Vaidika Kala Mapana (वैदिककालमापनम्)

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Vaidika Kala Mapana (Samskrit: वैदिककालमापनम्) refers to the various divisions of time discussed in Vedic literature.

परिचयः ॥ Introduction

People of the vedic times engaged seriously in the performance of yajnas at specific times prescribed by the shastras. Thus, it was necessary to have accurate knowledge of the science of time so that the times prescribed for performing the various vedic yajnas could be correctly predicted well in advance. Thus, it was essential to study the natural divisions of time caused by the motion of the Sun and Moon, such as days, months, seasons, and years, with special attention to the study of the times of occurrence of new moons, full moons, equinoxes, and solstices that is included under the purview of the science of Astronomy. Therefore, Astronomy in the vedic times, was essentially the science of time-determination that was motivated by the need to fix time for the various yajnas that were performed at different times in different seasons.

In fact, this is the definition of astronomy given in Vedanga Jyotisha, the earliest available work dealing exclusively with astronomy that gives all necessary information needed by the vedic hota to predict times for the vedic yajnas and other observances.

However, the Vedic literature also has references to astronomical events and observations. For eg. The Kaushitaki brahmana states that the year ended with the full moon at the Purva Phalguni.

मुखम् वा एतत् संवत्सरस्य यत् फाल्गुनी पौर्णमासी । मुखम् उत्तरे फल्गू । पुच्छम् पूर्वे । तद् यथा प्रवृत्तस्य अन्तौ समेतौ स्याताम् । एवम् एव एतौ संवत्सरस्य अन्तौ समेतौ ।5.1

mukham vā etat saṁvatsarasya yat phālgunī paurṇamāsī । mukham uttare phalgū । puccham pūrve । tad yathā pravr̥ttasya antau sametau syātām । evam eva etau saṁvatsarasya antau sametau ।5.1

Thus, ancient Indian astronomy may be classified into two main categories:

1. Vedic astronomy
2. Post-vedic astronomy.

Vedic astronomy is the astronomy of the vedic period, i.e., the astronomy found in the vedic samhitas, brahmanas and allied literature. And that is elaborated in this article below.

Day in Vedic Astronomy

The day, in vedic literature was called Vasara (वासरः) or ahan (अहन्). And was reckoned from sunrise to sunrise. The variability of its length was known. For, the Rgveda invoking Somaraja says,

“O Somaraja, prolong thou our lives just as the Sun increases the length of the days.”

सोम राजन्प्र ण आयूंषि तारीरहानीव सूर्यो वासराणि ॥७॥

soma rājanpra ṇa āyūṁṣi tārīrahānīva sūryo vāsarāṇi ॥7॥

On the analogy of a civil day, a lunar day was also sometimes reckoned from one moonrise to the next and the name tithi was given to it.

तदाहुर्यद्दर्शपूर्णमासयोरुपवसति न ह वा अव्रतस्य देवा हविरश्नन्ति तस्मादुपवसत्युत मे देवा हविरश्नीयुरिति। पूर्वां पौर्णमासीमुपवसेदिति पैङ्ग्यमुत्तरामिति कौषीतकं या पूर्वा पौर्णमासी साऽनुमतिर्योत्तरा सा राका। या पूर्वाऽमावास्या सा सिनीवाली योत्तरा सा कुहूः। यां पर्यस्तमियादभ्युदियादिति सा तिथिः.....॥7.11॥ (Aitareya brahmana 32.10)

tadāhuryaddarśapūrṇamāsayorupavasati na ha vā avratasya devā haviraśnanti tasmādupavasatyuta me devā haviraśnīyuriti। pūrvāṁ paurṇamāsīmupavasediti paiṅgyamuttarāmiti kauṣītakaṁ yā pūrvā paurṇamāsī sā'numatiryottarā sā rākā। yā pūrvā'māvāsyā sā sinīvālī yottarā sā kuhūḥ। yāṁ paryastamiyādabhyudiyāditi sā tithiḥ.....॥7.11॥

However, the term tithi in the sense in which it is used now occurs in the Vedanga Jyotisha. It does not occur in the vedic samhitas and brahmanas, but there are reasons to believe that tithis were used even in those times.

