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

Vedanga Jyotisha is the earliest work dealing exclusively with astronomy. Available in two recensions, viz. the Ṛgvedic recension (called Archa Jyotisha) and the Yajurvedic recension (called Yajusha Jyotisha), they give an account of days and day-divisions, months, years, nakshatras, new moons and full moons, solstices seasons occurring in the cycle of five solar years and lay down rules for determining the beginning of a season, the length of a day, etc.

This work defines jyotisha (astronomy) as the science of time-determination and deals with months, years, muhurtas, rising nakshatras, new moons, full moons, days, seasons, and solstices. It states rules to determine the nakṣatra occupied by the Sun or Moon, the time of the Sun’s or Moon’s entry into a nakṣatra, the duration of the Sun’s or Moon’s stay in a nakṣatra, the number of new moons or full moons that occurred since the beginning of the yuga, the position of the Sun or Moon at the end of a new moon or full moon day or tithi, and similar other things. It gives also the measure of the water-clock, which was used to measure time, and tells when an intercalary month was to be added or a tithi was to be omitted. In short, it gives all necessary information needed by the vedic priest to predict times for the vedic sacrifices and other religious observances.

Ancient Indian astronomy may be classified into two main categories:

(1) the vedic astronomy and

(2) the post vedic astronomy.

The vedic astronomy is the astronomy of the vedic period, i.e., the astronomy found in the vedic saṃhitās and brāhmaṇas and allied literature. The principal avocation of the people in the vedic times being the performance of the vedic sacrifices at the times prescribed by the śāstras, it was necessary to have accurate knowledge of the science of time so that the times prescribed for performing the various vedic sacrifices could be correctly predicted well in advance. Astronomy in those times, therefore, was essentially the science of time-determination. It centred round the Sun and Moon and its aim was to study the natural divisions of time caused by the motion of the Sun and Moon, such as days, months, seasons, and years, special attention being paid to the study of the times of occurrence of new moons, full moons, equinoxes, and solstices.

The culture of astronomy in vedic times was motivated by the need of fixing time for the various religious sacrifices which were performed at different times in different seasons.

The Kauṣītaki-brāhmaṇa records the occurrence of the winter solstice on the new moon day of Māgha.2 (2Kauṣītaki-brāhmaṇa, xi. 3.)

It is also stated there that the year ended with the full moon at the Pūrva-Phālgunī,3 (3Ibid, v. 1.) and that the spring commenced one day after the new moon of Caitra.4 (4Ibid, xix. 3.)

This shows that the beginning of the year under the amānta reckoning synchronised with the beginning of the seasons.

The Vedāṅga-jyautiṣa astronomy suffered from two main defects. Since there are actually 1826.2819 days in a yuga of five solar (sidereal) years and not 1830 as stated in the Vedāṅga-jyautiṣa, therefore if one yuga was taken to commence at a winter solstice the next one commenced about four days later than the next winter solstice and not at the next winter solstice. Similarly, since there are actually 1830.8961 days in a period of 62 lunar months and not 1830 as stated in the Vedāṅga-jyautiṣa, therefore there was a deficit of about one tithi in the yuga of five solar years. These discrepancies must have been rectified but we do not know when and how this was done.

There is one more work on jyotisha belonging to the later vedic period. It is known as Atharva-jyautiṣa. This work describes the muhurtas, tithis, karaṇas, nakshatras, and week days, and prescribes the deeds that should be performed in them. The names of the lords of the week days stated in this work viz. Āditya (Sun), Soma (Moon), Bhauma (the son of Earth), Bṛhaspati, Bhārgava (the son of Bhṛgu), and Śanaiścara (the slow-moving planet), are undoubtedly of Indian origin and must have been in use in India from very early times.6

Day in Vedic Astronomy

The day, called vāsara or ahan in the vedic literature, was reckoned from sunrise to sunrise. The variability of its length was known. The Ṛgveda (8. 48. 7) invoking Somarāja says: “O Somarāja, prolong thou our lives just as the Sun increases the length of the days.”

सोम राजन्प्र ण आयूंषि तारीरहानीव सूर्यो वासराणि ॥७॥

The duration of daylight, reckoned from sunrise to sunset, was divided into two parts called pūrvāhṇa (forenoon) and aparāhṇa (afternoon), three parts called, pūrvāhṇa, madhyāhna, and aparāhṇa, four parts called pūrvāhṇa madhyāhna, aparāhṇa and sāyāhna,4 and five parts called prātaḥ, saṅgava, madhyāhna, aparāhṇa, and sāyāhna (Śatapatha-brāhmaṇa, 2. 2. 3. 9).

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]

Of these names the first three occur in Ṛgveda, 5. 76. 3;

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

and sāyam (evening) occurs in Ṛgveda, 8. 2. 20;

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

10. 146. 3, 40.

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

Kauṭilya (Arthaśāstra, 1.19), Dakṣa, and Kātyāyana divided the day and night each into eight parts.

