Part 1.5 - The theory of Sankhyana in Sanskrit prosody

6.5. sankhyana (laksanalagakriyankasamuhamelana, saika-uddistankasamahara ) - 8 Aphorism: lagakriyankasandohe bhavet sankhya vimisrite | uddistankasamaharah saiko va janayedimam || 8 || lagakriyankasandohe bhavet sankhya vimisrite| uddistankasamaharah saiko va janayedimam||8|| caturthapanktyamadho'dhah sthitakosthadvayasthankayormelananke sthapyah| saisa caturthi pankih syatsarvavarnabadhini | - Vritta-ratnakara pp. 207, 208 630

Construe: la-ga-kriya +anka-sandohe vimisrite sankhya bhavet | sa ekaih uddista +anka-samaharah va imam janayet | Word to word Meaning: la-ga-kriya +anka-sandohe = When the aggregate of numbers of ekadvayadilagakriya; vimisrite = is added or combined; sankhya = the total number of [all possible] forms or metres [in a particular chandas]; bhavet | = there would be; sa+ekeh = together with an additional number one; uddista +anka-samaharah = the sum of the numbers in the uddista; va = otherwise; imam = this [sankhyana or total of metres]; janayet | = may produce. Literal Meaning: When the aggregate of numbers of ekadvayadilagakriya is added or combined, there would be the total number of all possible forms or metres in a particular chandas; otherwise the sum of the numbers in the uddista together with an additional number one may produce this (sankhyana or total of metres). Import: This is about the process of the fifth cognitive rule sankhyana which the addition of the lagakriya numbers or that of the uddista numbers. Notes: The writer introduces the fifth cognitive rule sankhyana through the above verse. The term lagakriyankasandoha means the number group of the lagakriya (anantarodiritaya lagakriyaya ye'nkah sankhyah sanketavacakarekhavisesah tesam sandohah samuhah lagakriyankasandohah | ); The word vimisrita is for addition (vimisrite pindikrte | ekatra sammilite | samyojite | ); The term sankhya is the title of the cognitive rule (sankhya bhavet vrttaganana vrttarupasankhya jayate | ); The word uddistankasamahara shows the sum of the number series of the uddista (uddistavrttavarnanam mastake samsthapitankanamekibhavah | ); The term saika means the extra number one which is needed to be added to the sum of the uddista numbers 631

(saikah punarekasahitah | ). The cognitive rule which can be obtained by adding the entire number sequences of the lagakriya or by adding an additional number one to the sum of the uddista numbers called sankhyana-pratyaya (lagakriyankasandohe vimisrite pindikrte sati sankhya bhavet vrttaganana jayate| saika uddistankasamaharo va imam vrttasankhyam janayedutpadayet | ). 69 Another method mentioned in the Pancika for the sankhyana is by doubling the last number of the uddista number series. 70 Pingala does not introduce a separate cognitive theory by the name of sankhyana because the matter fulfilled by it can be achieved by means the numbers of the lagakriya or meru-prastara. Therefore, if necessary, his two aphorisms given for the lagakriya can be taken for this purpose too ('pare purnam| pare purnamiti | ' - °Chandahshastra viii. 34, 35). However, this rule is important 71 because it provides the knowledge to discover the total number of varieties possible in a chandas consisting of a specified number of syllables or morae. Furthermore, this theory is tally with the theory known as 'Geomatric progression' in the modern mathematics. However, it seems in general that there are three patterns to discover the sankhyana. In the operation of this rule, it is essential to note down separately each number series of the lagakriya and uddista. The rule under the aforesaid three patterns is enumerated with illustrations below. 6.5.1. Sankhyana of syllabic chandas In the work of the discovery of the Sankhyana of syllabic chandas, the above three patterns can equally be applied. The followings are the examples: Example I: Find the sankhyana of the tri-syllabic chandas. Patterns 1 No series of lagakriya Addition 2 No series of uddista Addition with one Calculation Sankhyana 1, 3, 3, 1 1+3+3+1= 8 1, 2, 4 1+2+4=7+1= 8 69 Vritta-ratnakara p. 95; °Vrittaratnakara pp. 325, 326; VRSN. pp. 120, 121; Vritta-ratnakara pp. 201, 202; °Vrttaratnakara-parisista p. 143; Vritta-ratnakara pp. 209, 210 70 Vritta-ratnakara p. 95; °Vrittaratnakara p. 326 71 DCPSPV. p. 6; °Classical Sanskrit Prosody p. 534 632

3 Doubling last no of uddista no. series 1, 2, 4 x 2= 8 Table 6.54: Discovery of the sankhyana of the tri-syllabic chandas Example II: Find the sankhyana of the four syllabic chandas. Patterns 1 No series of lagakriya Addition 2 No series of uddista Addition with one Calculation Sankhyana 1, 4, 6, 4, 1 1+4+6+4+1= 16 1, 2, 4, 8 1+2+4+8=15+1= 16 16 3 Doubling last no of uddista no. series 1, 2, 4, 8 x 2= Table 6.55: Discovery of the sankhyana of the four syllabic chandas Above examples are for even metres of the syllabic chandas whose sankhyana can be found with the help of those three means. The same process can be applied for the discovery of the sankhyana of half-even and uneven metres of the syllabic chandas too. 6.5.2. Sankhyana of moraic chandas 72 In order to get the sankhyana in the moraic chandas, only the first pattern except other two can similarly be applied. Anyway, since the last of the number series of the moraic uddista (or moraic nasta) is usually the total of the desired moraic chandas, it can be treated as the sankhyana of that category. The following is its example: Example I: Find the sankhyana of the six moraic chandas. Patterns Calculation Sankhyana 1 No series of lagakriya 1, 6, 5, 1 Addition 1+6+5+1= 13 UU 3 U 13 13 13 2 No series of uddista Last no. Table 6.56: Discovery of the Sankhyana of the six moraic chandas Example II: Find the Sankhyana of the nine moraic chandas. Patterns Calculation 1 No series of lagakriya 5, 20, 21, 8, 1 Addition 2 No series of uddista Last no. 5+20+21+8+1= 13 8 34 U 55 I U 3 US BU 21 U 55 55 Sankhyana 55 55 Table 6.57: Discovery of the sankhyana of the nine moraic chandas 72 Vritta-ratnakara p. 95; °Vrittaratnakara pp. 325, 326: Vritta-ratnakara p. 210; vide. °Classical Sanskrit Prosody pp. 532-535; DCPSPV. pp. 56-58 73 vide. Section 6.2.4; 6.3.4 633