Divisions of a Day

The duration of daylight, reckoned from sunrise to sunset, was variously divided into,

1. Two parts called Purvahna (forenoon) and Aparahna (afternoon)
2. Three parts called Purvahna, Madhyahna, and Aparahna.
3. Four parts called Purvahna, Madhyahna, Aparahna and Sayahna
4. Five parts called Pratah, Sangava, Madhyahna, Aparahna, and Sayahna

The names of these five parts occur together in the Shatapatha brahmana,

आदित्यस्त्वेव सर्व ऋतवः । यदैवोदेत्यथ वसन्तो यदा संगवोऽथ ग्रीष्मो यदा मध्यन्दिनोऽथ वर्षा यदापराह्णोऽथ शरद्यदैवास्तमेत्यथ हेमन्तस्तस्मादु मध्यंन्दिन एवादधीत तर्हि ह्येषोऽस्य लोकस्य नेदिष्ठं भवति तन्नेदिष्ठादेवैनमेतन्मध्यान्निर्मिमीते - २.२.३.९

ādityastveva sarva r̥tavaḥ । yadaivodetyatha vasanto yadā saṁgavo'tha grīṣmo yadā madhyandino'tha varṣā yadāparāhṇo'tha śaradyadaivāstametyatha hemantastasmādu madhyaṁndina evādadhīta tarhi hyeṣo'sya lokasya nediṣṭhaṁ bhavati tannediṣṭhādevainametanmadhyānnirmimīte

While the first three words ie. Pratah, Sangava and Madhyahna occur in Rgveda (Mandala 5),

उता यातं संगवे प्रातरह्नो मध्यंदिन उदिता सूर्यस्य । दिवा नक्तमवसा शंतमेन नेदानीं पीतिरश्विना ततान ॥३॥

utā yātaṁ saṁgave prātarahno madhyaṁdina uditā sūryasya । divā naktamavasā śaṁtamena nedānīṁ pītiraśvinā tatāna ॥3॥

The term Saya (evening) occurs in Rgveda (Mandala 8 and 10),

मो ष्वद्य दुर्हणावान्सायं करदारे अस्मत् । अश्रीर इव जामाता ॥२०॥

उत गाव इवादन्त्युत वेश्मेव दृश्यते । उतो अरण्यानिः सायं शकटीरिव सर्जति ॥३॥

mo ṣvadya durhaṇāvānsāyaṁ karadāre asmat । aśrīra iva jāmātā ॥20॥

uta gāva ivādantyuta veśmeva dr̥śyate । uto araṇyāniḥ sāyaṁ śakaṭīriva sarjati ॥3॥

The days and nights were also divided into 15 parts each called as muhurta. According to Taittiriya brahmana (3. 10. 1. 1–3), the muhurtas falling during the days and nights of the shukla and krshna pakshas (fortnights) were respectively given specific names.

The Taittiriya brahmana (3. 10. 1. 1–3; 3. 10. 10. 2) also assigns specific names to the fifteen days and nights of the shukla as well as krshna pakshas.

However, by the time of the Kautiliya Arthashastra, the day and night came to be divided into eight parts each.

नालिकाभिरहरष्टधा रात्रिं च विभजेत् । छाया-प्रमाणेन वा ।। ०१.१९.०६ ।।

nālikābhiraharaṣṭadhā rātriṁ ca vibhajet । chāyā-pramāṇena vā ।। 01.19.06 ।।

Week in Vedic Astronomy

In vedic literature, six days were taken to form a week that was called a Shadaha. 5 shadahas made a month and 12 months, a year. As to the names of the six days of a shadaha, there is no reference in the vedic literature. However, this six-day week was later replaced by the present seven day week (called saptaha) which had attained popularity and was in general use at the time of composition of the Atharva Jyotisha - a work on Jyotisha belonging to the later vedic period.

Months, Seasons and Year

In vedic astronomy, months were lunar or synodic and were measured from full moon to full moon and also from new moon to new moon as mentioned in the Taittiriya samhita (7.5.6.1) Originally, these months were named as Caitra etc. based on the nakshatras occupied by the Moon at the time of full moon. And these names do not occur in the early samhitas and brahmanas. Some of their occurrences are as follows:

1. phalgunī-pūrnamāsī, citrā-pūrnamāsī, etc. are found to occur in the Taittirīyasaṃhitā (7. 4. 8).
2. They occur in the Saṅkhāyana and Tāṇḍya-brāhmaṇas, the Vedāṅga-jyautiṣa, and the Kalpa-sūtras.5
3. 5Māgha is mentioned in Sāṅkhāyana-brāhmaṇa (= Kauṣītaki-brāhmaṇa) 19. 3;
4. Phālguna in Tāṇḍya-brāhmaṇa, 5. 9. 7–12;
5. and Srāvana, Māgha and Pauṣa in Ārca-jyautiṣa, 5, 6, 32, and 34 and Yājuṣa-jyautiṣa 5, 6, and 7;
6. and Mārgaśīrṣa and Śrāvana in Āśvalāyanagṛhyasūtra, 2. 3. 1 and 3. 5. 2 respectively.