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

The days and nights were also divided into 15 parts each, and these parts were called muhūrta. The muhurtas falling during the days of the light and dark fortnights as well as those falling during the nights of the light and dark fortnights were given specific names (Taittirīya-brāhmaṇa, 3. 10. 1. 1–3). The fifteen days and nights of the light fortnight as well as the fifteen days and nights of the dark fortnight were also assigned special names (Taittirīya-brāhmaṇa, 3. 10. 1. 1–3; 3. 10. 10. 2). 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 (Aitareyabrāhmaṇa, 32. 10).

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। पूर्वां पौर्णमासीमुपवसेदनिर्ज्ञाय पुरस्तादमावास्यायां चन्द्रमसं यदुपैति यद्यजते तेन सोमं क्रीणन्ति तेनोत्तरामुपवसेदुत्तराणि ह वै सोमो यजते सोममनु दैवतमेतद्वै देवसोमं यच्चन्द्रमास्तस्मादुत्तरामुपवसेत्॥7.11॥ (32.10) (134)

The use of the term tithi in the sense in which it is used now occurs in the Vedāṅga-jyautiṣa (Ārca-jyautiṣa, 20, 21, 31; Yājuṣa-jyautiṣa, 20–23, 25, 26). It does not occur in the vedic saṃhitās and brāhmaṇas, but there are reasons to believe that tithis were used even in those times.

Week in Vedic Astronomy

Six days were taken to form a ṣaḍaha (six-day week); 5 ṣaḍahas, a month; and 12 months, a year. As to the names of the six days of a ṣaḍaha, there is no reference in the vedic literature. However, the six-day week was later replaced by the present seven day week (saptāha) which had attained popularity and was in general use at the time of composition of the Atharva-jyautiṣa.

Months, Seasons and Year

The year of vedic astronomy seems to have been a tropical one. The months were lunar and measured from full moon to full moon and also from new moon to new moon. 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 year, generally called by the terms samā, vatsara, and hāyana in the vedic literature, was seasonal or tropical and was measured from one winter solstice to the next, but in due course it was used in the sense of a sidereal year. In the early stages, therefore, the names of the seasons were used as synonyms of a year.

The Kauṣītaki-brāhmaṇa (19. 3) gives an interesting account of how the year-long sacrifice was commenced at one winter solstice and continued until the next winter solstice: “On the new moon of Māgha he (the Sun) rests, being about to turn northwards. They (the priests) also rest, being about to sacrifice with the introductory Atirātra. Thus, for the first time, they (the priests) obtain him (the Sun). On him they lay hold with the Caturviṃśa rite; that is why the laying hold rite has that name. He (the Sun) goes north for six months; him they (the priests) follow with six day rites in continuation. Having gone north for six months, he (the Sun) stands still, being about to turn southwards. They (the priests) also rest, being about to sacrifice with the Viṣuvanta (summer solstice) day. Thus, for the second time, they obtain him (the Sun). He (the Sun) goes south for six months; they (the priests) follow him with six day rites in reverse order. Having gone south for six months, he (the Sun) stands still, being about to turn north; and they (the priests) also rest, being about to sacrifice with the Mahāvrata day. Thus, they (the priests) obtain him (the Sun) for the third time”.

The Taittirīya-brāhmaṇa (3. 9. 22) calls the year “the day of the gods”, the gods being supposed to reside at the north pole.

अमुं तैः  । अनवरुद्धो वा एतस्य संवत्सर इत्याहुः ।  य इतेतश्चातुर्मास्यानि संवत्सरं प्रयुङ्क्त इति  ।  एतावान्वै संवत्सरः  । यच्चातुर्मास्यानि  ।  यदेते चातुर्मास्याः पशव आलभ्यन्ते  । प्रत्यक्षमेव तैः संवत्सरं यजमानोऽवरुन्धे ।  वि वा एष प्रजया पशुभिरृध्यते  ।  यः संवत्सरं प्रयुङ्क्ते  । संवत्सरः सुवर्गो लोकः  २

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)

The lunar or synodic month was measured from full moon to full moon or from new moon to new moon (Taittirīya-saṃhitā, 7. 5. 6. 1) as is the case even now.

The names Caitra etc. based on the nakshatras in which the Moon becomes full do not occur in the early saṃhitās and brāhmaṇas but such terms as phalgunī-pūrnamāsī, citrā-pūrnamāsī, etc. are found to occur in the Taittirīyasaṃhitā (7. 4. 8).

They occur in the Saṅkhāyana and Tāṇḍya-brāhmaṇas, the Vedāṅga-jyautiṣa, and the Kalpa-sūtras.5

5Māgha is mentioned in Sāṅkhāyana-brāhmaṇa (= Kauṣītaki-brāhmaṇa) 19. 3;

Phālguna in Tāṇḍya-brāhmaṇa, 5. 9. 7–12;

and Srāvana, Māgha and Pauṣa in Ārca-jyautiṣa, 5, 6, 32, and 34 and Yājuṣa-jyautiṣa 5, 6, and 7;

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. 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॥

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).