The following three verse-senses are cited as the Viṣṇu Purāṇa time ladder. They are included here so every citation used above is covered in one place.

VP I.3.8

काष्ठा पञ्चदशाख्याता निमेषा मुनिसत्तम । काष्ठा त्रिंशत्कला त्रिंशत्कला मौहूर्तिको विधिः ॥ ८ ॥

Translation: "Fifteen nimeṣas, O best of sages, are called one kāṣṭhā; thirty kāṣṭhās make one kalā; and thirty kalās constitute the measure of a muhūrta."

VP I.3.9

तावत्संख्यैरहोरात्रं मुहूर्तैर्मानुषं स्मृतम् । अहोरात्राणि तावन्ति मासः पक्षद्वयात्मकः ॥ ९ ॥

Translation: "One day-and-night (ahorātra) of mortals is said to consist of that many (thirty) muhūrtas. A month, consisting of two fortnights, consists of that many (thirty) day-and-nights."

VP I.3.10

तैः षड्भिरयनं वर्षं द्वेऽयने दक्षिणोत्तरे । अयनं दक्षिणं रात्रिर्देवानामुत्तरं दिनम् ॥ १० ॥

Translation: "Six months make one ayana; the two ayanas are the southern and northern. The southern ayana is the night of the gods; the northern ayana is their day."

IV. Sūrya Siddhānta 1.11-13

SS 1.11

प्राणादिः कथितो मूर्तस्त्रुट्याद्योऽमूर्तसंज्ञकः । षड्भिः प्राणैर्विनाडी स्यात् तत्षष्ट्या नाडिका स्मृता ॥ १. ११ ॥

Translation: "The (time-unit) beginning with prāṇa is called mūrta (with form); that beginning with truṭi is called amūrta (formless). Six prāṇas make one vināḍī; sixty of those make one nāḍikā."

SS 1.12

नाडीषष्ट्या तु नाक्षत्रमहोरात्रं प्रकीर्तितम् । तत्त्रिंशता भवेन् मासः सावनोऽर्कोदयैस्तथा ॥ १. १२ ॥

Translation: "Sixty nāḍīs make one nākṣatra (sidereal) day-and-night. Thirty of those make one sāvana month; likewise from sunrise (to sunrise)."

SS 1.13

ऐन्दवस्तिथिभिस्तद्वत् सङ्क्रान्त्या सौर उच्यते । मासैर्द्वादशभिर्वर्षं दिव्यं तदह उच्यते ॥ १. १३ ॥

Translation: "Likewise, the cāndra (lunar) month is by tithis; the saura (solar) month is by saṅkrānti. Twelve months make one year; that is called the divine day."

V. Ṛgveda 1.164.11

RV 1.164.11

द्वादशारं न हि तज्जराय वर्वर्ति चक्रं परि द्यामृतस्य । आ पुत्रा अग्ने मिथुनासो अत्र सप्त शतानि विंशतिश्च तस्थुः ॥

Translation: "The twelve-spoked Wheel of Order (ṛta) revolves around the heavens without aging. Upon it, O Agni, the sons (days) stand in pairs — seven hundred and twenty in all." (Interpreted as 360 days × 2 = day + night, the wheel of the year.)

VI. Ṛgveda 1.164.48

RV 1.164.48

द्वादश प्रधयश्चक्रमेकं त्रीणि नभ्यानि क उ तच्चिकेत । तस्मिन्त्साकं त्रिशता न शङ्कवोऽर्पिताः षष्टिर्न चलाचलासः ॥

Translation: "Twelve are the fellies (spokes), the wheel is one; three are the hubs (naves) — who has understood this? Upon it are set three hundred and sixty pins (nails) that move not and that move." (Interpreted as 12 months = 12 fellies, 3 seasons (or 3 worlds) = 3 hubs, 360 days = 360 pins.)

VII. Atharvaveda 19.53.1-2 (Kālasūkta)

AV 19.53.1

कालोऽश्वो वहति सप्तरश्मिः सहस्राक्षो अजरो भूरिरेताः । तं वर्तमानाः कवयो विपश्चितस्तस्य चक्रा भुवनानि विश्वा ॥

Translation: "Time, the steed, runs with seven reins (rays), thousand-eyed, ageless, rich in seed. The inspired sages mount him as he moves; his wheels are all the worlds."

