(Previously: Chapter 1, Chapter 2, Chapter 3, Chapter 4.)

I mentioned earlier my impression that this work Chandogati is structured like a mathematics book. If you’ve read enough of them, you’ll be familiar with the experience of everything appearing to be straightforward, until you hit a chapter or section where the going suddenly gets tough, things are suddenly much more “nontrivial”, and you’re no longer sure you understand everything. To me, that happened with this, the middle chapter of this book (pariccheda 5 of 9). And I found myself wishing for some exercises at the end of the chapter, to check my understanding. Let’s see how it goes :-)

Always starts with a summary that also simultaneously somehow elaborates and clarifies.103 0.081 0.474

To be attractive, it needs to be “different”, unusual — have a striking gati.103 0.452 0.673104 0.107 0.429

Fn 33.103 0.673 0.908

Fn 34: We’ll discuss “vṛtta-gandhi” gadya later.104 0.837 0.908

gati in SRK. He says ”gati is an arrangement of Ls and Gs that follows some system and is attractive”. Lots of Gs $\implies$ vilamba-gati, lots of Ls $\implies$ druta-gati,104 0.428 0.833

and all combinations thereof: druta+madhya, etc.105 0.109 0.303

Fn 35: Examples of metres with druta etc. gati105 0.314 0.761

Fn 35 contd: Not the same as speed of recitation.105 0.752 0.913106 0.241 0.803

Fn 35 contd: Teaser for something to come.106 0.797 0.912

Why does SRK go into this at all? gati-saundarya of gadya.105 0.261 0.303106 0.112 0.226107 0.113 0.602

But really, gati is hard to pin down in gadya108 0.109 0.290

Adduces Bhoja. [For the first time in this book, I see “ವಿವರಣೆ ಬೇಕೇ?” and feel “ಬೇಕು”.]107 0.620 0.914108 0.576 0.908

Rāga = pleasing scale (↗↘) of svaras. Gati = pleasing sequence of Ls and Gs. 108 0.292 0.583

Such a pleasing gati carried out to some particular extent is a pāda; thence padya.109 0.106 0.202

Again: gati is not needed for definition; it simply follows as a consequence.109 0.206 0.453

Fn 37: Except for Vedic metre and the Vedic-like Anuṣṭup Śloka. (More on them in Chapter 9.)109 0.645 0.734

Fn 38: This “follows as a consequence” does not apply to the trimūrti-gaṇa in Kannada. See other part of other book.109 0.728 0.910

Yet Piṅgala seems [to SKB, as no one else seems to have noticed] to talk about them. Follows.109 0.446 0.521

Chapter 5, 1–9. (Of these, 6, 7, 8 are of interest; the rest included for context.)109 0.516 0.637110 0.107 0.299

Explains the meanings of the others (1–5 and 9) and gets them out of the way; they were included for context.110 0.294 0.563

The meanings of the three crucial sūtras.110 0.556 0.726

These are not the names of 3 specific metres (vṛtta-s).111 0.110 0.492112 0.100 0.238

Fn 39: The trika (gaṇa) trick probably originates with Piṅgala.111 0.495 0.695

Fn 40: SKB seems sure that Piṅgala 7.23, which stands out, is an interpolation (prakṣipta). [I don’t see this confidence yet, but it doesn’t really matter…]111 0.691 0.907

Fn 41: Jayakīrti and Hemacandra seem to have been puzzled too.112 0.433 0.651

Fn 42: Examples of the use of the word tāna.112 0.645 0.906

Fn 42 contd: Today, Hindustani and Carnatic music use tāna in different meanings, but hints of the original meaning remain.113 0.636 0.903

So what do these 3 sūtras indicate? A clue in ‘vitāna’. As ‘tāna’ = monotonous tone.112 0.191 0.418

So samānī = trochaic, pramāṇī = iambic.113 0.106 0.414

Examples.113 0.404 0.528

And Vitāna = the rest. See named examples of metres.113 0.522 0.619114 0.098 0.232

Fn 43: reminder.114 0.776 0.901

So Samānī/Pramāṇī/Vitāna are not names of 3 vṛtta-s, but classification of all vṛtta-s into 3 gati.114 0.226 0.361

Why does Halāyudha give a weird commentary?114 0.360 0.651

Halāyudha was 10th century.114 0.642 0.760

By then Piṅgala’s work was old; Jayadeva was popular and would have influenced.115 0.103 0.512

Jayadeva has mistake and Halāyudha didn’t suspect.115 0.487 0.757116 0.097 0.259

Fn 44: Some more polite criticism of everyone for not realizing that S/P/V are properties common to many.115 0.764 0.904

Another reason for not suspecting that S/P/V are not names of vṛttas but are gati: they only considered vṛttas and strict mātrā bandhas… not trimūrti-gaṇa or solely tāla based. (These are discussed in music?) Gati is not usually discussed in chandaḥśāstra works.116 0.250 0.505117 0.098 0.385

So why then does Piṅgala go into the topic at all? Maybe his predecessors did. So P mentioned briefly even though his system doesn’t need it.117 0.385 0.876118 0.107 0.229

Fn 45: Maybe vṛttas were classified by gati at some point, as rāgas were once divided into families based on their “feeling”. Consider their names.118 0.397 0.659

Fn 46: Nice example of not ignoring predecessors: Hemacandra includes the uninteresting pratyaya.118 0.653 0.826

[I actually recognize this example: Sanskrit works on prosody (chandaḥśāstra) had a section on mathematics, where they discussed six problems or pratyayas. (See Wikipedia.) Hemacandra, in his Chandonuśāsana (that is written much more clearly than earlier works), sees that one of them (the total space required to write them) is pointless and utterly mathematically uninteresting, and says so, but discusses it anyway.]

