Vuttodaya, The Composition of Metre

[6. Chappaccayavibhāgo] Sid: Chaṭṭho Paricchedo; Th: Chappaccayavibhāga-chaṭṭhapariccheda.
The Analysis of the Six Procedures

[Making a Table]

Dvikau glau; miśrau ca; pthaglā miśrāḥ; vasuvastrikāḥ || ChŚā 8:20–23 ||
Pāde sarvagurāvādyāllaghuṁ nyasya guroradhaḥ |
Yathopari tathā śeṣaṁ bhūyaḥ kuryādamuṁ vidhim || VR 197 ||
Ūne dadyādgurūneva yāvatsarvalaghurbhavet |
Prastāro ’yaṁ samākhyātaśchandovicitivedibhiḥ || VR 198 ||

−−−−¦⏑−−−¦¦−⏑−−¦⏑−⏑−
Patthāre: sabbage pāde pubbagādho lpare samā;
−−⏑−¦−⏑⏑−¦¦−−−−¦⏑−⏑−
Pubbe garutvevam-ime; kattabbā yāva sabbalo. a) MR14: Patthāro; c) MR14, MR93, Dīp, Laṅk: guru-; Fry, Kat, Th: garu te camime; d) MK, Fry, Kat, Th: sabbalā; Sid adds the end-title: Iti Pattharavidhi (sic = Patthāra-) after this verse. [127]

Patthāre = in tabulation (loc.); sabba = all; ge = heavy syllables (loc.); pāde = in the line (loc.); pubba = first; ga = heavy syllable; adho = under; la = light syllable; pare = after; samā = same; pubbe = before; garū = heavy syllables; tu = but; evam = this; ime = this; kattabbā = should be made (fut. pass. part); yāva = until; sabba = all; lo = light syllables.

In tabulation:
1) in the line that has all heavy syllables: under the first heavy syllable (write) a light syllable;
2) after (that light syllable) (write) the same (as in the line above);
3) but before this (write) heavy syllables;
4) this should be done until (there is a line with) all light syllables.

This describes the way to create a table that shows all the different permutations that are possible in any given metre. The method is as follows:

Write a line with only heavy syllables in it (we may take a Patiṭṭhā line, having 4 syllables as an example).

1. Write a light syllable under the first heavy syllable in the line (when starting the first syllable is always a heavy syllable, but, as we will see, it occurs in other positions later):

−−−−

2. After that light syllable write the same syllables as in the line above:

−−−−
⏑−−−

3. Before this light syllable write heavy syllables (here the light syllable stands at the beginning of the line, so we cannot write any heavy syllables before it).

4. This should be done until there is a line where all are light syllables (so we now continue the procedure with the third line):

1. Write a light syllable under the first heavy syllable in the line:

−−−−
⏑−−−
  ⏑

2. After that light syllable write the same syllables as in the line above:
−−−−
⏑−−−
  ⏑−−

3. Before this light syllable write heavy syllables:
−−−−
⏑−−−
−⏑−−

4. This should be done until there is a line where all are light syllables (so we now continue the procedure with the fourth line):

1. Write a light syllable under the first heavy syllable in the line:
−−−−
⏑−−−
−⏑−−

2. After that light syllable write the same syllables as in the line above:
−−−−
⏑−−−
−⏑−−
⏑⏑−−

3. Before this light syllable write heavy syllables (here the light syllable stands at the beginning of the line, so we cannot write any heavy syllables before it).

4. This should be done until there is a line where all are light syllables (so we now continue the procedure with the fifth line):

1. Write a light syllable under the first heavy syllable in the line:
−−−−
⏑−−−
−⏑−−
⏑⏑−−
     ⏑

2. After that light syllable write the same syllables as in the line above:
−−−−
⏑−−−
−⏑−−
⏑⏑−−
     ⏑−

3. Before this light syllable write heavy syllables...
−−−−
⏑−−−
−⏑−−
⏑⏑−−
−−⏑−

If we continue with this procedure we will eventually have a table like this:

1. −−−−
2. ⏑−−−
3. −⏑−−
4. ⏑⏑−−
5. −−⏑−
6. ⏑−⏑−
7. −⏑⏑−
8. ⏑⏑⏑−
9. −−−⏑
10. ⏑−−⏑
11. −⏑−⏑
12. ⏑⏑−⏑
13. −−⏑⏑
14. ⏑−⏑⏑
15. −⏑⏑⏑
16. ⏑⏑⏑⏑

By following this procedure we have created a table which shows the 16 possible permutations for the Patiṭṭhā metre.

For the possible numbers of permutations that each metre can have in theory, refer to the table accompanying v. 14 above.