AV 19.53.2

अतीतं अनागतं वर्तमानं भुवनं यच्च कालः प्रविष्टः। सप्त रश्मीन् अजिघ्रति कालः केशान् वि मुञ्चति ॥

Translation: "That which has passed, that which is to come, that which is present, and whatever world Kāla has entered — he sniffs at the seven rays, he shakes loose the hairs."

VIII. Taittirīya Brāhmaṇa 3.10 Time-Segment Names

VIII.A Day-Time Names (TB 3.10.1.1-3 — Bright Fortnight)

TB 3.10.1.1 (first five)

संज्ञानं विज्ञानं प्रज्ञानं जानदभिजानत् । संकल्पमानं प्रकल्पमानम् ॥

Translation: "Awareness, discernment, wisdom, knowledge, recognition, resolve, planning..."

TB 3.10.1.2 (continuation)

उपकल्पमानं संवत्सरं संवत्सरप्रज्ञानं स्वर्गं स्वर्गप्रज्ञानम्। उत्तममुत्तमप्रज्ञानं कल्याणम् ॥

Translation: "...preparation, year-cycle, year-wisdom, heavenly, heavenly-wisdom, supreme, supreme-wisdom, auspicious."

VIII.B Night-Time Names (TB 3.10.1.1-3 — Bright Fortnight)

TB 3.10.1.3 (first five)

दर्शा दृष्टा दर्शता विश्वरूपा सुदर्शना । आप्यायमाना प्र्यायमाना प्र्याया सुनृतेतिरा ॥

Translation: "The visible, the seen, the visible one, all-formed, beautiful to see; swelling, swelling forth, swelling, truth-filled, flowing..."

TB 3.10.1.4 (continuation)

आपूर्यमाण पूर्यमाण पुरयन्ती पूर्णा पौर्णमासी ॥

Translation: "...filling, being filled, making full, complete, full-moon day."

VIII.C Muhūrta Names (TB 3.10.1.1-4 — Bright Fortnight)

TB 3.10.1.1 (15 Daytime Muhūrtas)

चित्रः केतुः प्रभा नभान् सम्भान् ज्योतिष्मान् तेजस्वान् । आतपन्तपन्नभितपन् रोचनो रोचमानः शोभनः शोभमानः कल्याणः ॥

Translation: "Variegated, banner, radiance, firmament, gathering, luminous, radiant; heating, heating upon, delighting, delighting, beautiful, beautifying, auspicious."

TB 3.10.1.2 (15 Nighttime Muhūrtas)

सविता प्रसविता दीप्ता दीपायन् दीप्यमानः ज्वलन् ज्वालिता तपन् । वितपन् शान्तपन् रोचनो रोचमानः शुम्भः शुम्भमानो वामः ॥

Translation: "The sun, the procreator, blazing, kindling, blazing forth, flaming, enkindled, heating; heating upon, pacifying, delighting, delighting, adorning, adorning, beloved."

VIII.D Prati-Muhūrtas (TB 3.10.1.1-4 — Sub-divisions of Each Muhūrta)

TB 3.10.1.3-4 (15 Prati-Muhūrtas)

इदानीं तदानीमेतर्हि क्षिप्रमजिरमाशु निमेषः फणो द्रवन्नतिद्रवन् । त्वरन्त्वरमाण आशुरासीयन् जवः ॥

Translation: "Now, then, at this time, swiftly, nimbly, swiftly, the blink, the hood, flowing, flowing rapidly; hurrying, hurrying oneself, swift, being, speed."

(Source: B.V. Subbarayappa & K.V. Sarma, "Indian Astronomy: A Source Book", 1985, Chapter 7 — Measures of Time, citing Taittirīya Brāhmaṇa 3.10.1.1-4)

IX. Śatapatha Brāhmaṇa 10.4.2.18

ŚB 10.4.2.18

तद् यद् एव तद् अहोरात्रं तद् एव मुहूर्तेषु प्रतिष्ठितम् ॥

Translation: "That very day-and-night (ahorātra) is established in the muhūrtas." (The muhūrtas are the subdivisions through which the full day-and-night is realized.)

X. Mahābhārata 12.224.12-15

MBh 12.224.12

काष्ठा निमेषा दश पञ्च चैव त्रिंशत्तु काष्ठा गणयेत्कलां ताम् । त्रिंशत्कलाश्चापि भवेन्मुहूर्तो भागः कलाया दशमश्च यः स्यात् ॥ १२॥

Translation: "Ten and five nimeṣas make one kāṣṭhā; thirty kāṣṭhās are counted as one kalā; thirty kalās make one muhūrta; and the tenth part of a kalā is also known."

