Two Weights, Twenty-Five Windows: The Arithmetic Behind a Pancha Pakshi Rating

The first thing to get straight is that your bird is doing two things at once.

It holds a main activity for the whole of a yama, roughly two and a half hours. Inside that block it moves through a sub-activity that changes every few minutes as each of the five birds takes its turn.

Your strength in any given window is a function of both. Not the main activity alone, which is why two windows inside the same block can be worth wildly different amounts. Not the sub-activity alone, which is why the same sub-activity is worth different amounts in different blocks.

The classical sources rank the five activities and the ratios are clean:

An even ladder from one down to a fifth. Nothing exotic.

Multiply the two.

Main activity weight × sub-activity weight = the raw strength of that window.

That is the whole of it. Ruling inside Ruling gives 1.0 × 1.0 = 1.00, the maximum the system can produce. Dying inside Dying gives 0.2 × 0.2 = 0.04, the minimum. Everything else falls between.

We tested this against 219 individual rows drawn from published tables. Every row, without a single exception, is exactly the product of its two weights. There is no fudge factor, no hidden adjustment, no table of special cases.

Twenty-five combinations. Main activity down the side, sub-activity across the top.

Print it. It is the whole system on one card.

Two things fall out of it that are worth saying aloud.

The diagonal is you. Within any yama, your own bird always takes the first sub-slot, and in that slot its sub-activity equals the main activity. So the five bolded cells down the diagonal are the only windows in the day that belong to your own bird. Every other cell is a window in which some other bird is acting, and your strength is being read through it.

The matrix is symmetric. Eating inside Ruling and Ruling inside Eating both come to 0.80. The system does not care which of the two is the larger container. That is a real structural fact and it surprises people who expect the main activity to dominate.

Raw strength is not the final verdict, because it does not yet account for whose window you are sitting in.

Every one of the four off-diagonal windows in a yama belongs to another bird, and that bird stands in one of two relations to yours. It is a friend or it is an enemy. There is no neutral. Which birds are your friends depends on the phase of the Moon, and flips between the waxing and waning halves.

The adjustment is a single step in either direction

• Your own bird (the diagonal): no adjustment.
• A friendly birdone step better.
• An enemy birdone step worse.

Scaling the raw strength to a ten-point ladder and applying that step gives the published verdicts exactly. We checked every distinct combination of strength and relation that appears in the source tables — twenty-five of them — and the model reproduces all twenty-five with no exceptions.

The dashes are not omissions. A raw strength of 1.00 can only ever occur on the diagonal, so it can only ever be your own bird. A strength of 0.80 can only occur off the diagonal, so it is always somebody else's window.

Look at the 0.80 row. Same arithmetic, same two activities, and the verdict swings from Very Good to Good depending on which bird is holding the slot.

Now look further down. At 0.24 the swing is from Average all the way to Very Bad — three full bands on identical arithmetic.

This is the most practically useful thing in the entry. Two windows with the same number are not the same window, and a weaker window can outrank a stronger one. A window at 0.48 held by a friend comes out Good, while a stronger window at 0.60 held by an enemy comes out only Average. Further down the range the effect is starker still: 0.16 with a friend reads Average, while 0.24 with an enemy reads Very Bad.

If you are scanning a table for somewhere to put a difficult conversation, read the relation column before the number.

Suppose your bird is the Vulture, the Moon is waxing, and you are in a yama where the Vulture's main activity is Eating. Four minutes into the second sub-slot you find the Owl walking.

• Main activity, Eating: 0.8
• Sub-activity, Walking: 0.6
• Raw strength: 0.8 × 0.6 = 0.48
• In the waxing half, the Owl is a friend of the Vulture. One step better.
• Verdict: Good

Change one thing. Run the same window in the waning half, when the Owl becomes the Vulture's enemy. Identical arithmetic, 0.48 again, and the verdict drops to Average.

The window did not move. The Moon did.

Not every lineage grades on five bands. The Pulippani-derived tables in circulation use seven — Excellent, Good, Fair, Average, Inadequate, Poor, Worst — and they add something the five-band tables do not have.

In those tables the raw strength is multiplied by a further figure that varies with the bird and with the segment. One published report gives the Crow 1.125 by day and 0.875 by night. Another gives the Vulture 0.844. Every cell in those reports is exactly that figure times the two activity weights, so the underlying multiplication is identical to the one above. There is simply a third number in front of it.

Where the two figures for a single bird are both available, they sum to exactly 2.000. That is one data point and we are not going to build anything on it.

Two things about that second scale we cannot resolve, and we would rather say so.

Nobody has told us where the multiplier comes from. Neither source explains how 1.125 or 0.844 is arrived at. They are simply present.

The seven bands are not reproducible. In one report a Ruling-Ruling window scoring 1.125 is graded Excellent, while a Ruling-Ruling window scoring 0.875 in the same report is graded only Fair. In another report a window scoring 0.844 is graded Excellent. No single threshold explains all three. Worse, the accompanying text states that the Ruling-Ruling combination produces an Excellent window twice a day, once by day and once by night — and the report's own night table contradicts it.

To be clear about what is and is not in dispute there: your bird does reach Ruling inside Ruling exactly twice in every twenty-four hours, once in each segment, and that follows from the structure of the day rather than from anyone's table. What is unresolved is only how that window gets labelled on the seven-band scale.

We are not saying the seven-band scale is wrong. We are saying that from the material we hold, we cannot derive it, and neither can anyone else working from the same material. The five-band scale we set out above is fully determined and we verified it on every row we had.

Most of what is written about Pancha Pakshi asks you to accept a table. This entry asks you to check one.

The distinction is not academic. A system whose ratings can be recomputed by hand from two numbers is a system that can be audited, argued with, and corrected. A system whose ratings arrive as pronouncements cannot be. The Tamil material has the first kind of structure underneath it, and it is worth surfacing, because it is the strongest thing about the subject and it has been almost entirely buried.

You now have the bird, the two layers of the day, and the arithmetic that grades every window in it.

The obvious next question is a practical one. You already have Rāhu Kāla, Choghadiya and the planetary hora, and all of them will happily give you an opinion about three o'clock this afternoon. When they disagree with your Pancha Pakshi table, which one wins? The next entry answers that, and the answer is cleaner than you would expect.

The argument of this entry is that a Pancha Pakshi rating is auditable — two weights multiplied, adjusted one step for friend or enemy, and nothing hidden. That argument is only worth something if you have a real table in front of you to run it against.

Navashi is our panchāng app. It carries your Pancha Pakshi reading built from your own sunrise and sunset, alongside the full daily reckoning — tithi, nakshatra, muhurats, choghadiya, and festivals across eight calendar traditions.

• iPhone and iPad — Navashi on the App Store
• Android — Navashi on Google Play

Then do the thing this entry is actually for. Take a window off the screen, find its main and sub activities, multiply the two weights from the matrix above, and apply the single step for friend or enemy. If the verdict you compute does not match the one you are shown, we would much rather hear about it than not.