 


[Finding the Lost Metre]

Lardhe; saike g || ChŚā 8:24–25 ||
Naṣṭasya yo bhavedaṅkastasyārdhe ’rdhe same ca laḥ |
Viṣame caikamādhāya syādardhe ’rdhe gururbhavet || VR 199 ||

−−⏑−¦⏑−−−¦¦−−−⏑¦⏑−⏑−
Naṭṭhassa: yo bhaveyyaṅko tasmiṁ loddhikate same;
⏑⏑−−¦⏑⏑⏑−¦¦⏑−−⏑¦⏑−⏑−
Visame tvekasahite bhaveyyaddhikate garu. a) MP: -aṁke; MK, MR14, MR93: -aṁko; b) Fry: tasmin (sic); MP, MR93, Vim, Sid: loddhīkate; c) MR93: tvetosihite (sic); d) Vim, Sid: -addhīkate; MR14: āddhīkate; MR93, MR93, Laṅk, Sid: guru; Sid adds the end-title: Iti Naṭṭhavidhi after this verse. [128]

Naṭṭhassa = for the lost (gen.); yo = that; bhaveyya = if it is (opt.); aṅko = number (this meaning not in PED); tasmiṁ = in that (loc.); lo = light syllable; addhikate = divide in half (loc.); same = even; visame = odd; tu = but; eka = one; sahite = with; bhaveyya = if it is; addhikate = divide in half; garu = heavy syllable.

For the lost (metre): if the number in the (series) is even: divide it in half, (and write) a light syllable;
but if it is odd: (put) one with (it), (then) divide it in half, (and write) a heavy syllable.

This verse explains a quick method to find out the shape of a metre in its serial position in the table. Let’s say we want to know what the 9th metre of Patiṭṭhā looks like:

9 is an odd number, therefore add one (= 10), divide it in half (= 5), and write a heavy syllable = .
5 is also an odd number, therefore add one (= 6), divide it in half (= 3), and write a heavy syllable = −− .
3 is also an odd number, therefore add one (= 4), divide it in half (= 2), and write a heavy syllable = −−− .
2 is an even number, therefore divide it in half (= 1); and write a light syllable = −−−⏑ .

As the metre is four syllables we stop there (compare the result with the table for Patiṭṭhā above).

 


[Finding a Metre’s Serial Position]

Pratilomagaṇaṁ dvirlādyam; tatogyekaṁ jahyāt || ChŚā 8:26–27 ||
Uddiṣṭaṁ dviguṇānādyāduparyaṅkānsamālikhet |
Laghusthā ye ca tatrāṅkāstaiḥ saikairmiśritairbhavet || VR 200 ||

−−⏑−¦⏑−−−¦¦−−−⏑¦⏑−⏑−
Ekādinukkamenaṅke pubbādho dviguṇe likhe;
−⏑−⏑¦⏑−−−¦¦−−−−¦⏑−⏑−
Missitehi lahuṭṭhehi sekehuddiṭṭhakaṁ bhave. a) MR93, Dīp: Ekādī; MR14, MR93: -aṁke; b) Vim, Dhm, Dīp, Laṅk, Sid: diguṇe; c) MK, Laṅk, Th: missatehi; Fry: lahutthehi; d) MR14, Vim: -diṭṭhakam-bhave; Sid adds the end-title: Iti Uddiṭṭhavidhi after this verse. [129]

Eka = one; ādi = beginning with; anukkamena = in succession; aṅke = numbers (this meaning not in PED); pubba = first; adho = below; dvi + guṇe = doubled; likhe = should write (opt.); missitehi = from the combination (abl.); lahu = light syllables; ṭhehi = standing; sa + ekehi = together with one; uddiṭṭhakaṁ = designation (this form not in PED); bhave = will give (opt.).

1) Beginning with one, and in succession, numbers (should be) doubled and written below (starting from) the first (syllable);
2) from the combination (of numbers) the ones standing (below) the light syllables (are added up) together with one (more), (that) will give the (serial) designation (of the Metre).

This is the procedure for finding out the serial designation of the metre in the table. Let’s say the metre is a Patiṭṭhā metre showing the following form: − ⏑ − ⏑ .
1) Beginning with one, and in succession, numbers should be doubled and written below starting from the first syllable:

1 2 4 8

2) The ones standing below the light syllables are added up, together with one more:

1 2 4 8

2 + 8 + 1 = 11; that gives the serial designation of the metre (compare the result with the table for Patiṭṭhā above).

Now let’s say we want to find the serial position of Vaṁsaṭṭhā in the Jagatī class of metres (there are a possible 4,096 metres in the Jagatī class).

