ज्योतिषे विश्वासटिप्पन्यः

Akṣara the Basic Unit of Time Measure in Ancient India
R. N. Iyengara∗, H. S. Sudarshan, Anand Viswanathan
Distinguished Professor, and Research Associates,
Centre for Ancient History and Culture, Jain University, Bangalore.
(Received 15 August 2020)

Abstract

In this paper after a brief review of ancient Indian time units, the ingenious method of Indian astronomers for calibrating the small time unit of vighaṭikā (24 seconds) phonetically by the recitation of a Sanskrit verse in the līlākhelā meter with sixty gurvakṣaras, is experimentally verified by sixty independent sample recitations. This is followed by exploring the concept of congruence of akṣara count and time periods such as the month and the year in Vedic texts. This leads to the symbolic equivalence of the bṛhatī meter of 36 syllables to the Year and several other numerical synchronies between phenomenal time and akṣara. The 1000 bṛhatī verses of the prātaranuvāka nocturnal performance in the atirātra ritual is the traceable most ancient origin and inspiration for gauging and estimating lapse of time by recognizing audible syllable as a time measure. To verify this, apart from text based theoretical estimates, real time information from a famous śrauta expert on his prātaranuvāka performance is presented. It is further demonstrated empirically that the rate of 3600 gurvakṣara per ghaṭikā of siddhānta astronomy is closely correlated with the speed of present day traditional chanting of the Ṛgveda, the fidelity of which has remained stable over millennia.

Key words: Bṛhatī-chandas, Gurvakṣara, Līlākhelā, Oral calibration, Prātaranuvāka, Time unit, Vedic recitation, Vighaṭikā, Water-clock.

Introduction

A large number of time measures with a variety of nomenclature and conversion values are mentioned in ancient Indian texts. In a recent publication Hayashi (2017) has presented a detailed review of time units in ancient and medieval India. He has discussed almost all important texts numbering sixty. There are some extremely small measures such as aṇu and truṭi as well as some very large time measures such as yuga, and kalpa. It would be clear that for practical purposes muhūrta, nāḍikā (ghaṭikā), ahorātra, pakṣa, tithi, māsa, ayana, ṛtu, varṣa with their simple multiples should have been in vogue. The smallest measures samaya, truṭī, paramāṇu must have been proposed by philosophers and mathematicians to imaginatively indicate that Time is continuous with no gaps in between. Texts describing instruments for measurement of time within an ahorātra provide evidences to two types of devices; the gnomon (śaṅku) and the water clock (jalayantra). A detailed description of such devices found in Sanskrit texts with relevant historical background and available photographs has been presented by Sarma (1994, 2001) (Figure 1). Several of his investigations on the water clock and time determination in medieval India with in sightful discussions are available in his monograph The Archaic and the Exotic (2008). Further recently Sarma (2018) has presented a detailed exposition on how the Jaina text Jyotiṣkaraṇḍakam by Pādalipta Sūri (c 100 CE) describes time measurement using the water clock and the steelyard.

Jalayantra

Two major types of water clocks, with some minor vari ants, were popular in ancient India.

nālikāyantra

The nālikāyantra, perhaps the more ancient device, consisted of a tall jar or a pot with an outflow orifice at the bottom. The device when filled up with water at sunrise (prātaḥ) would get emptied at the next sunrise representing 60 nāḍikā. Assuming that on the equinoctial day, sun at midday (mad hyāhna) and sunset (sāyaṁ) were observed, two more time markings could have been done on the device. Measuring finer intervals in such a device would be complex since the relation between time elapsed from sunrise to the water level is not necessarily linear. For example, if a cylindrical vessel of uniform cross section empties in one ahorātra of 60 nāḍikā (30 muhūrta), the time elapsed from sunrise to the point when the water is at mid-height will not be 15 but will be (15/√2) or between 10 and 11 muhūrta. However, by trial and error one may be able to mark two more graduations when sun is halfway between horizon and zenith and when sun is between midday and sunset.

ghaṭikāyantra

The other device, namely the ghaṭikāyantra is the sinking-bowl type of water clock. This appears to have been popular among astronomers, administrators and priests who had to specify time periods within a day in advance to conduct the rituals during prescribed intervals. In the ghaṭikāyantra, the bowl would sink 60 times in one ahorātra or once in a ghaṭikā same as nāḍikā that is half muhūrta. The shape and dimensions of this bowl are men tioned in a few texts. This must have been arrived at by experimentation and continuous refinements. Based on available textual information, Kulkarni (1986) verified an alytically, applying the laws of Mechanics, that the spherical pot mentioned in the Arthaśāstra when filled fully, would take nearly 24 minutes or one ghaṭī to discharge one pala of water. ‘सुवर्ण-माषकाश् चत्वारश् चतुरङ्गुलायामाः कुम्भच्छिद्रम् आढकम्(=परिमाणम्) अम्भसो वा नालिका ॥

Whichever device was in use, there must have been an independent way to calibrate the unit of muhūrta or of ghaṭī or some part thereof. Only after such verification the water clock could get marked for measuring and announcing time routinely for administrative purposes. This was well known to ancient Indian scientific thinkers who proposed several smaller natural markers of time; akṣara (syllable), nimeṣa (eye wink), prāṇa or asu (breath or pulse rate). It is easy to note that these parameters are dependent on the subject selected for observation and hence vary from person to person. Whichever fundamen tal unit one may prefer, the accuracy of dividing ahorātra into 30 or 60 equal parts would depend on the accuracy of equating a convenient longer time unit on the device to the equivalent number of akṣara, or nimeṣa or prāṇa. In the medieval texts several equalities for time units are available, sometimes with same name but with different equations. Fortunately, all authors belonging to widely differing time periods and regions, are in agreement that ahorātra should be taken as 30 muhūrta as in the Vedas, and reckon it as 60 nāḍi(kā) or ghaṭi(kā). This must have helped standardization of time measure with akṣara as the fundamental unit all over India. Before we consider akṣara in detail, a brief reality check on the other units would be useful.

Figure 1

(a) Copper bowl water clock sinking in half ghaṭi from Uva Province, Sri Lanka in the Pitt Rivers Museum of Ethnology, Oxford. (photo by S. R. Sarma);
(b) Coconut shell water clock sinking in one ghaṭi. Government Museum, Chennai. (photo by S. Ramaratnam)

Source: Sarma S. R. A Descriptive Catalogue of Indian Astronomical Instruments, 2019, pp. 3821–26. Reproduced with permission.

Nimeṣa, Asu, Prāṇa

Nimeṣa refers to the time taken for one eye-wink or blink. This word appears in the Ṛgveda and in several other Vedic texts. Notably the Maitrāyaṇīya-āraṇyaka (c 1800 BCE) which declares sun as the generatrix of Time (sūryo yoniḥ kālasya), mentions nimeṣa as a time unit, but does not quantify the term. अथान्यत्राप्य् उक्तम् अन्नं वा अस्य सर्वस्य योनिः, कालश् चान्नस्य, सूर्यो योनिः कालस्य । तस्यैतद् रूपं यन् निमेषादिकालात् सम्भृतं द्वादशात्मकं वत्सरम् । एतस्याग्नेयम् अर्धम्, अर्धं वारुणम् । MAU (6.14).