MBh 12.224.13

त्रिंशन्मुहूर्तश्च भवेदहश्च रात्रिश्च संख्या मुनिभिः प्रणीता । मासः स्मृतो रात्र्यहनी च त्रिंशत्संवत्सरो द्वादशमास उक्तः । संवत्सरं द्वे अयने वदन्ति संख्याविदो दक्षिणमुत्तरं च ॥ १३॥

Translation: "Thirty muhūrtas make one day and one night — the reckoning established by the sages. A month is said to be thirty day-and-nights; twelve months make one year. The two ayanas, southern and northern, are spoken of as making the year."

MBh 12.224.14

अहोरात्रे विभजते सूर्यो मानुषलौकिके । रात्रिः स्वप्नाय भूतानां चेष्टायै कर्मणामहः ॥ १४॥

Translation: "The sun divides the day and night of mortals. Night is for the sleep of beings; the day is for the performance of actions."

MBh 12.224.15

पित्र्ये रात्र्यहनी मासः प्रविभागस्तयोः पुनः । कृष्णोऽहः कर्मचेष्टायां शुक्लः स्वप्नाय शर्वरी ॥ १५॥

Translation: "For the pitṛs (ancestors), a month is the division of their day and night. The dark (kṛṣṇa) fortnight is their day for activity; the bright (śukla) night is for their sleep."

XI. Brahmāṇḍa Purāṇa 1.13.16-18

Brahmāṇḍa Purāṇa 1.13.16

पर्वाण्यस्तिथयः संध्याः पक्षा मासार्धसंमिताः । निमेषाश्च कलाः काष्ठा मुहूर्ता दिवसा क्षयाः ॥ १६॥

Translation: "Parvans (fortnights) are tithis; junctions; pakṣas are half-months; nimeṣas, kalās, kāṣṭhās, muhūrtas, days — all are divisions (of time)."

Brahmāṇḍa Purāṇa 1.13.17

द्वावर्धमासौ मासस्तु द्वौ मासावृतुरुच्यते । ऋतुत्रयं चाप्ययनं द्वे अयने दक्षिणोत्तरे ॥ १७॥

Translation: "Two half-months make a month; two months are called one ṛtu; three ṛtus make one ayana; two ayanas — the southern and the northern."

Brahmāṇḍa Purāṇa 1.13.18

संवत्सरः समेतश्च स्थानान्येतानि स्थानिनाम् । ऋतवस्तु निमेः पुत्रा विज्ञेयास्ते तथा एव षट् ॥ १८॥

Translation: "The saṃvatsara is the complete assembly; these are the stations of those who have stations. The six ṛtus are known as the sons of Niṃeṣa."

XII. Bhaviṣya Purāṇa 1.2.86-91

Bhaviṣya Purāṇa 1.2.86

निमेषा दश चाष्टौ च अक्ष्णः काष्ठा निगद्यते ।। ८६॥

Translation: "Ten and eight nimeṣas of the eye are called one kāṣṭhā."

Bhaviṣya Purāṇa 1.2.87

त्रिंशत्काष्ठाः कलामाहुः क्षणस्त्रिंशत्कलाः स्मृताः । मुहूर्तमथ मौहूर्ता वदन्ति द्वादश क्षणम् ।। ८७॥

Translation: "Thirty kāṣṭhās are called one kalā; thirty kalās are remembered as one kṣaṇa; and twelve kṣaṇas, O experts in muhūrtas, are called one muhūrta."

Bhaviṣya Purāṇa 1.2.88

त्रिंशन्मुहूर्तमुद्दिष्टमहोरात्रं मनीषिभिः । मासस्त्रिंशदहोरात्रं द्वौ द्वौ मासावृतुः स्मृतः ।। ८८॥

Translation: "Thirty muhūrtas are declared as one day-and-night by the wise; thirty day-and-nights make one month; two months are remembered as one ṛtu."

Bhaviṣya Purāṇa 1.2.89

ऋतुत्रयमप्ययनमयने द्वे तु वत्सरः । अहोरात्रे विभजते सूर्यो मानुषदैविके ।। ८९॥

Translation: "Three ṛtus make one ayana; two ayanas make one year. The sun divides the human and divine day-and-night."