1) Beginning with one, and in succession, numbers should be doubled and written below starting from the first syllable:

1 2 4 8 16 32 64 128 256 512 1024 2048

2) The ones standing below the light syllables are added up together with one more:

1 2 4 8 16 32 64 128 256 512 1024 2048

1 + 4 + 32 + 64 + 256 + 1024 + 1 = 1,382.
Vaṁsaṭṭhā is therefore the 1,382nd metre in the Jagatī series.

 


[Calculating the Heavy and Light Syllables]

Varṇānvttabhavānsaikānauttarādharyataḥ sthitāt |
Ekādikramataścaitānuparyupari nikṣipet || VR 201 ||

−−⏑⏑¦⏑−−−¦¦−⏑−−¦⏑−⏑−
Vuttakkharasamā saṅkhyā likhya sekoparūpari;
−−⏑−¦⏑−−−¦¦−−−−¦⏑−⏑−
Ekekahīnam-ekādīnuṭṭhāne sabbagādikaṁ. a) MP, MR14, MR93: saṁkhyā; b) MK, Fry, Kat: likkhya; MP: likkhyā; MR93: likhyā ... ūparī; c) MK, MP, MR14, MR93, Sid, Kat, Th: -ekādi-; Sid adds the end-title: Iti Lagakriyāvidhi after this verse. [130]

Vutta = metre; akhara = syllables; samā = same; saṅkhyā = numbers; likhya = having written (abs.); sa + eko = together with one; uparu + upari = above and after; ekeka = one by one ; hīnam = less; eka = one; ādīna = from the beginning; uṭṭhāne = by adding (loc.) (this meaning not in PED); sabbagā = all heavy syllables; ādikaṁ = beginning with.

1) Having written the same (number of) numbers as (there are) syllables in the metre, together with one (more), above and after (each other);
2) by adding one by one – less (the end) one – from the beginning (we get the metres) beginning with (that which is) all heavy syllables.

This is a procedure for finding out how many metres there are in a given class, which have, say, one heavy syllable, or two, or three, etc. The table itself is an application of what became known in the West as Pascal's Triangle, which can be used for various calculations of combinatorics and binomial coefficients, but which was first discovered in the context of Indian Prosody (see: https://en.wikipedia.org/wiki/Pascal's_triangle). The procedure as given here is rather elliptic, but the method can be illustrated as in the table below. Let’s say we want to examine the Patiṭṭhā class of metres, which has 4 syllables to the line.

One: write 4 cyphers + 1 extra (= 5) above and after each other.
Two: add the first two numbers of the line together, (and write it below).
Three: add the first three numbers of the line together, (and write it below).
Four: add the first four numbers of the line together, (and write it below).
We must leave out the end number.
Five: add the first two numbers on the second line, (and write it below).
Six: add the first three numbers on the second line, (and write it below).
We must leave out the end number.
Seven: add the first two numbers on the 3rd line, (and write it below).
We must leave out the end number.
Eight: shows the completed table.

Vuttodaya-194

We can check this against the Patiṭṭhā table above.

Here are three tables giving a listing of all the types of metres in the various classes:

Table 1 An example of the way to read this table is as follows: reading down the Patiṭṭhā column, we can see that in this class of metres there is:
1 metre that has no heavy syllables;
4 metres have 1 heavy syllable;
6 metres have 2 heavy syllables;
4 metres have 3 heavy syllables; &
1 metre that has 4 heavy syllables.
The same numbers apply to the light syllables also.

Vuttodaya-195

Table 2

Vuttodaya-196

Table 3

Vuttodaya-197

 

[Finding the Number of Metres in a Class]

Lagakriyāṅkasandohe bhavetsaṁkhyā vimiśrite |
Uddiṣṭāṁkasamāhāraḥ saiko vā janayedimām || VR 203 ||

⏑−⏑−¦⏑−−−¦¦⏑−−−¦⏑−⏑−
Garukriyāṅkasandohe bhave saṅkhyā vimissite;
−−−⏑¦⏑−−−¦¦−−−−¦⏑−⏑−
Uddiṭṭhaṅkasamāhāro seko vemaṁ samānaye. a) MR14, MR93, Dīp, Laṅk: Guru-; Sid reads Lagakriyā-, and has a footnote stating: “In the Vuttodaya and its Tikā (sic) the term Gurukrayā (sic) is used for the term Lagakriyā. But the term Lagakriyā is the one generally used and the more appropriate”, which makes it clear that the reading in S here is an emendation of the text by Siddhartha himself; Vim: -kriyaṇka-; MK, MP, MR93: -kriyāṁka-; MK: -aṁka-; MR14: -kriyaka-; MR93: -sandehe; b) MP, MR14, MR93: saṁkhyā; c): MP, MR14, MR93: -aṁka-; d) MR93: dvenaṁ samāniye; Sid adds the end-title: Iti Vuttasaṅkhyāvidhi after this verse. [131]

Garu + kriyā = arrangement of the heavy syllables; aṅka = number; sandohe = aggregate (not in PED); bhave = will be (opt.); saṅkhyā = numbers; vimissite = total (not in PED); uddiṭṭha = designation; aṅka = number; samāhāro = collection (not in PED); sa + eko = together with one; vā + imaṁ = or that; samānaye = same (not in PED).