Blinking of eyes is a normal activity for all humans, but can be voluntary or involuntary. The rate of blink is sure to vary since continuous voluntary blinking fatigues the muscles. The natural clock with reference to which the experimental value had to be obtained was the position of the sun in the sky divided into two, three or four observably equalspatial intervals. The Viṣṇupurāṇa and the Samarāṅgaṇa-sūtradhāra of King Bhoja (1055 CE) report 1 muhūrta = 13500 nimeṣa. The famous astronomical text Siddhānta-śiromaṇi of 12th century also reports the same value. Quite interestingly all the above four texts state two smaller units of time kāṣthā and kalā before muhūrta in the same way as 1 kāṣṭhā = 15 nimeṣa; 1 kalā = 30 kāṣṭha and 1 muhūrta = 30 kalā. Several other texts also refer to the nimeṣa, but this parameter must have been difficult to count in practice, particularly for fixing parts of a muhūrta. This limitation seems to have been circumvented by accepting nimeṣa to be equivalent to laghvakṣara time.

The other basic unit asu is the breath rate and prāṇa the pulse rate. But the two words are often used with varying meanings in different contexts. The Śatapatha-brāhmaṇa (ŚB 12.3) divides muhūrta into four smaller units namely, kṣipra, etarhi, idānīm and prāṇa each being 15 times the next one in the same order.3

‘दश च वै सहस्राण्य् अष्टौ च शतानि संवत्सरस्य मुहर्ताः। यावन्तो महर्तास्तावन्ति पञ्चदशकृत्वः क्षिप्राणि। यावन्ति क्षिप्राणि तावन्ति पञ्चचदशकृत्व एतहीणि। यावन्त्येतहीणि तावन्ति पञ्चदशकृत्व इदानीनि। यावन्तीदानीनि तावन्तः पञ्चदशकृत्वः प्राणाः। यावन्तः प्राणास्तावन्तोऽक्तनाः। यावन्तोऽक्तनास्तावन्तो निमेषाः। यावन्तो निमेषास्तावन्तो लोमगर्ताः। यावन्तो लोमगर्तास्तावन्ति स्वेदायनानि। यावन्ति स्वेदायनानि तावन्त एते स्तोका वर्षन्ति॥ SB (12.3.2.5).

The pulse rate as per modern measurements is about 70 per minute. This gives approximately 3360 heart beats per muhūrta. This value is quite close to 3375 idānīm for one muhūrta of ŚB. It is to be noted that the same word idānī of the Taittirīya Brāhmaṇa (TB) and of the ŚB carry different values. Also, the prāṇa unit of ŚB in the present context is not the heart beat. On the other hand the rate of breathing of normal humans is around 15 per minute. This leads to 720 asu (breaths) per muhūrta leading to 21600 breaths per ahorā tra, which count is reported in several texts. Some texts such as the Siddhānta-śekhara (10th cent.) denote asu as prāṇa and report 21600 prāṇa for one ahorātra, as in the Sūrya-siddhānta.

Nimeṣa, asu and/or prāṇa were not imaginary units, but were based on experiments. However, they were not robust for arriving at a scale that can be impersonally applied for measuring ghaṭī or muhūrta repetitively like a short rope or stick (śulba/daṇḍa) that was used repetitively in length measurements.

akShara

It can be easily gathered from the review of Hayashi (2017) or otherwise, that muhūrta was the older unit inherited from the Vedas but half-muhūrta or the nāḍikā/ghaṭikā, was perhaps more convenient for day to day work. A further interesting shift is in the recognition of akṣara as more practical than nimeṣa/prāṇa, although the two units are not independent of each other. The most ancient traceable text to mention akṣara or syllable as a unit of time is Lagadha’s Vedāṅga-jyotiṣa (LVJ). Both the Ṛgvedic and the Yajurvedic recensions (Sastry and Sarma 1985) mention the length of ahorātra as 30 muhūrta equivalent to 60 nāḍikā, as in the works of Āryabhaṭa, Varāhamihira and others. However, the relation between the akṣara and the nāḍikā of LVJ is different from the equation stated by later astronomers. In the LVJ the two units are related as 1 nāḍika= 6231 akṣara, which is different from 1 nāḍikā = 3600 gurvakṣara of the siddhānta texts. Even though Sastry and Sarma (1985) mention that the akṣara of LVJ is equal to one gurvakṣara of two mātrā time duration there is no statement in the original text to that effect. Here it is to be noted that the word akṣara normally translated as ‘syllable’ carries different shades of meaning in technical subjects. In the present context it should be interpreted as the time taken to produce audible sound of one syllable of a particular type.

Unless specified clearly, akṣara can be one of the four types; hrasva (short), laghu (light), guru (heavy), dīrgha (long). The time taken by a hrasva and a laghu and similarly by a guru and a dīrgha syllable need not be exactly equal. In Sanskrit prosody it is by definition the long and heavy syllables take twice the time relative to the short and light ones that are as signed one mātrā measure. The word mātrā (measure) is inherited from the antecedent oral tradition wherein the Prātiśākhya texts describe and fix the Vedas in minute details of chandas, akṣara, svara, and mātrā. In classical literature the mātrā is by definition not divisible, unlike in the Vedic tradition where mātrā is divided into at least four fractions. Without further digression, it suffices to point out that the akṣara of LVJ might be referring to a particular definition of Vedic syllable as a time unit which need not closely match with the syllabic time of classical Sanskrit prosody (Tripathi 2008).

There are also references to laghvakṣara (light or short syllable) as in the Purāṇa,4 which equate nimeṣa and laghvakṣara leading to 13500 short syllables per muhūrta.

निमेषकालतुल्यं हि विद्याल् लघ्वक्षरं च यत् ॥
काष्ठा निमेषा दश पञ्च चैव
त्रिंशच् च काष्ठा गणयेत् कलां तु।
त्रिंशत् कलाश् चापि भवेन् मुहूर्तस्
तै त्रिंशता रात्र्य्-अहनी समे ते॥
Brahmānda Purana (I. 29.5-6).

Suśruta Saṁhitā also equates nimeṣa and laghvakṣara, but present day texts lead to 9045 syllables per muhūrta.5

तत्र लघ्वक्षरोच्चारणमात्रो ऽक्षिनिमेषः, पञ्चदशाक्षिनिमेषाः काष्ठा, त्रिंशत्काष्ठाः कला, विंशतिकलो मुहूर्तः कलादशभागश्च, त्रिंशन्मुहूर्तमहोरात्रं, पञ्चदशाहोरात्राणि पक्षः। स च द्विविधः शुकः कृष्णश्च। तौ मासः। Susruta Samhita (6.5).

This seems to be based on the misreading of the word triṁśat as viṁśat in later day manuscripts which has formed the basis for present day printed versions. If we take the original reading as triṁśat, (30 kalā per muhūrta) we get the same value of 13500 laghvakṣara per muhūrta as in other texts. There is also mention of vikṛtākṣara (dis torted syllable) in the Parāśara Tantra (Iyengar 2013) as quoted by Bhaṭṭotpala that equates 16000 vikṛtākṣara to one muhūrta.