Bhaviṣya Purāṇa 1.2.90

रात्रिः स्वप्नाय भूतानां चेष्टायै कर्मणामहः । पित्र्ये रात्र्यहनी मासः प्रविभागस्तु पक्षयोः ।। ९०॥

Translation: "Night is for the sleep of beings; the day is for the performance of actions. For the pitṛs, a month is the division of day and night between the two fortnights."

Bhaviṣya Purāṇa 1.2.91

कर्म चेष्टास्वहः कृष्णः मुक्तः स्वप्नाय शर्वरी । दैवे रात्र्यहनी वर्षं प्रविभागस्तयोः पुनः ।। ९१॥

Translation: "The dark fortnight is their day for activity; the bright night is for sleep. For the gods, the year is the division of their day and night."

XIII. Kūrma Purāṇa 5.4-6

Kūrma Purāṇa 5.4

काष्ठा पञ्चदश ख्याता निमेषा द्विजसत्तमाः । काष्ठास्त्रिंशत् कला त्रिंशत् कला मौहूर्त्तिकी गतिः ॥५.४॥

Translation: "Fifteen nimeṣas, O best of twice-born, are known as one kāṣṭhā; thirty kāṣṭhās make one kalā; thirty kalās make the measure of a muhūrta."

Kūrma Purāṇa 5.5

तावत्संख्यैरहोरात्रं मुहूर्त्तैर्मानुषं स्मृतम् । अहोरात्राणि तावन्ति मासः पक्षद्वयात्मकः ॥५.५॥

Translation: "One day-and-night of mortals is said to consist of that many (thirty) muhūrtas. A month, consisting of two fortnights, consists of that many (thirty) day-and-nights."

Kūrma Purāṇa 5.6

तैः षड्भिरयनं वर्षं द्वेऽयने दक्षिणोत्तरे । अयनं दक्षिणं रात्रिर्देवानामुत्तरं दिनम् ॥५.६॥

Translation: "Six months make one ayana; the two ayanas are the southern and northern. The southern ayana is the night of the gods; the northern ayana is their day."

XIV. Mārkaṇḍeya Purāṇa 46.23-25

Mārkaṇḍeya Purāṇa 46.23

निमेषैर्दशभिः काष्ठा तथा पञ्चभिरुच्यते । कलास्त्रिंशच्च वै काष्ठा मुहूर्तं त्रिंशत्ताः कलाः ॥२३॥

Translation: "Ten and five nimeṣas make one kāṣṭhā; thirty kāṣṭhās make one kalā; thirty kalās make one muhūrta."

Mārkaṇḍeya Purāṇa 46.24

अहोरात्रं मुहूर्तानां नृणां त्रिंशत्तु वै स्मृतम् । अहोरात्रैश्च त्रिंशद्भिः पक्षौ द्वौ मास उच्यते ॥२४॥

Translation: "One day-and-night of mortals is remembered as thirty muhūrtas. Thirty day-and-nights make the two fortnights, and that is called a month."

Mārkaṇḍeya Purāṇa 46.25

तैः षड्भिरयनं वर्षं द्वेऽयने दक्षिणोत्तरे । तद्देवानामहोरात्रं दिनं तत्रोत्तरायणम् ॥२५॥

Translation: "Six months make one ayana; the two ayanas are the southern and northern. That (year) is the day-and-night of the gods; there, the northern solstice is their day."

XV. Vāyu Purāṇa 50.168

Vāyu Purāṇa 50.168

काष्ठा निमेषा दश पञ्च चैव त्रिंशच्च काष्ठा गणयेत् कलान्तम् । त्रिंशत् कलाश्चैव भवेन्मुहूर्त्तस्तैस्त्रिंशता रात्र्यहनी समेते ॥ ५०.१६८ ॥

Translation: "Ten and five nimeṣas make one kāṣṭhā; thirty kāṣṭhās are counted up to the kalā; thirty kalās make one muhūrta; and thirty of those make one day-and-night (combined)."

XVI. Matsya Purāṇa 141.4 and 142.5-6

Matsya Purāṇa 141.4

काष्ठा निमेषा दश पञ्च चैव त्रिंशच्च काष्ठाङ्गणयेत् कलान्तु । त्रिंशत्कलाश्चैव भवेन् मुहूर्तस्तैस्त्रिंशता रात्र्यहनी समेते ॥ १४१.४ ॥

Translation: "Ten and five nimeṣas make one kāṣṭhā; thirty kāṣṭhās are counted up to the kalā; thirty kalās make one muhūrta; and thirty of those make one day-and-night (combined)."