   मार्गशीर्ष्यां प्रत्यवरोहणं चतुर्दश्याम् १

   ओषधीनां प्रादुर्भावे श्रवणेन श्रावणस्य २

   Twelve lunar months constituted a lunar year.

However, in due course they were linked with the solar months. Thus, the lunar month (reckoned from one new moon to the next) in which the Sun entered the sign Aries was called Chaitra or Madhu; that in which the Sun entered the sign Taurus was called Vaishakha or Madhava; and so on. And the lunar month in which the Sun did not enter a new sign was treated as an intercalary month.

While the year, generally called by the terms sama, vatsara, and hayana in the vedic literature, was measured from one winter solstice to the next. In fact, Kaushitaki brahmana (19.3) gives an interesting account of how the year-long yajna commenced at one winter solstice and continued until the next. It says, “On the new moon of Magha, the Sun rests, about to turn northwards. The hotas also rest, about to begin with the introductory Atiratra. Thus, for the first time, the hotas obtain the Sun. On him, they lay hold with the Chaturvimsha rite; that is why the laying hold rite has that name. The Sun then goes north for six months, while the hotas follow him with six day rites in continuation. Having gone north for six months, the Sun stands still, about to turn southwards. The hotas also rest, about to begin with the Vishnuvanta (summer solstice) day. Thus, for the second time, they obtain the Sun. The Sun then goes south for six months and the hotas follow him with six day rites in reverse order. Having gone south for six months, the Sun stands still, being about to turn north and the hotas also rest, about to begin with the Mahavrata day. Thus, they obtain the Sun for the third time."

In this context, it is worth observing that the Taittiriya brahmana (3. 9. 22) calls the year “the day of the deities” who are supposed to reside at the north pole.

एकं वा एतद्देवानामहः  । यत्संवत्सरः  । ekaṁ vā etaddevānāmahaḥ । yatsaṁvatsaraḥ ।

This year of vedic astronomy seems to have been a seasonal or tropical one. Therefore, in the early stages, the names of the seasons were used as synonyms of a year.

but in due course it was used in the sense of a sidereal year.

The year was supposed to consist of six seasons and each season of two (solar) months. The relation between the seasons and months was as shown in Table 1.

Relation between Vedic seasons and months

Seasons	Months
Vasanta (Spring)	Madhu Madhava
2. Grishma (Summer)	3. Shukra 4. Shuchi
3. Varsha (Rainy)	5. Nabhas 6. Nabhasya
4. Sharada (Autumn)	7. Isha 8. Urja
5. Hemanta (Winter)	9. Sahas 10. Sahasya
6. Shishira (Chilly Winter)	11. Tapas 12. Tapasya

Two (solar) months commencing with the winter solstice were called Śiśira; the next two months, Vasanta; and so on. Sometimes Śiśira and Hemanta were treated as one season and the number of seasons was taken as five (Aitareyabrāhmaṇa, 1. 1; Taittirīya-brāhmaṇa, 2. 7. 10)

In order to preserve correspondence between lunar and solar years, intercalary months were inserted at regular intervals. Mention of the intercalary month is made in the Ṛgveda (1. 25. 8), but how it was arrived at and where in the scheme of months it was introduced in that time is not known.

वेद मासो धृतव्रतो द्वादश प्रजावतः । वेदा य उपजायते ॥८॥

There is evidence to show that to make the lunar year correspond to the solar year 12 days were intercalated after every lunar year and one month was dropped after every 40 years.5 (5Law, N. N., Age of the Ṛgveda, pp. 20, 28–29.) At a later stage this correspondence was established by evolving a cycle of five solar years with 62 lunar months. This cycle was called a yuga.

The Vedāṅga-jyautiṣa prescribes insertion of an intercalary month after every 30 lunar months (Yājuṣa-jyautiṣa, 37). Thus, a year sometimes contained 12 lunar months and sometimes 13 lunar months.

The Taittirīya-saṃhitā (5. 6. 7) refers to 12 as well as 13 months of a year and calls the thirteenth (intercalary) month by the names saṃsarpa and aṃhaspati (1. 4. 14).

1.4.14 अनुवाक 14 ऋतुग्रहाः

1 मधुश् च माधवश् च शुक्रश् च शुचिश् च नभश् च नभस्यश् चेषश् चोर्जश् च सहश् च सहस्यश् च तपश् च तपस्यश् च । उपयामगृहीतो ऽसि सꣳसर्पो ऽसि । अꣳहस्पत्याय त्वा ॥

The Vājasaneyī-saṃhitā (7. 30; 22. 31) calls the intercalary month on one occasion by the name aṃhasaspati and on another by the name malimluca (22. 30).