Gurvakṣara Scale

Definition of time in terms of different akṣara type points to the wide spread practice of estimating elapsed time using oral recitation of some texts. This should not be sur prising since the learning of the Vedas has remained an oral tradition to this day. But the time covered naturally depends on the internal structure of the syllabic compositions and the speed of oral reproduction. Indian astronomers in their search for accuracy in the use of the water clock must have experimented with different texts to finally arrive at the attractive result that 60 gurvakṣara sound-string would need one vināḍī or vighaṭī. Sixty of such vināḍī make up one nāḍikā or ghaṭikā equal to the time needed for the bowl type water clock to sink once. While the Soma-, Brahma-siddhānta (Dvivedi 1912) and the Vṛddhavasiṣṭha-siddhānta (Dvivedi 1917) know the above relation of 60 gurvakṣara being equal to one vināḍī, it is the Pañcasiddhāntikā (PS) that standardizes this for calibration of the water clock. Varāhamihira (c 530 CE) the author of this text gives in the 14th Chapter, a verse of 60 gurvakṣara that can be used as an objective audible scale for measuring longer time by simply repeating it the required number of times. The relevant text and the translation by Sastry and Sarma (1993) are as follows;

द्युनिशिविनिःसृत-तोयाद्
इष्ट-च्छिद्रेण षष्टिभागो यः ।
सा नाडी (स्वमथो) वा
श्वासाशीतिः शतं पुंसः ॥ ३१॥

कुम्भार्धाकारं ताम्रं पात्रं कार्यं मूले छिद्रं
स्वच्छे तोये कुण्डे न्यस्तं - तस्मिन् पूर्णे नाडी स्यात् ।
मूलाल्पत्वाद् वेधो वा षष्टिर् योज्या चाह्ना रात्र्या वर्णाः
षष्टिर् वक्राः श्लोको यत् तत् षष्ट्या वा सा स्यात् ॥ ३२॥ (VM)

One-sixtieth of the time taken by water to flow out through a desired hole during a nychthe meron is defined as the duration of a nāḍī. Or it is the time of 180 breaths of a man. ||31||

Construct a copper vessel resembling one-half of a spherical pot and pierce a hole at its bot tom. Put it in pure water in a basin. The time in which the vessel is filled up is the duration of a nāḍī. The hole at the bottom of the vessel should be so small that on account of its small size, the vessel may sink into water exactly sixty times during nychthemeron. Or, it is the time in which one may recite 60 times a verse composed of 60 long syllables (as verse 32 itself is). ||32||

The above verse 32 (denoted as VM) has fifteen gurvakṣaras in each foot in the meter līlākhelā (also called kāmakrīḍā or sāraṅgikā) belonging to the class of atiśakvarī chandas. Varāhamihira in PS reviews five older astronomical texts (Pauliśa, Romaka, Vasiṣṭha, Sūrya and Paitāmaha siddhānta) but in Chapter 14 there is no attribution to other authors for the above verse on the water clock.

Before we verify the accuracy of VM, it is noted that there is another verse in the same meter in the commentary by Bhāskara-I (7th cent.) on the kālakriyāpāda of Āryabhaṭa (5th cent.). This verse with its correct ver sion (B-I) as in the manuscript ghaṭīyantra-ghaṭanā-vidhi along with two more in the same meter has been un earthed by Sarma (2001).6 The verse given by Bhāskara for calibrating the vināḍī is:

मा कान्ते पक्षस्यान्ते
पर्याकाशे देशे स्वाप्सीः
कान्तं वक्त्रं वृत्तं पूर्णं
चन्द्रं मत्वा रात्रौ चेत् ।
क्षुत्-क्षामः प्राटंश् चेतश्
चेतो राहुः क्रूरः प्राद्यात्
तस्माद् ध्वान्ते हर्म्यस्यान्ते
शय्यैकान्ते कर्तव्या ॥(B-I)

6Sarma, S. R. (2018, p. 165). Two more verses in the same meter from the above manuscript follow:

मार्ताण्डस् तारानाथः क्षोणीसूनुः सूनुश् चेन्दोः
वागीशो दैत्याचार्यः छायापुत्रो राहुः केतुः।
नक्षत्रैर् अश्विन्याद्यैस् तारा-युक्तैश् चाभिः सर्वे
कुर्यासुः कल्याणं वो नित्यारोग्यं लक्ष्मीमायुः।।12।।

लोकक्षेमायासीन् मत्स्यः कूर्मः क्रोडः पुंसिंहो
यो ह्रस्वाकारो रामो रामः कृष्णो बुद्धः कल्की।
एवं नानारूपं नानाकारं नानानामानं
योगि-ध्येयं देवं देवानां वन्देऽहं गोविन्दम्।।13।।

In the previous section different akṣara types and their measures were mentioned. In the absence of a clear definition of the syllabic time it would be reasonable to say that about 13500–16000 short syllables per muhūrta was the prevalent understanding before the astronomers introduced their refinement. The above approximates to 7375 long/heavy syllables per muhūrta as per the conventional understanding that laghu and guru are for one and two mātrā duration respectively. This evidence of measuring muhūrta in terms of akṣara counting in the early purāṇas and other texts originating before the common era natu rally points to Vedic oral tradition as the progenitor of the concept of akṣara-kāla or syllabic-time. This point will be further discussed and demonstrated to be so in the present study.

Astronomers before and after Āryabhaṭa being aware of the prevalent use of akṣara count as a time measuring artifice, standardized one vināḍī (vighaṭi) to the audible scale of 60 gurvakṣaras embedded by verses in a particular meter known aslīlākhelā, with 15 long/heavy syllables per quarter. The speed of recitation is said to be neither too fast nor too slow but in medium pace as pointed out by Bhāskara.7

This must have existed as a culturally in herited trait followed in the medieval schools aptly called ghaṭikāsthāna, where a ghaṭīyantra the sinking type wa ter clock was also operated probably by the students. Ex istence of such a school with a time measuring device is well attested in the inscription dated 1058 CE at Nagai, in Gulbarga District. This record mentions about the school, the number of teachers and students and the donation made for the upkeep of the institution including payment for the ghaṭikā-praharī, whose work was to announce the passage of each ghaṭikā by beating a gong.8

An Experiment

An interesting question arising out of the above prescrip tion is, how accurate are the verses for representing one vighaṭikā that is equal to 24 seconds in current parlance? To understand this issue we conducted an experiment with the help of 30 volunteers drawn from in and around Bangalore. The group included persons knowledgeable in Sanskrit as well as some who could not understand the language, but had the tradition of reciting Sanskrit texts in their families for religious and spiritual practices. The members were requested to recite audibly the verse (B-I) in private at medium pace, as is normal for them, and sub mit the audio tracks. After a lapse of several months the verse (VM) from the Pañcasiddhāntikā was tested in simi lar fashion by another group that included a few members 7गुवर्क्षरेषु मڌमवृࣉ،ग्रहणम्| “ गुवर्क्षरा࣊ण षࠋࣇः” इؖत्र मڌमायां वृ،ौ षࠋࣇः गुवर्क्षरा࣊ण ࣆवनाࣅडकाकाल इࣆत वнߢम् । अڬथा ࣅह ࣆतसृषु अࣅप वृࣉ،षु अࣆवशेषेण ग्रहणं प्राܔोࣆत । त٦था – द्रतायां वृ،ौ षࠋࣇः गुवर्क्षरा޷רेन कालेन ु प֫ڢ ,ेࣆवलݼ࣎तायां महता कालेन इࣆत, मڌमायां पुननर् अ޷ेन, न महता कालेन । त،ࣅहर् मڌमवृࣉ،ग्रहणं कतर्ߢम् । कथमनुԖमानमवगݿते, लोकप्र࣊स٠ेः। त٦था – लोके अࣄनࣅदर्ࠋेषु कायϸषु मڌमप्राܒࣆः॥ Commentary of Bhāskara-I on the Āryabhaṭīya. 8The Inscriptions of Nagai, published in Hyderabad Archaeological Series, No. 8. Calcutta, 1928, p.16.