Matsya Purāṇa 142.5

अहोरात्रे विभजते सूर्यो मानुषलौकिके । रात्रिः स्वप्नाय भूतानाञ्चेष्टायै कर्म्मणामहः ॥ १४२.५ ॥

Translation: "The sun divides the day and night of mortals. Night is for the sleep of beings; the day is for the performance of actions."

Matsya Purāṇa 142.6

पित्र्ये रात्र्यहनी मासः प्रविभागस्तयोः पुनः । कृष्णपक्षस्त्वहस्तेषां शुक्लः स्वप्नाय शर्वरी ॥ १४२.६ ॥

Translation: "For the pitṛs, a month is the division of their day and night. The dark fortnight is their day; the bright night is for their sleep."

XVII. Padma Purāṇa 1.3.4-6

Padma Purāṇa 1.3.4

काष्ठा पंचदशाख्या ता निमेषा नृपसत्तम । काष्ठा स्त्रिंशत्कला त्रिंशत्कला मौहूर्त्तिको विधिः ॥ ४ ॥

Translation: "Fifteen nimeṣas, O best of kings, are called one kāṣṭhā; thirty kāṣṭhās make one kalā; thirty kalās constitute the measure of a muhūrta."

Padma Purāṇa 1.3.5

तावत्संख्यैरहोरात्रं मुहूर्त्तैर्मानुषं स्मृतम् । अहोरात्राणि तावंति मासः पक्षद्वयात्मकः ॥ ५ ॥

Translation: "One day-and-night of mortals is said to consist of that many (thirty) muhūrtas. A month, consisting of two fortnights, consists of that many (thirty) day-and-nights."

Padma Purāṇa 1.3.6

तैः षड्भिरयनं वर्षं द्वेऽयने दक्षिणोत्तरे । अयनं दक्षिणं रात्रिर्देवानामुत्तरं दिनम् ॥ ६ ॥

Translation: "Six months make one ayana; the two ayanas are the southern and northern. The southern ayana is the night of the gods; the northern ayana is their day."

XVIII. Kauṭilīya Arthaśāstra Time-Ladder Prose

Kauṭilīya Arthaśāstra (prose time-ladder)

त्रुटो लवो निमेषः काष्ठा कला नाळिका मुहूर्तः पूर्वापरभागौ दिवसो रात्रिः पक्षो मास ऋतुरयनं संवत्सरो युगमिति काला । द्वौ त्रुटौ लवः । द्वौ लवौ निमेषः । पञ्च निमेषाः काष्ठा । त्रिंशत्काष्ठाः कला । चत्वारिंशत्कला नाडिका । दिनाळिका मुहूर्तः ।

Translation: "Truṭi, lava, nimeṣa, kāṣṭhā, kalā, nāḍikā, muhūrta, the eastern and western halves, day, night, fortnight, month, ṛtu, ayana, saṃvatsara, yuga — these are the divisions of time. Two truṭis make one lava; two lavas make one nimeṣa; five nimeṣas make one kāṣṭhā; thirty kāṣṭhās make one kalā; forty kalās make one nāḍikā; two day-nāḍikās make one muhūrta."

XIX. Nārada Purāṇa (Pūrvārdha) 1.56.109-135

Nārada Purāṇa 1.56.109

ब्रह्मदेवमनोर्मानं पित्र्यं सौरं च सावनम्। चांद्रमार्क्षं गुरोर्मानमिति मानानि वै नव ॥ १०९ ॥

Translation: "The measure of Brahmā, the divine measure, the measure of Manu, the ancestral measure, the solar measure, the civil measure, the lunar measure, the nakṣatra measure, and the measure of Bṛhaspati (Jupiter) — these are the nine measures."

Nārada Purāṇa 1.56.110

एतेषां नवमानानां व्यवहारोऽत्र पञ्चभिः। तेषां पृथक्पृथक्कार्यं वक्ष्यते व्यवहारतः ॥ ११० ॥

Translation: "Among these nine measures, practical transactions here proceed through five. Their separate and distinct functions will be explained in due order."