1) The total number (of metres) will be the aggregate of the number (obtained from) the arrangement of the heavy syllables (as in v. 130);
2) or, the same as that (will be) the collection of the numbers (used in finding) the (serial) designation (as in v. 129) together with one (more).

We can find the total number of metres in any given class in two ways.
1) by adding up the aggregate of the arrangement of the heavy syllables, an example of which was given in the commentary to v. 130.
There we saw that there was
1 metre with 4 heavy syllables;
4 metres with 3 heavy syllables;
6 metres with 2 heavy syllables;
4 metres with 1 heavy syllable; and
1 metre with 0 heavy syllables (sabbalahu).
1 + 4 + 6 + 4 + 1 = 16. There are 16 metres in the Patiṭṭhā class of metres.

2) we can add together the numbers used to find the designation of the metre, and then add one more to it. In v. 129 we wrote the numbers below the Patiṭṭhā metre thus:
− ⏑ − ⏑
1 2 4 8
Now we can see that 1 + 2 + 4 + 8 (+ 1) = 16. That is the same result as before.

 

[Finding Out the Extent of the Table]

Saṁkhyaiva dviguṇaikonā sadbhiradhvā prakīrtitaḥ |
Vttasyāṅgulikī vyāptiradhaḥ kuryāttathāṅgulim || VR 204 ||

−−⏑⏑¦⏑−−−¦¦−−−−¦⏑−⏑−
Saṅkhyeva dviguṇekūnā vitthārāyāmasambhavo;
−−−−¦⏑−−−¦¦⏑⏑−−¦⏑−⏑−
Vuttassaddhantarānañ-ca garulānañ-ca aṅgulaṁ. a) MP: Saṁkheva; MR14, MR93: Saṁkhyedva (sic); MK: -unā; MR14, Sid: ūna; b) MK, Fry, Kat, Th: sambhavā; c) MP, MR93: -ānta-; Kat: -antarānaṁ ca; d) MR93, Dīp: guru-; Dhm, Kat: garulānaṁ ca. After this verse Sid adds the end-title: Iti Patthārabhūmimānavidhi. [132]

Saṅkhyā + eva = number (+ emphatic particle, untranslated); dvi + guṇa = doubled; eka + ūnā = minus one; vitthāra = width; āyāma = depth; sambhavo = gives (i.e. produces); vuttassa = for the metre (gen.); addha = space; antarānañ = between (gen.); ca = and; garulānañ = heavy syllables and light syllables (gen.); ca = and; aṅgulaṁ = one unit (lit: a finger[-breadth]).

The numbers doubled, minus one, gives the width and depth (of the table); the space for the metre, and for the heavy syllable and the light syllable and between them (should be) one unit.

This is the procedure for calculating the exact expanse of any given table. Working with Patiṭṭhā again as an example, we can see that there are 4 syllables, 4 x 2 = 8–1 = 7. If there is one unit for each of the metrical markings, and one unit between them, we can see that the table will be 7 units wide.

There are 16 metres in the Patiṭṭhā class, 16 x 2 = 32–1 = 31. If there is an unit for each of the metres and a unit between the metres, we can see that the table will be 31 units deep.

Iti Vuttodaye Chandasi Chappaccayavibhāgo Nāma Chaṭṭho Paricchedo MK: Iti Saṅgharakkhitamahāsāmi pādaviracite Vuttodaye...; Dhm, Laṅk: Iti Saṅgharakkhitattherapādaviracite Vuttodaye...; Dīp: Iti Saṅgharakkhitattherapādaviracite Vuttodayaṁ Niṭṭhitaṁ; Fry, Vim: Iti Saṅgharakkhitatherapādaviracite Vuttodaye Chandasi Chappaccayavibhāgo Nāma Chaṭṭho Paricchedo; Sid: Iti Chappaccayavibhāgo Nāma Chaṭṭho Paricchedo; and follows it with Iti Saṅgharakkhitattherapādaviracitaṁ Vuttodayaṁ Niṭṭhitaṁ, which concludes the book; MP places this end-title at the end of the text (after 137d); MR14, MR93 place variants of this title at the end of the work, s.v.
Such is the Sixth Chapter in the Prosody the Composition of Metre
which is called The Analysis of the Six Procedures.