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from the former group. The time taken for recitation was extracted from the sample audio tracks. The results ob tained for both the verses are shown below in seconds. Time samples for B-I: 23.28, 23.13, 22.23, 23.76, 22.4, 23.68, 25.2, 23.22, 24.15, 26.65, 23.42, 22.1, 24.72, 25.59, 24.47, 23.94, 25.91, 22.62, 25.04, 25.74, 23.06, 24.02, 23.31, 24.23, 23.19, 24.13, 24.15, 23.29, 24.31, 23.3. Time samples for VM: 22.61, 21.45, 24.62, 23.81, 23.16, 25.51, 22.52, 21.98, 21.35, 23.55, 25.83, 24.86, 23.05, 23.12, 23.84, 23.48, 24.86, 23.07, 23.57, 25.04, 21.95, 25.18, 23.17, 23.5, 23.74, 24.24, 23.81, 24.29, 22.68, 23.76. The average time in seconds taken for B-I is 23.94 with standard deviation of 1.1 seconds. The average time for the VM verse is 23.59 seconds, the standard deviation be ing 1.12 seconds. The sample variation in both the cases is about 5%. Verse B-I is easier to recite with lesser number of conjunct syllables and hence seems to be more accurate than VM. 7 Vedic Prelude Vedic texts characterize kāla (Time) in a variety of ways. While some of these are abstract and philosophical, oth ers are about time as related to the sun, the moon and the stars. The latter is the mūrta-kāla (concrete or phenomenal time) such as year, month, day, night etc. Maitrāyaṇiya Āraṇyaka Upaniṣad (MAU) extols Time as Brahman, with and without form.9 Time with form, that is nameable time divisions, starts with Sun. The ahorātra (day-night) based on counting sunrises is the most natural time unit, so much so the MAU declares sun to be the ori gin/generator of time.10 This and such other evidences in dicate that with the help of the sun and the moon, longer periods such as pakṣa, māsa,ṛtu, ayana,saṃvatsara were conceptualized and used. It is no exaggeration to say that Vedic sacrifices, rites and rituals couched in legends of me ters as deities show a deep sense of preoccupation with time measures, short and long, synchronized with num bers and syllables. 9٥े वाव ब्रࡱणो रूपे काल߱ाकाल߱ ॥ MAU (6.15). 10See footnote 2. 8 Prajāpati’s Choice of 15 and 30 The concept of māsa, the time interval from full moon to full moon and from amāvāsyā to amāvāsyā is central to Vedic culture. It is easy to note that sunrise to sunrise is one ahorātra and hence this can be counted in integral numbers. But the māsa measure of sunset or sunrise as related with moon will not be a round number but will be between 29 and 30. The naming of both the pūrṇamāsa and the amāvāsyā as the Fifteenth that is pañcadaśī in the Taittirīya Brāhmaṇa (TB 1.5.10) is due to the idea of pakṣa synchronizing with the number 15. The Śatapatha Brāhmaṇa provides the heuristics for selecting the num bers 15 and 30 through a legend connected with Prajāpati one of his forms being the Year. After creation of the cos mos the joints of Prajāpati became slack at the meeting of day and night and at full moon and at amāvāsya. His joints at the syzygy were fixed by conducting the darśa pūrṇamāsa rites.11 The text further works out by recur sion how the 360 days and 360 nights, that make up the year of 720 (ahas + rātri), can be factored into integers starting from 2 and increasing by unity at every step up to 24. The number 720 is divided by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20 to get 360, 240, 180, 144, 120, 90, 80, 72, 60, 48, 45, 40, 36. The text says, for each of these possibilities, Prajāpati could not envelop (sa naiva vyāpnot).12 When divided by 7, 11, 13, 14, 17, 19, 21, 22, and 23 Prajāpati could not manifest himself (na vyabhavat).13 Then, He sat there in that 15 boxed figure. Since he settled in the Fif teen, there are 15 forms (for moon) in the waxing and 15 forms in the waning fortnight.14 Twenty-four is the num ber of ardhamāsa (half-months) in a year.15 In similar 11प्रजापतेहर् वै प्रजाः ससृजानࡆ पवЂ࣊ण ࣆवसस्रंसुः। स वै संव؛र एव प्रजापࣆतः तࡆैताࣄन पवЂרहोरात्रयोः सڥी पौणर्मासी चामावाࡆा चतुर्मुखाࣄन ॥ स ࣆवस्र࠼ैः पवर्ࣉभः न शशाक संहातुम्। तमेतैहर्ࣆवयर्ज्ञैदϸवा अࣉभषԷࣇڦҔहोत्रेणैवाहोरात्रयोः सڥी तؑवЂࣉभषԷं؛࠼मदधुः पौणर्मासेन चैवामावाࡆेन च । पौणर्मासीं चामावाࡆां च तؑवЂࣉभषԷं؛࠼मदधुः। चातुमЂࡆैरेवतुर्मुखाࣄन तؑवЂࣉभषԷं؛࠼मदधुः॥ ŚB (1.6.3). 12स ٥ेधाؕानं ߢौहत् षࠋࣇ ߱त्री࣊ण च शताڬڬतरࡆेࠋका अभवڦेवमڬतरࡆ स न ߢाܔोत्। त्रीनाؕनोऽकु रुत। ࣆतस्र࠼࣒स्रोऽशीतय एकै कࡆेࠋका अभवۈ नैव ߢाܔोत्। [..] ࣆवंशࣆतमाؕनोऽकु रुत षࣇं֖शࣅदࠋकाۈ नैव ߢाܔोत् ॥ ŚB (10.4.2; 2–14). 13न सܒधा ߢभवत्। [..] नैकࣆवंशࣆतधा ߢभवڦ ٥ाࣆवंशࣆतधा न त्रयोࣆवंशࣆतधा॥ ŚB (10.4.2; 8-16). 14चतुࣆवϴशࣆतमाؕनोऽकु रुत ࣆत्रंशࣅदࠋकाۈोऽत्राࣆतࠌत पՑदशे ߢूहे त٦ؑՑदशे ߢूहेऽࣆतࠌत। तࡅात् पՑदशापूयर्माणࡆ रूपा࣊ण पՑदशापक्षीयमाणࡆ ॥ ŚB (10.4.2; 17). 15अथ यԎतुࣆवϴशࣆतमाؕनोऽकु रुत, तࡅाԎतुࣆवϴशؖधर्मासः संव؛रः । ŚB