Nārada Purāṇa 1.56.111

ग्रहाणां निखिलश्चारो गृह्यते सौरमानतः। वृष्टेर्विधानं स्त्रीगर्भः सावनेनैव गृह्यते ॥ १११ ॥

Translation: "The complete motion of all planets is ascertained by the solar measure; the ordering of rainfall and the gestation of women are known by the civil measure alone."

Nārada Purāṇa 1.56.112

प्रवर्षणां समे गर्भो नाक्षत्रेण प्रगृह्यते। यात्रोद्वाहव्रतक्षौरे तिथिवर्षेशनिर्णयः ॥ ११२ ॥ पर्ववास्तूपवासादि कृत्स्नं चांद्रे ण गृह्यते।

Translation: "The gestation of pregnancy is determined by the nakṣatra measure; journeys, marriages, vows, and shaving ceremonies are determined by tithi-lord decisions. The entirety of parva, vāstu, fasting, and similar observances is governed by the lunar measure."

Nārada Purāṇa 1.56.113

गृह्यते गुरुमानेन प्रभवाद्यब्दलक्षणम् ॥ ११३ ॥

Translation: "The character of years beginning with Prabhava is known through the Jupiter-based measure."

Nārada Purāṇa 1.56.114

तत्तन्मासैर्द्वादशभिस्तत्तदष्टौ भवेत्ततः। गुरुमध्यमचारेण षष्ट्यब्दाः प्रभवादयः ॥ ११४ ॥

Translation: "By the respective twelve months of each, then by their eight; through the mean motion of Jupiter, the sixty years beginning with Prabhava (are established)."

Nārada Purāṇa 1.56.115

प्रभवो विभवः शुक्लः प्रमोदोऽथ प्रजापतिः। अंगिराः श्रीमुखो भावो युवा धाता तथैव च ॥ ११५ ॥

Translation: "Prabhava, Vibhava, Śukla, Pramoda, Prajāpati, Āṅgirasa, Śrīmukha, Bhāva, Yuvā, Dhātā, and so on." (First ten of the sixty year-names.)

Nārada Purāṇa 1.56.116

ईश्वरो बहुधान्यश्च प्रमाथी विक्रमो वृषः। चित्रभानुस्सुभानुश्च तारणः पार्थिवोऽव्ययः ॥ ११६ ॥

Translation: "Īśvara, Bahudhānya, Pramāthī, Vikrama, Vṛṣa, Citrabhānu, Subhānu, Tāraṇa, Pārthiva, Avyaya." (Year-names eleven through twenty.)

Nārada Purāṇa 1.56.117

सर्वजित्सर्वधारी च विरोधी विकृतः खरः। नंदनो विजयश्चैव जयो मन्मथदुर्मुखौ ॥ ११७ ॥

Translation: "Sarvajit, Sarvadhārī, Virodhī, Vikṛta, Khara, Nandana, Vijaya, Jaya, Manmatha, Durmukha." (Year-names twenty-one through thirty.)

Nārada Purāṇa 1.56.118

हेमलंबो विलंबश्च विकारी शार्वरी लवः। शुभकृच्छोभनः क्रोधी विश्वावसुपराभवौ ॥ ११८ ॥

Translation: "Hemalamba, Vilamba, Vikārī, Śārvarī, Lava, Śubhakṛt, Śobhana, Krodhī, Viśvāvasu, Parābhava." (Year-names thirty-one through forty.)

Nārada Purāṇa 1.56.119

प्लवंगः कीलकः सौम्यः सामाप्तश्च विरोधकृत्। र्प्भावी प्रमादी च आनन्दो राक्षसोऽनलः ॥ ११९ ॥

Translation: "Plavaṅga, Kīlaka, Saumya, Sāmāpta, Virodhakṛt, Paribhāvī, Pramādī, Ānanda, Rākṣasa, Anala." (Year-names forty-one through fifty.)

Nārada Purāṇa 1.56.120

पिंगलः कालयुक्तश्च सिद्धार्थो रौद्र दुर्मतीः। दुंदुभी रुधिरोद्गारी रक्ताक्षः क्रोधनः क्षयः ॥ १२० ॥

Translation: "Piṅgala, Kālayukta, Siddhārtha, Raudra, Durmatī, Dundubhi, Rudhirodgārī, Raktākṣa, Krodhana, Kṣaya." (Year-names fifty-one through sixty.)

