Patyayini Dasha

What is Patyayini dasha?

Patyayini is a dasha of the Tajika (annual) chart, and the one dasha in the system that is not nakshatra-based. Where Mudda compresses the Vimshottari cycle into the year, Patyayini reads the Varsha Pravesh chart itself: the seven grahas from the Sun to Saturn, together with the ascendant, are ranked by how far each stands into its own sign, and the gaps between those ranks become the periods.

The name comes from the patyamsa — the “deducted degrees” that give each body its share. Because the whole construction is arithmetic on the annual positions, a Patyayini timeline is fully reproducible from a printed ranking, with no reference to the birth star at all.

The four steps

1. Who takes part

“All the planets and the ascendant” — the seven from the Sun to Saturn, plus the lagna. Eight bodies. Rahu and Ketu take no period. The lagna is a participant in every sense the method cares about: it has a longitude and it takes a share.

2. Reduced degrees — the krishamsa

Each body’s longitude with its completed signs removed: the position within its own sign, discarding which sign that is. The list is then sorted ascending — “the planet that has the fewest degrees of all, leaving out the zodiacal signs, should be written down first.”

So a graha at 8°14′ of Leo and one at 8°14′ of Pisces rank identically; only the degree within the sign counts.

3. Deducted degrees — the patyamsa

Successive differences down the sorted list. The first body keeps its own reduced degrees; every later body takes its reduced degrees minus its predecessor’s. “Subtracting the lesser from the greater in order.”

Illustrative shape only — the figures are not from any published table.

4. The scale

“The duration of the year should be divided by the converted sum of the deducted degrees.”

Here the construction pays a dividend that is easy to miss: the sum of the deducted degrees telescopes to the largest reduced degree. Every intermediate value cancels, so the divisor is never a separate measurement — it is simply the last row of the ranking. That is why the whole timeline can be rebuilt from the printed working, and why the periods provably tile the year with no gap and no overlap.

Sub-periods take the same proportions again: a sub-lord’s share of a period is that lord’s share of the year, applied to the period. The order runs in the same krishamsa sequence, starting from the major lord and wrapping — the convention Mudda already uses, so one dasha shape holds across the app.

The boundaries are solved on the Sun, not multiplied out

This is where AstroShruti’s implementation differs from a naive one, and the difference is worth understanding.

Balabhadra’s instruction is explicit about how a period begins:

“The solar days of the periods should be added to [the longitude of] the sun at the time of the revolution of the year, in zodiacal signs and so on. When [the longitude of] the sun equals that, the periods will commence.”

A “solar day” is one degree of the Sun’s travel. So a Tajika year is 360 of them, a month is 30, a day is 1 — and a Patyayini boundary is a daily pravesh at a non-integral degree count. The rule does not convert degrees into days by arithmetic; it converts them through the real Sun.

AstroShruti implements it exactly that way: each boundary is the instant the Sun reaches (Varsha Pravesh Sun) + (accumulated solar days) degrees, found on the ephemeris. An author working without an ephemeris could not do this, which is why the same texts also give the proportions in days.

The fork the source itself names

Balabhadra gives the year as 360 solar days or 365;15,31,30 civil days. These are not interchangeable, because the Sun does not cover a degree in a constant time — it moves faster near perihelion in early January and slower near aphelion in early July.

We measured the difference on a real chart. Running the same proportions as civil days and adding them as clock time puts interior boundaries up to 3.47 days — 83 hours — away from where the Sun actually reaches the stated degree, worst where a period straddles perihelion. And yet both methods agree at the year’s first and last instant to within about fifteen minutes.

That asymmetry is worth stating plainly, because it defeats the obvious check: if you compare two Patyayini calculators by asking does the year start and end in the right place, you are running exactly the test that cannot see this disagreement. Compare an interior boundary instead.

AstroShruti ships the solar form — the one the primary source’s own boundary instruction describes — and carries that choice through to the API and the screen, so you can see the decision rather than wonder why another tool differs.

The working table

Beside the timeline, AstroShruti prints the ranking the dasha is derived from: each body’s longitude, its sign, its krishamsa, its patyamsa, and the solar days that patyamsa scales to. Two columns are worth checking against each other:

• The patyamsa column sums to the largest krishamsa — the telescoping identity above. If a printed table anywhere fails this, one of its rows is wrong.
• The solar days sum to 360, by construction.

Read this way, a Patyayini timeline is not a black box: it is eight subtractions and a proportion, and you can redo all of it on paper.

How to read a Patyayini timeline

• The first period belongs to the body least far into its sign — the one just arrived in a new sign. There is a natural reading here: the year opens under whatever has most recently changed ground.
• A body deep into its sign takes a large patyamsa and therefore a long period, but it arrives late in the year. Position in the sign controls both when and how long.
• Read each lord’s condition in the annual chart — its dignity, its house, and any Ithasala or Ishrafa it holds. A Patyayini period of a lord carrying an applying Ithasala is when that promise delivers.
• Where Patyayini and Mudda point at the same lord over the same stretch, the two independent methods agree, which is the strongest timing signal the annual chart offers.
• Looking ahead to a future year, no period is running now. AstroShruti reports the running lord as none rather than mislabelling a period as live.

Sources, and what is not claimed

Three witnesses agree on every step of the construction:

• Balabhadra, Hayanaratna (1649), ed. and tr. Martin Gansten (Brill, 2020), chapter “The periods (dasha) based on deducted degrees” — the primary text, and the only one of the three that states the boundary rule as a solar longitude.
• K.S. Charak, A Textbook of Varshaphala (UMA Publications) — the same construction expressed in days, with the sub-period rule (major × sub) ÷ year.
• B.V. Raman, Varshaphal — krishamsa to patyamsa to the scaled year, with worked examples.

Raman and Charak state the rule in days; Balabhadra states it in degrees and adds the boundary instruction the other two do not need.

No published Patyayini table has been reproduced here, and none was invented. The illustrative figures above are shaped to show the arithmetic, not copied from any source’s worked chart. AstroShruti’s own regression tests pin its output against itself, so we do not claim to match any particular book’s printed example — only to implement the rule those books state.