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ity with the śukla- and the kṛṣṇa-pakṣa (bright- and dark fortnight) being presided over by the number 15, the day and the night in an ahorātra are equated with 15 muhūrta of time. This choice of taking ahorātra as equal to 30 muhūrta must be more ancient than the Brāhmaṇa texts. The word muhūrta occurs twice (RV III.33.5 & III.53.8) in the Ṛgveda, but from the context of the hymns it is not clear whether the word stands for one-thirtieth of ahorā tra or is used in the sense of vague time. However, there are three instances where the number 30 is invoked re ferring to Uṣas (twilight) or Sun specifically illuminating and crossing 30 divisions every day.16 In the first instance (RV I.123.8) it is 30 yojana which is generally taken as a distance measure. In the other two cases (RV VI. 59.6 & X. 189.3) the larger context of the sūkta (hymn) is about time as aharahaḥ (day by day) and hence Sāyaṇācārya’s interpretation of 30 dhāma and 30 pada as equivalent to 30 muhūrta of time should be acceptable. This conven tion of taking parts of time and space to be numerically congruent is preserved in the Parāśaratantra where it is asserted kāla-kṣetrayoḥ sāmyam.17 This principle is re flected in (RV V. 76.3) where the day is divided into five parts. Starting from sunrise these intervals are named prā taḥ, saṅgava, madhyāhna, aparāhna and sāyaṁ. Each of these intervals dependent on the position (kṣetra) of sun in the sky are notionally three muhūrta long, as attested in the Viṣṇu Purāṇa.18 The Taittirīya Brāhmaṇa (TB) fine tunes this time division to introduce individual names for the 15 day and 15 night muhūrta for the dark and bright fortnights19 separately and also mentions that each such muhūrta (48 minutes) is made of 15 further parts called (10.4.2; 18). 16अनव٦ाःࣆत्रंशतं योजनाڬेकै का क्रतुं पिर यڢ࣎ स٦ः। RV (I.123.8 b). ࣅहؘी ࣊शरो ࣊जࡴया वावदԎरح࣎ंशؑदा ڬक्रमीत् । RV (VI. 59.6 b). ࣆत्रंश٠ाम ࣆवराजࣆत वाсतग्ӂाय धीयते। प्रࣆत व࠼ोरह ٦ࣉभः॥ ु RV (X.189.3). 17Quoted by Bhaṭṭotpala in his commentary on the Bṛhatsamhitā. Ref: Parāśaratantra (Iyengar 2013). 18रेखाप्रभृؖथाࣅदؖे ࣆत्रमुहूतर्गते रवौ। प्रातः ࡅृत࠼तः कालो भाग߱ाࡰः स पՑमः ॥ तࡅात् प्रात࠼ना׽ालात् ࣆत्रमुहूतर्࠼ ुसӂवः। मڌाࡓ࣌ࡰमुहूतर्࠼ ुतࡅा׽ाला،ु सӂवात् ॥ तࡅाګाڌाࡰࣅका׽ालात् अपराࡰ इࣆत ࡅृतः। त्रय एव मुहूतЂ࠼ ुकालभागः ࡅृतो बुधैः ॥ आपराࡰ ेߢतीते तु कालः सायाࡰ एव च। दशपՑ मुहूतϴ वै मुहूतЂࡓय एव च ॥ VP (2.8.61-64). 19ࣉचत्रः के तुः प्रभानाभाڢ ्सݽान्। [..]। आभूवЂभूः प्रभूः शݽूभुर्वः। TB (3.10.1.1-3). muhūrta-of-muhūrta20 also called prati-muhūrta. If such a small division as the pratimuhūrta (3 minutes 12 sec onds) were to be important, what artifice might have been used to estimate the muhūrta measure in Vedic times? While there is no direct answer for this question in the sacred texts, it can be verified that akṣara count had signif icant role in stating, estimating and keeping vigil through specific time intervals. 9 Akṣara Congruence The two prominent meanings of the word akṣara are i) imperishable, ii) syllable. Without going further into etymology, nuances and definitions of the word, we note that there is a hoary tradition of preserving the counts of the chapters, subdivisions, hymns, verses, words and the syllables of Vedic texts (Vaidya 1930). In some of the sacrificial rites the sacred formulas ritualistically state the number of syllables a particular hymn or a set of hymns contain. These statements are like recognizing equiva lence between the number of akṣara and some important character and distinctive property of the deity that is in voked through the laudatory hymn. A typical example is about statements that enunciate connections between samvatsara as Prajāpati and the number of akṣara in a hymn or the number of stanzas in a ritual. Here we cite only a few such cases to illustrate the germination and growth of the idea of linking phenomenal time mea sure with syllable counts. The Taittirīya Saṃhitā refers to 15 Sāmidhenī verses that together make up 360 sylla bles to obtain the year of 360 days.21 Aitareya Brāhmaṇa (3.41) synchronizes 360 hymns with the length of the year counted as 360 ahorātra in the ukthya sacrifice:22 This ukthyā sacrifice has fifteen stotras and fif teen śastras. These make, if taken together, one 20इदानीं तदानीमेतࣅहर् ࣊क्षप्रम࣊जरम् । आशुࣄनर्मेषः फणो द्रवࣆڦतद्रवन् । ؘरंࡔरमाण आशुराशीयाՓवः। TB (3.10.1.4). इदानीं तदानीࣆमࣆत | एष एव तत् | एषࡲेव ते मुहूतЂनां मुहूतЂः || TB (3.10.9.9). 21पՑदश साࣆमधेनीरڮाह पՑदश वा अधर्मासࡆ रात्रयः। अधर्मासशः संव؛र आܙते तासां त्री࣊ण च शताࣄन षࠋࣇ߱ाक्षरा࣊ण तावतीः संव؛रࡆ रात्रयः। अक्षरश एव संव؛रमाܔोࣆत। TS (2.5.8). 22This is the summary as per the Mysore Palace Edition of the Ṛgveda, MPRV, Vol. 31 pp. 858–62.