Anyway, doesn’t matter why Piṅgala discussed it.118 0.223 0.380

Next begins Footnote 47, which touches 5 pages and is probably the most important thing in this chapter.

Fn 47: Piṅgala’s samānī – pramāṇī – vitāna classification isn’t satisfactory either.118 0.820 0.900119 0.129 0.219

Fn 47 contd: Because a vṛtta like Vidyunmālā (GGGGGGGG), which has the maximum possible tāna, would be classified as “vitāna” under this classification. Similarly vṛttas that obviously have tāna, like Bhujaṅga-prayāta [LGG×4 in each pāda] and Toṭaka [LLG×4 in each pāda].119 0.215 0.430

Fn 47 contd: Maybe the Piṅgala text available to us is incomplete.119 0.404 0.885

Fn 47 contd: A proper classification would have more, as follows.120 0.131 0.221

Fn 47 contd: Proposes new system:
• ēkatānī = repetition of G (like Vidyunmālā) or L.
• pramāṇī, samānī = repetition of LG or GL respectively.
• daṇḍakī = repetition of length 3 (any of the 8 trika gaṇas other than na=LLL or ma=GGG).
= atidaṇḍakī = repetition of something longer.120 0.215 0.605

I find this clearer with some mathematical terminology. Consider the word – sequence over the alphabet ${\mathsf{L}, \mathsf{G}}$ – obtained by scansion of a padya. If this word is periodic, i.e. if the word $w$ can be written as $w = w_1 w_1 \dots w_1$ for some $w_1$ repeated some number ($>1$) of times, then the metre is called satāna. And the above classification is on the period (the length of $w_1$): period $1$ is ēkatānī, period $2$ is samānī or pramāṇī, period $3$ is daṇḍakī, and period $>3$ is atidaṇḍakī. (Note there are $2$ possible choices of “thing repeated” in ēkatānī, $2$ in {samānī, pramāṇī}, $6$ in daṇḍakī, etc.: the number of different possible “thing repeated” of length $1, 2, 3, 4, \dots$ is $2, 2, 6, 12, \dots$ as in OEIS A027375.)

Fn 47 contd: Examples of each. Good to read and make sure you understand.120 0.601 0.889121 0.133 0.650

Fn 47 contd: Periodic, aperiodic. English has only satāna metres.121 0.650 0.726

Fn 47 contd: All satāna (periodic) are layānvita, and some vitāna ones are too. Other vitāna ones are without laya. (See named examples.)121 0.708 0.881

[TODO(shreevatsa): These are quite easy to understand with some examples. Add them.]

Fn 47 contd: Summary. [This is probably the main thing in this chapter.]122 0.560 0.898

Hints of gati: Piṅgala sometimes suggests how to read/recite.122 0.098 0.232

E.g. for Udgatā, which Halāyudha interprets as “read without pausing between pādas 1 and 2”.122 0.201 0.539

‘L’ at end of pāda 1 is not to be made ‘G’.123 0.106 0.332

But that’s not it!123 0.330 0.491

He means read the whole padya as two halves (not as four separate pādas), with no pause either between pādas 1 and 2 or between 3 and 4.123 0.491 0.657

Read like:
8|8|8|2–
8|8|8|8.123 0.630 0.860

The “incomplete” chunk at the end (catalexis) is for pause. This is almost always seen in layānvita metres.123 0.831 0.888124 0.106 0.210

(Read this carefully to understand.) Has 8–8–8–8, but like mṛdaṅga-playing, has variation.124 0.186 0.424

(Another example, TODO need to look this up to understand.)124 0.418 0.584

Other places where gati is indicated: let’s see example of tanumadhyā124 0.561 0.874

Tanumadhyā, [GGLLGG]×4125 0.099 0.325

When read naturally, reads as:
GGLL | GG— (four times). The laya is apparent only if pausing for 2 mātrās after each pāda. [I wonder: is this really unarguably true? What is natural? Why not —GG|LLGG say? To me it sounds like that may be possible too…]125 0.300 0.605

Thus it’s clear that Piṅgala must have thought about gati. Another point in support: changing yati changes gati, resulting in different vṛttas.125 0.603 0.903

Examples of three vṛttas all having pattern [L14G], but with different yati (and therefore different gati). (We’ll look at a couple)126 0.099 0.307

One:
4|4|4|4
LLLL–LLLL–LLLL–LLG126 0.300 0.407

Another:
6|6|4–
LLLLLL–LLLLLL–LLG. 126 0.402 0.561

So, 4s and 6s respectively: āditāla/ēkatāla, and rūpaka-tāla respectively. [Unfortunately I don’t know enough about tāla, and especially about setting words to tāla, to understand this properly.]126 0.556 0.743

Reiteration126 0.720 0.902

chandas = padya.
What makes a padya distinctive is its gati, not just its laghu-guru-vinyāsa.127 0.106 0.548