Nārada Purāṇa 1.56.121

नामतुल्यफलाः सर्वे विज्ञेयाः षष्टिवत्सराः। युगं स्थात्पंचभिर्वर्षैर्युगान्येवं तु द्वादश ॥ १२१ ॥

Translation: "All sixty years are to be known by results corresponding to their names. A yuga is established by five years; and there are twelve such yugas (in the sixty-year cycle)."

Nārada Purāṇa 1.56.122

तेषामीशाः क्रमाज्ज्ञेया विष्णुर्देवपुरोहितः। पुरंदरो लोहितश्च त्वष्टाहिर्बुध्न्यसंज्ञकः ॥ १२२ ॥

Translation: "The lords of these yugas are to be known in order: Viṣṇu, Devaguru (Bṛhaspati), Purandara (Indra), Lohita (Maṅgala), Tvaṣṭā, Ahi (Rāhu), and Budhnya-saṃjñaka."

Nārada Purāṇa 1.56.123

पितरश्च ततो विश्वे शशींद्रा ग्न्यश्विनो भगः। तथा युगस्य वर्षेशास्त्वग्निनेंदुविधीश्वराः ॥ १२३ ॥

Translation: "Then the Pitṛs, the Viśvedevas, Soma, Indra, Agni, the Aśvinīs, Bhaga. Thus the year-lords of each yuga: Agni, Soma, and the lord of beings (Prajāpati)."

Nārada Purāṇa 1.56.124

अथाद्वेशचमूनाथसस्यपानां बलाबलम्। तत्कालं ग्रहचारं च सम्यग् ज्ञात्वा फलं वदेत् ॥ १२४ ॥

Translation: "Then, having correctly known the strength and weakness of the lord of the year, the lord of the army, the crops, and the rains, as well as the planetary motions of that time, one should declare the results."

Nārada Purāṇa 1.56.125

सौम्यायनं मासषट्कं मृगाद्यं भानुभुक्तितः। अहः सुराणां तद्रा त्रिः कर्काद्यं दक्षिणायनम् ॥ १२५ ॥

Translation: "The six-month northern course beginning with Capricorn, reckoned from the Sun's motion, is the day of the gods; the southern course beginning with Cancer is their night."

Nārada Purāṇa 1.56.126

गृहप्रवेशवैवाहप्रतिष्ठामौंजिबन्धनम्। मघादौ मंगलं कर्म विधेयं चोत्तरायणे ॥ १२६ ॥

Translation: "House-entering, marriage, consecration, and the sacred-thread ceremony — these auspicious rites are to be performed in the northern course beginning with Maghā."

Nārada Purāṇa 1.56.127

याम्यायने गर्हितं च कर्म यत्नात्प्रशस्यते। माघादिमासौ द्वौ द्वौ च ऋतवः शिशिरादयः ॥ १२७ ॥

Translation: "In the southern course (dakṣiṇāyana), rites are to be avoided; they are commended with effort in the northern course. The months beginning with Māgha, taken two by two, form the seasons beginning with śiśira."

Nārada Purāṇa 1.56.128

मृगाच्छिशिरवसंतश्च ग्रीष्माः स्युश्चोत्तरायणे। वर्षा शरच्च हेमंतः कर्काद्वै दक्षिणायने ॥ १२८ ॥

Translation: "From Capricorn, the seasons śiśira and vasanta, and then grīṣma, are in the northern course. Varṣā, śarad, and hemanta are in the southern course beginning with Cancer."

Nārada Purāṇa 1.56.129

चांद्रो दर्शावधिः सौरः संक्रात्या सावनो दिनैः। त्रिंशद्भिश्चंद्र भगणो मासो नाक्षत्रसंज्ञकः ॥ १२९ ॥

Translation: "The lunar month is bounded by new moon (darśa); the solar month begins with saṅkrānti; the civil month is by days (sāvana); the month of the Moon's revolution is called the nakṣatra month."

Nārada Purāṇa 1.56.130

मधुश्च माधवः शुक्रः शुचिश्चाथ नभस्ततः। नभस्य इषः ऊर्जश्च सहाश्चैव सहस्यकः ॥ १३० ॥ तपास्तपस्य क्रमशश्चैत्रादीनां समाह्वयाः।

Translation: "Madhu, Mādhava, Śukra, Śuci, Nabhas, Nabhasya, Iṣa, Ūrja, Saha, Sahasyaka, Tapas, Tapasya — these are the respective names of the months beginning with Caitra."