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month of thirty days. By performing this sac rifice they commence the year as divided into months. This ukthyā sacrifice has 360 stotriya verses as many as the year has days. By per forming this sacrifice, they commence the year as divided into days. A special character stated for the year is the number 36 made of 12 full moons, 12 aṣṭakā (half-moon in the dark fortnight) and 12 new moons. This is said to be homol ogous to the bṛhatī meter that consists of 36 syllables.23 Such concepts built around the number 36, 360, 3600, 36000 and the bṛhatī meter appear in several Vedic texts. The Aitareya Āraṇyaka represents 100 years each of 360 days, in terms of 1000 bṛhatī verses each of 36 akṣara.24 Since the total number of days and the total number of syl lables are both equal to 36,000, apparently here one day is matched with one syllable. But there are instances where the match is made differently; the constant component being bṛhatī the 36-akṣara and its simple multiples. We have seen above how the numbers 15 and 30 were arrived at in ŚB (10.4). The text in similar fashion contin ues to state the number of muhūrta in a year as 10,800. Along with the year, seasons, months, fortnights, day and nights, muhūrta is also a form or limb of Prajāpati. In the construction of the sacred Vedic altar described in minute detail in the ŚB, the 10,800 muhūrta are represented by that many lokaṁpṛṇā bricks which fill the small space in between the specially consecrated bricks which represent longer time elements. In addition to such a theoretical equivalence between Prajāpati as Time (year and its parts) and Prajāpati as Space (mahāvedi and other altars) one more equation in terms of the syllables of the three Vedas is stated. As per ŚB the Ṛgveda has 432,000 akṣaras; the Yajurveda and the Sāmaveda have 288,000 and 144,000 akṣaras respectively.25 These together, adding to 864,000 23य٥ेव संव؛रमࣉभसݺ٦ते त٢हतीमࣉभसݺ٦ते ृ बृहती ࣅह संव؛रो ٥ादश पौणर्माࡆो ٥ादशाࠋका ٥ादशामावाࡆा࠼ؚࣇं֖शत् षࣇं֖शदक्षरा बृहती..॥ ŚB (6.4.2.10). ٥ादशपौणर्माࡆः। ٥ादशाࠋकाः। ٥ादशामावाࡆाः। एषा वाव सा देवाक्षरा बृहती ॥ TB (1.5.12.2). 24त٥ा इदं बृहतीसहस्रं सڦݺ ंतࡆ वा एतࡆ बृहतीसहस्रࡆ संपࡆڦ षࣇं֖शतमक्षराणां सहस्रा࣊ण भवڢ࣎ तावڢ࣎ शतसंव؛रࡆाࡰां सहस्रा࣊ण भवڢ࣎। Aitareya Araṇyaka (2.2.4). 25स ऋचो ߢौहٲादश बृहतीसहस्राרेतावؖो हचЇ याः प्रजापࣆतसृࠋाः ताࡓ࣌ंश،मे ߢूहे पࣇӘࠗࣆतڢࠌ ता यح࣎ंश،मे ߢूहेऽࣆतڢࠌ तࡅाح࣎ंशګासࡆ रात्रयोऽथ यؑࣇӘषु तࡅाؑाӘः प्रजापࣆत࠼ा अࠋाशतं शताࣄन पӘयोऽभवन् ॥ अथेतरौ वेदौ ߢौहत् ٥ादशैव बृहतीसहस्राࠋרौ यजुषां चؘािर syllables, too form the body of Prajāpati. This number is 80 times 10,800 the number of muhūrta in a year. Thus, an akṣara is smaller in its esoteric magnitude than the muhūrta. Following such an argument the text discerns congruence between one muhūrta and 80 Vedic syllables. This is not still an equation suggested or speculated for the real time muhūrta. ŚB mentions about Prajāpati’s 1000- year sacrifice and asks the performer to imagine scaling up all the parameters of the sacred altar by 1000. Here, the muhūrta and the corresponding syllable relation remain same at 80 akṣara. But the total lokampṛṇa space filling bricks become one crore eight lakh (1,08,00,000) hair pits, on the body of the self-similar Great Prajāpati, that are stated to be equal to the number of stars seen in the sky.26 We need not digress on the doctrines and theories of the Vedic Brāhmaṇa texts. It suffices to point out that an un derlying axiomatic relation between time and the Vedic chants forms the doctrinal basis for maintaining temporal sequencing and work flow discipline in the rituals carried out in real time. Though muhūrta was given prominence as a division of the day, it was not the smallest such Vedic measure. TB defines prati-muhūrta that divides ahorātra into 450 parts. As per the ŚB legend about Prajāpati and the num ber 15, muhūrta was divided further by fifteens several times. In the 12th kāṇḍa of ŚB this division goes up to 50625 parts of ahorātra. The Śāṅkhāyana Śrautasūtra a later text is an exception to the above rule of sequential division into 15 parts. This text divides muhūrta into 10 nimeṣa which is further divided into 10 dhvaṁsī. The commonality among the different Vedic texts is in the ahorātra divided into 30 equal muhūrta parts and an ef fort to visualize close affinity among day, night, month and year with the number 36 of the bṛhati meter. 10 Real Time Leaving aside ideological musings about very long and very small time periods, division of the ahorātra should have been a practical necessity in the conduct of the sac साݹामेताव٠ैतयोवϸदयोयर्سजापࣆतसृࠋ ंतौ ࣆत्रंश،मे ߢूहे पࣇӘࠗࣆतࠌेताम् । तौ यح࣎ंश،मे ߢूहेऽࣆतࠌेतां तࡅाح࣎ंशګासࡆ रात्रयः। अथ यؑࣇӘषु तࡅाؑाӘः प्रजापࣆत࠼ा अࠋाशतमेव शताࣄन पӘयोऽभवन्॥ ŚB (10.4.2.23-24). 26तࡆ तप࠼ेपानࡆ एݫो लोमगतϸݫ ऊڎЂࣄन Էोतींࠔायं࠼٦ाࣄन ताࣄन Էोतींࠔेताࣄन ताࣄन नक्षत्रा࣊ण। यावۅेताࣄन नक्षत्रा࣊ण तावڢो लोमगतЂ, यावڢो लोमगतЂ࠼ावڢः सहस्रसंव؛रࡆ मुहूतЂः॥ ŚB (10.4.4.2).

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rifices that were of various durations, from one day to one year and even longer. We have already seen that RV (V.76.3) attests five divisions of the day. These five di visions are elaborated qualitatively further in TB (1.5.3). Such a description with demarcation is not explicitly avail able for the night even though all the 15 day and 15 night muhūrta of the dark and bright fortnight are named sepa rately in TB (3.10.1). However, allegorical explanation of how the night rites are to be carried out during the Atirā tra sacrifice, which is a one-day soma-yāga already cited in RV (VII.103.7), is available in the Aitareya Brāhmaṇa (16.5). This starts with the legend of Indra clearing away asurās through the night with the help of the seven chan das (meters), that are defined in terms of the number of syllables contained in the hymns. This night ritual is car ried out by the ordained group of priests in three cycles (paryāya) each comprising four camasa-gaṇa. The text reads: ताڮ ैप्रथमेनैव पयЂयेण पूवर्रात्रादनुदڢ मڌमेन मڌरात्रादु،मेनापररात्रात्। Here, there is clear mention of three-part division of the night each of which was taken to be of equal duration. Sāyaṇācarya the renowned representative of the practic ing sacrificial tradition explains that each division of the night is meant to be of ten ghaṭikā (five muhūrta).27 The time unit ghaṭikā is not met in Vedic texts, but widely used in the medieval period as measured by a water clock. Hence we can infer that Sāyaṇācarya’a commentary refers to actual practice among yājñika groups during his time. Vedic rituals continue to be performed in India to this day and it should not be surprising to find modern time keep ing methods in vogue. How equality of time periods was kept up in the most ancient period is not known but men tion of paryāya indicates chanting, oblations and ritual acts that should have been nearly identical in the three cycles and carried out at the same speed. Section (16.6) of the above Brāhmaṇa text describes in detail the hymns to be sung in the three cycles on the night of the Atirātra yāga which is a type of Agniṣṭoma sacrifice. But this does not make any direct or indirect statement about akṣara and the purported time divisions. However, the immedi 27क्रमेण ࣄनराकरणप्रकारं दशर्यࣆत – दशदश घࣅटका एकै को भाग इؖेवं रात्रेࡓयो भागाؘ߱ार߱मसगणा एकः पयЂय इؖेवं ٥ादशानां चमसगणानां त्रयः पयЂयाः, तैः क्रमेण राࣆत्रभागत्रयादसुरानपानुदڢ॥ Sāyaṇa Bhāṣya on the Aitareya Brāh maṇa (16.5). ate next Chapter 17 of the text prescribes the Aśvinaśas tra hymns to be chanted covering a part of the night till sunrise. These lauds are made up of all the meters such that the recitation consists effectively 1000 bṛhatī verses. This is a modification of the standard prātaranuvāka com posed of 1000 bṛhati verses which is chanted in the night during the somayāga and several other Vedic sacrifices. A brief review of this leads to interesting new results on the measure of Vedic akṣara in real time, going beyond hym nal congruencies. 11 The Prātaranuvāka The Aitareya Brāhmaṇa and the Aitareya Āraṇyaka ex pound the legends, doctrines and theories connected with the prātaranuvāka. Several Vedic Brāhmaṇa and Śrauta texts also describe in detail the composition and chanting of the prātaranuvāka during different Vedic sacrificial ses sions. An in depth study of this set of Vedic hymns has been carried out by Gonda (1981) in his monograph The Vedic Morning Litany, by collecting and comparing differ ing details as stated in several ancient texts. For our pur pose it is sufficient to determine as closely as possible the starting time and ending time of this important nocturnal recitation. The earliest reference to the prātaranuvāka is in the Taittirīya Saṁhitā (TS) where it is enjoined that this should be completed before other voices are heard, indi rectly meaning the chant should end by early morning before sunrise.28 The same text in another place men tions that the chant should commence in the deep of the night.29 Both the commentators of TS namely, Bhaṭṭa Bhāskara and Sayaṇācārya take the phrase mahati rātryai, for the beginning of the chant, as the vague middle part of the night. This is elaborated in the Aitareya Brāhmaṇa (7.5) with the injunction mahati rātryā anūcyaḥ repeated four times. The commentary of Sāyaṇācārya leaves no doubt about the approximate beginning and ending time of this litany.30 The chant had to start after midnight when large part of the night was remaining and should end before the birds started chirping early in the morn 28पुरा वाचः प्रवࣅदतोः प्रातरनुवाकमुपाकरोࣆत यावؖेव वाक् तामवरुڥे। TS (6.4.3). 29यࣅद सोमौ संसुतौ ࡆाताम् महࣆत राࣆत्रयै प्रातरनुवाकमुपाकु यЂत् । TS (7.5.5). 30रात्रेः साࣄڥ࣎ݼन शेषे महؖवࣆतࠌमाने सࣆत प्रातरनुवाका҃ ऋъमूहो वнߢः॥ Sāyaṇa Bhāṣya of AB (7.5).