In later works the synodic month with two saṃkrantis is called aṃhaspati, the synodic month without any saṃkrānti, occurring before it, is called saṃsarpa, and the synodic month without any saṃkrānti occurring after it is called adhimāsa (intercalary month, Tantrasaṃgraha i. 8)

Originally the lunar (or synodic) months Caitra etc. were named after the nakshatras occupied by the Moon at the time of full moon. But in due course they were linked with the solar months. Thus, the lunar month (reckoned from one new moon to the next) in which the Sun entered the sign Aries was called Caitra or Madhu; that in which the Sun entered the sign Taurus was called Vaiśākha or Mādhava; and so on. The lunar month in which the Sun did not enter a new sign was treated as an intercalary month.

Periods bigger than a year are also met with in the vedic literature. They were called yuga. One such yuga consisted of 5 solar years. The five constituent years of this yuga were called saṃvatsara, parivatsara, idāvatsara, anuvatsara and idvatsara. The Ṛgveda (7. 103. 7–8) mentions two of these, viz. saṃvatsara and parivatsara.

ब्राह्मणासो अतिरात्रे न सोमे सरो न पूर्णमभितो वदन्तः । संवत्सरस्य तदहः परि ष्ठ यन्मण्डूकाः प्रावृषीणं बभूव ॥७॥

ब्राह्मणासः सोमिनो वाचमक्रत ब्रह्म कृण्वन्तः परिवत्सरीणम् । अध्वर्यवो घर्मिणः सिष्विदाना आविर्भवन्ति गुह्या न के चित् ॥८॥

The Taittirīya-saṃhitā (5. 5. 7. 1–3), the Vājasaneyi-saṃhitā (27. 45; 30. 16), and the Taittirīya-brāhmaṇa (3. 4. 11; 3. 10. 4), mention all the five names, with some alteration.

यम्यै यमसूम् । अथर्वभ्योऽवतोकाम् । संवत्सराय पर्यारिणीम् । परिवत्सरायाविजाताम् । इदावत्सरायापस्कद्वरीम् । इद्वत्सरायातीत्वरीम् । वत्सराय विजर्जराम् । सर्वंत्सराय पलिक्नीम् । वनाय वनपम् । अन्यतोऽरण्याय दावपम् १

संवत्सरोऽसि परिवत्सरोऽसि । इदावत्सरोऽसीदुवत्सरोऽसि । इद्वत्सरोऽसि वत्सरोऽसि ।

The Taittirīyasaṃhitā calls them saṃvatsara, parivatsara, idāvatsara, iduvatsara, and vatsara; the Vājasaneyi-saṃhitā, saṃvatsara, parivatsara, idāvatsara, idvatsara, and vatsara, and the Taittirīya-brāhmaṇa saṃvatsara, parivatsara, idāvatsara, idvatsara, and vatsara respectively. The names Kṛta, Tretā, Dvāpara, and Kali which are used in later astronomy as the names of longer yugas are also used in the vedic literature to indicate different grades, each inferior to the preceding. But Dvāpara, as a unit of time, is found to be used in the Gopatha-brāhmaṇa (1. 1. 28).

1.1.28 असमीक्ष्यप्रवल्हितानि श्रूयन्ते द्वापरादाव् ऋषीणाम् एकदेशो दोषपतिर् इह चिन्ताम् आपेदे त्रिभिः सोमः पातव्यः समाप्तम् इव भवति...

The five-year yuga of the Vedāṅga-jyautiṣa contained 61 civil, 62 lunar, and 67 sidereal months. The year consisted of 366 civil days which were reckoned from sunrise to sunrise. After every thirty lunar months one intercalary month was inserted to bring about concordance between solar and lunar years. Similarly, to equate the number of tithis and civil days in the yuga of five solar years, the thirty full moon tithis which ended between sunrise and midday were omitted. There were six seasons of equal duration in every year, each new season beginning after every 61 days. Besides tithis and nakshatras, the yoga called Vyatīpāta was also in use.

The five-year yuga was taken to commence at the winter solstice occurring at the beginning of the first tithi of the light half of the month Māgha. Since the Sun and Moon were supposed to occupy the same position at the beginning of each subsequent yuga and all happenings in one yuga were supposed to be repeated in the subsequent yugas in the same way, the calendar constructed on the basis of the Vedāṅga-jyautiṣa was meant to serve for a long time.

The date of this work (Vedanga Jyotisha) is controversial, but the situation of the Sun and Moon at the beginning of the yuga of five years mentioned in this work, according to T. S. Kuppanna Sastry, existed about 1150 bc or about 1370 bc, according as the first point of nakṣatra Śraviṣṭhā stated there means the first point of the nakṣatra-segment Śraviṣṭhā or the nakṣatra-group Śraviṣṭhā (Sastry 1984, 3, p. 13).