Nārada Purāṇa 1.56.131

यस्मिन्मासे पौर्णमासी येन धिष्ण्येन संयुता। तन्नक्षत्राह्वयो मासः पौर्णमासी तदाह्वया ॥ १३१ ॥

Translation: "In whichever month the full-moon is conjoined with a particular nakṣatra, that month is named after that nakṣatra, and the full-moon (too) is so called."

Nārada Purāṇa 1.56.132

तत्पक्षौ दैव पित्राख्यौ शुक्लकृष्णौ तथापरे। शुभाशुभे कर्मणि च प्रशस्तौ भवतः सदा ॥ १३२ ॥

Translation: "Of its two fortnights, one is called divine (daiva) and the other ancestral (pitṛ); these are the bright (śukla) and dark (kṛṣṇa). They are always commended for auspicious and inauspicious rites respectively."

Nārada Purāṇa 1.56.133

क्रमात्तिथीनां ब्रह्माग्नी विरिंचिविष्णुशैलजाः ॥ १३३ ॥

Translation: "In order, the lords of the tithis are: Brahmā, Agni, Viriñci, Viṣṇu, Śailajā..." (Lords of tithis 1-5.)

Nārada Purāṇa 1.56.134

विनायकयमौ नागचंद्रौ स्कंदोऽकवासवौ। महेन्द्र वासवौ नागदुर्गादंडधराह्वयः ॥ १३४ ॥

Translation: "Vināyaka, Yama, the Serpent, the Moon, Skanda, the Sun, Vāsava, Mahendra, Vāsava, the Serpent, Durgā, Daṇḍadhara — these are the lords." (Lords of tithis 6-15.)

Nārada Purāṇa 1.56.135

शिवविष्णू हरिरवीकामः सर्वः कलीततः। चन्द्र विश्वेदर्शसंज्ञतिथीशाः पितरः स्मृताः ॥ १३५ ॥

Translation: "Śiva, Viṣṇu, Hari, Ravī, Kāma, Sarva, Kalī, and thereafter Soma, the Viśvedevas, and Darśa — these are the lords of the dark-fortnight tithis, remembered as the Pitṛs."


Appendix D: Complete Source Coverage Audit

All Primary Sources Included

  • Bhāgavata Purāṇa 3.11.1, 3.11.5-12
  • Manusmṛti 1.64-67
  • Viṣṇu Purāṇa I.3.8-10
  • Sūrya Siddhānta 1.11-13
  • Śatapatha Brāhmaṇa 10.4.2.18
  • Atharvaveda 19.53.1-2 (Kālasūkta)
  • Ṛgveda 1.164.11
  • Ṛgveda 1.164.48
  • Mahābhārata 12.224.12-15
  • Brahmāṇḍa Purāṇa 1.13.16-18
  • Bhaviṣya Purāṇa 1.2.86-91
  • Kūrma Purāṇa 5.4-6
  • Mārkaṇḍeya Purāṇa 46.23-25
  • Vāyu Purāṇa 50.168
  • Matsya Purāṇa 141.4 and 142.5-6
  • Padma Purāṇa 1.3.4-6
  • Taittirīya Brāhmaṇa 3.10.1.1-3 (day-time and night-time names for bright/dark fortnights)
  • Taittirīya Brāhmaṇa 3.10.1.1-4 (muhūrta names: 15 daytime + 15 nighttime + 15 prati-muhūrtas)
  • Kauṭilīya Arthaśāstra time-ladder prose
  • Nārada Purāṇa (Pūrvārdha) 1.56.109-135 (multi-māna framework and calendrical semantics)
  • Caraka Saṃhitā Sūtrasthāna 4/5 (akṣi-nimeṣa / mātra chain)
  • Suśruta Saṃhitā Sūtrasthāna 6/4 (akṣi-nimeṣa chain)
  • Vedic-ritual akṣara system (7200 akṣaras per muhūrta, ~0.4 s per syllable)
  • Phonetic calibration method (60 Gurvakṣaras = 24 s, Ghaṭī Yantra regulation)

Final Synthesis Statement

Hindu temporal metrology does not present one flat ladder where all names have one universal value. The proper reading of the sources is:

  • Bhāgavata preserves the full atomic-to-year chain.
  • Manu and Viṣṇu preserve parallel ritual chains from nimeṣa to muhūrta and upward.
  • The names overlap, but some magnitudes do not.
  • The strongest synthesis is therefore comparative and convergent, not homogenizing.