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ing. The Sūtra texts that give the procedural details also say that the chant starts in the mahārātri part of the night such that the 1000 verses could be completed (before sun rise).31 What is mahārātri; is it a particular marker like madhyarātri the boundary that divides the night into two equal parts? From the different texts, commentaries and introductory essays in the MPRV (1950) by practition ers of the Śrauta tradition, we can gather that in Vedic parlance this means some time after midnight but not too far away. The Śabdakalpadruma (Deva 1822) quotes an anonymous Tantra, stating that mahārātri starts two muhūrta after midnight.32 Even though the speed and time limits mentioned in the Vedic texts are qualitative and at best intuitive, the prātaranuvāka is a rare instance where the texts, in letter and spirit, exhibit tendency for synchronization with time shorter than ahorātra by ac tual real time chanting. This is not the same as the ax iomatic akṣara congruence with lunar and solar cycles in longer than ahorātra time scales such as the month and the year. Since the bṛhatī-sahasra is a long litany with a specified number of akṣara it would be interesting to find what might have been the duration of the chant even though the texts provide only vague starting and ending times. If we take the night (sunset to sunrise) to be of 15 muhūrta, the chanting had to start ½ to 1 muhūrta after midnight and end ½ to 1 muhūrta before sunrise. This essentially means the time taken for chanting would have been 5½ to 6½ or on average 6 muhūrta, at the rate of 6000 akṣara per muhūrta. This number, it may be noted, is based on the equinoctial night of 15 muhūrtas. But, in summer due to shorter nights the 1000 verses perhaps got completed in about 5 muhūrtas whereas in winter nights the rendering might have got extended. This conjecture, leads to a recitation speed of around 7000 to 6000 akṣara per muhūrta that is at best theoretical. However, in prac tice this may vary as the processes of the rituals, though not the Ṛgvedic hymns, differ in schools that branched off long before present. It is known that the Ṛgveda (śākalya branch) text has been maintained accurately all over the country for sev eral millennia. For maintaining the fidelity of the tradi 31अथ महारात्रे महाव्रताय प्रातरनुवाकमुपाकु वर्ڢ࣎। यथा पिरसहस्रमनुब्रूयात्। Śāṅkhāyana Śrauta Sūtra (17.7). 32महाराࣆत्रः - अ٠र्रात्रात् परं मुहू،र्٥यम् । यथा, “ अ٠र्रात्रात् परं यԎ मुहू،र्٥यमुԖते। सा महाराࣆत्ररुࣅदता तٟ،मक्षयं भवेत्॥” इࣆत तۆम् ॥ Śabdakalpadruma, vol.5. tional chanting a variety of techniques are adopted the theory of which is described in the ancillary prātiśākhya texts. As discussed previously the concept of akṣara as a countable discrete entity in a hymn is central to Vedic rituals and practices. However, the traisvarya (tri-tonal) and even the ekasvarya (mono tone) Ṛgveda chanting is a continuous process in time and hence marking akṣara boundary, for counting purposes, is a matter of definition. The traditional anukramaṇi texts have preserved the me ters of all the hymns with the stipulated number of akṣara. This is the only unambiguous definition we get for count ing syllables in continuous recitations or records of the Ṛgveda. Even though versification was the fashion among the siddhānta astronomers, the syllabic time in classical po etry remains notional and hence syllable counts can be based on orthography. But, the time of the astronomers being real their 60 gurvakṣara audio scale had to be made phonetically accurate by selecting a particular me ter, among many possibilities, such that 3600 syllables span half-muhūrta. For arriving at such specific refine ment there must have been some precedence for quanti fying a part of the day or night by a long count of akṣara. The readily traceable source for such an effort is the im portance given in the Vedas for the meter bṛhatī of thirty six akṣara for representing time intervals. This cannot be treated as a fortuitous coincidence since the astronomi cal half-muhūrta of 3600 akṣara is numerically congru ent, in true Vedic style, with 100 bṛhatī verses. Neverthe less, such comparison remains qualitative. Hence for get ting a better picture of the influence of the Vedic tradition on measuring time with the gurvakṣara scale we have col lected information on present day chanting of Ṛgveda by orthodox Veda specialists. 12 Prātaranuvāka of the Kauṣītakins Śrauta practices are preserved in India by followers of the Veda who perform soma-yāga and such other rituals oc casionally apart from regular gṛhya rites. Śri Itti Raveen dran Nambūdiri, (Head of the Veda Śrauta Gurukulam of Edappal, Kerala) is a venerated scholar renowned for his lifelong devotion to Vedic tradition and his expertise on Vedic practices. He has participated and conducted sev eral Atirātra as per the Kauṣītaki School. We contacted him to know about the details of prataranuvāka as re

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cited by him in long Vedic rites. He readily explained the procedure and mentioned that his recitals started in the night at 3 a.m. and got completed sometime after 4 a.m. We gathered that the chanting from start to end would need one hour and fifteen/twenty minutes. The chanting is enjoined to be done always in ekasvara (single tone), in medium pace maintaining medium loudness. When queried about the number of bṛhatī verses as mentioned in the Aitareya Brāhmaṇa, he was quite clear that he fol lows the Kauṣītaki Vidhi inherited from his teachers and not any printed book. He agreed to share all the Ṛgveda hymns that appear in the prātaranuvāka that consists of three subsets: āgneyaṁ, uṣasyaṁ and āśvinaṁ. He sent a written document noting down the maṇḍala and the sūkta so that we could identify all the 348 hymns and their canonical meters in the Ṛgveda. The number of akṣara in the litany as per the Kauṣītaki School adds up to 12,396. This gives the speed of chanting of prātaranuvāka to be 7500–7900 akṣara per muhūrta. 13 Recorded Ṛgveda The other data collected comprises of audio records of Śākalya-saṁhitā Ṛgveda traisvarya (tri-tonal) saṁhitā pāṭha that maintains continuity within a sūkta, from Mysore33 and Vārāṇasī.34 The chanters are professionals trained since their younger days, in the age old oral tra dition, inheriting the knowhow of their teachers. Thirty eight sūkta distributed over different maṇḍala that con sist of varying number of verses are selected for noting the durations of the chant. The akṣara (syllable) count and time taken for each sūkta of this sample data is presented in the Appendix. In Figure 2 for a quick appreciation of the results, the time taken for each sūkta is plotted against the syllable count. From the table in the Appendix, the mean and standard deviation of the chanting speed can be computed. It is found that the southern chant (Mysore) speed is on average 7296 akṣara per muhūrta, whereas for the northern chant (Vārāṇasī) the average speed is 14457 akṣara per muhūrta. In both the cases the standard devi ation is about 10% of the average value. 33Ṛgveda audio record of S. S. Sharma and S. K. Bhatta. Published by Sri Ranga Digital Software Technologies, (Pvt.) Ltd. Mysore, 2012. 34Ṛgveda audio record of Vishvanatha Sharma from Vārāṇasī, Private Collection. 14 Discussion Several interesting results emerge out of the above study. Firstly, the average recitation rate of 7296 akṣara per muhūrta, of the Mysore school in medium pace, is in mag nitude close to the 7200 gurvakṣara rate of siddhānta as tronomers that was the basis for time measurement in In dia till modern times. This is not a chance result nor a sub jective opinion but what can be verified objectively. This close quantitative match, beyond reasonable doubt, leads us to infer that the oral tradition of Vedic learning and chanting, by design or by its very nature, was getting syn chronized with numbers 15, 30 and 36 and their simple multiples, as time measures related with day/night, aho rātra, pakṣa, māsa, and saṁvatsara. The result of 14457 akṣara per muhūrta of the Vārāṇasī tradition is twice of its southern counterpart, the differ ence being less than 1%. This is easily explainable since in the Vedic and in the music tradition, three speeds vilamba, madhyama and druta; each twice faster than the previ ous one, are recognized. If recitation of a particular fixed text material in the madhyama (medium) speed takes one muhūrta, the same will take two muhūrta in the vilam aba (slow) speed, whereas in the druta (fast) speed only half muhūrta would be sufficient to complete the recita tion. Bhāskara-I, the commentator on the Āryabhaṭīya elaborates the importance (see footnote 7) of the speed being in the medium pace (madhyama vṛtti) for the cal ibration of one vighaṭikā by 60 gurvakṣara of the verse B-I, already experimentally verified for its accuracy in the present study. Bhāskara’s comment quite well points to the Vedic origins of the akṣara count method of time mea surement that was only fine-tuned by the astronomers us ing classical Sanskrit prosody. Tracing the akṣara concept backwards takes one to the Vedic Brāhmaṇa texts, which propose congruencies be tween a variety of akṣara counts and time periods and spatial designs of the altars. Jan Gonda (1984) cites more examples of this type of syllable congruence or homolo gation. The congruency relations are neither figurative nor realistic in present day parlance, but indicate grad ual growth of an idea following an urge to understand or characterize abstract time in terms of active rituals that use hymns already available to the followers of the Vedas. This represents a stage in the evolution of math ematical concepts in India wherein the mystical unitary

213 ARTICLES IJHS | VOL 55.3 | SEPTEMBER 2020 Figure 2 Ṛgveda chant time in seconds vs Akṣara count.

vision of the cosmos of the Vedic seers was transforming into tangible realities for the community through num bers and similarity relations, particularly in rectifying the year, months and still smaller intervals of time. The principle of correspondence of akṣara in sacred hymns to abstract and concrete objects was not limited to time divisions only. The Aitareya Brāhmaṇa (5.3) refers to this as a general principle called rūpasamṛddhi (fullness-of-form). This principle appears to be the motive force behind some ritualistic actions striving for accuracy in minute details tending towards rigour of a mathemat ical kind. Akṣara, no doubt played a very important role in handling phenomenal time, but it involves discretiza tion in the sense of counting by integer numbers. Going beyond such integral akṣara, Vedic texts in many places exhibit deeper analytical ideas about the akṣara-kāla it self being further divisible, as many times as one wishes, so much so time in reality is extolled to be continuous with no breaks. The Taittirīya Āraṇyaka (I. 2.4–5) in the very beginning describes that time is due to sun and that it is continuous like a river flow and is irreversible. Previously, we have referred to the Sāmidhenī verses and their per ceived syllabic congruence with the year. The Śatapatha Brāhmaṇa enjoins that these hymns should be recited continuously without breaks because ahorātra flows con tinuously uninterrupted.35 This continuity of time that is 35…तानीमाࣄन संव؛रࡆाहोरात्रा࣊ण सڢताߢڬवࣔԏڦाࣄन पिरܚवڢ े॥ ŚB (I.3.5.16). linked with the continuity in the observable movement of Sun might be leading to congruencies of a different kind. This aspect needs further investigation. 15 Summary and Conclusion Any physical measuring instrument needs to be calibrated by independent methods to maintain its accuracy. Indian astronomers of the varioussiddhānta texts recognized the necessity to calibrate the water clock that was used to mea sure time by a bowl sinking exactly 60 times from sun rise to sunrise. It was important to measure one ghaṭikā that is (1/60th) of an ahorātra by independent means so that the bowl could be fine-tuned properly. An ingenious method of calibrating using an audible oral scale of one vighaṭikā was developed in the form of a Sanskrit verse in the līlākhela meter composed of 60 gurvakṣaras. Sixty rep etitions of this verse in medium speed would indicate pas sage of one ghaṭikā equivalent to 24 minutes in modern parlance. In the present study the accuracy of this scale has been verified and shown to be very good. It is noted that the time value of this gurvakṣara in the particular me ter gets fixed phonetically as equal to 0.4 seconds. Such a practice of recitation to estimate passage of time is trace able to the Vedic oral tradition, wherein many ritualistic texts describe congruence relations between akṣara and time. We find that in the legend of Indra crossing over the night with the help of the seven chandas, followed by the

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starting and ending time prescriptions for the prātaranu vāka chanting of 1000 verses, adding to 36,000 akṣara (Vedic syllables) there is evidence to the ancient practice of estimating passage of night-time by Vedic recitation at medium pace. Quite interestingly the theoretical estimate from the books and the actual speed in real performances, al though approximations, match well with the classical count of 7200 gurvakṣara per muhūrta of the astronomers. The prātaranuvāka was not always recited with pitch ac cents. The count of verses to be chanted perhaps varied among the different branches of the Vedic schools. With out the three pitch accents an oral performance would be a mix of only laghu and guru syllables almost like in clas sical poetry. This is borne out by the personal informa tion provided by Iṭṭi Raveendran Nambūthiri. In such a chant the time measure of an arbitrary akṣara would be less than that of the astronomical gurvakṣara. But with the Vedic pitch accents included as in the Mysore record, the basic akṣara magnitude approaches that of the gur vakṣara time of Āryabhaṭa, Varāhamihira, Bhāskara and others. The Vārāṇasī performance rendered at twice the speed corroborates this observation. The above analysis and discussion makes a case for recognizing the night-time recitation of the prātaranu vāka in different Vedic schools as the precursor for a va riety of akṣara time units appearing in the works of La gadha, Parāśara, Suśruta, Vṛddha-Garga, the Brahmāṇḍa Purāṇa and other texts. The very diversity in the defini tion of the basic akṣara and its time value is a clear indica tion of the intellectual tradition in India striving to stan dardize the vague time-keeping methods inherited from antecedent sources. This eventually was achieved with the calibration of the vighaṭikā by the medium pace recita tion of a verse with sixty gurvakṣara which only could have led to the final design of the sinking bowl type wa ter clock. 16 Acknowledgement Software help received from M. T. Raghunath and Sunder Chakravarthy in modeling pronunciation rules is thank fully acknowledged. Abbreviations KAS – Kautilīya Artha Śāstra VM – Varāhamihira B-I – Bhāskara I MAU – Maitrāyṇīya Āraṇyaka Upaniṣad ŚB – Śatapatha Brāhmaṇa TB – Taittirīya Brāhmaṇa AB – Aitareya Brāhmaṇa RV – Ṛgveda LVJ – Lāgdha Vedāṅga Jyotiṣa VP – Viṣṇu Purāṇa TS – Taittirīya Saṃhitā

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