Ten weeks at once

The Balinese pawukon: ten concurrent weeks of 1 to 10 days on a 210-day wheel — weeks derived from other weeks, days repeated to make them fit, and no year anywhere. ← Calendar Contraptions

Bali runs two calendars side by side. One is lunar, with months and years — that is the Saka calendar, a cousin of the Indian one. The other is the pawukon, and it has no months, no years and no epoch at all: just a 210-day cycle that runs ten different weeks at the same time — one of 1 day, one of 2, up to one of 10 — so that every single day has ten names at once. The whole thing repeats endlessly, like a carillon: the same 210-day tune, forever. This page takes the machine apart: the reading, the arithmetic that derives some weeks from others, the days the calendar has to repeat to keep all ten wheels turning together — and the place where it quietly pays out the remainder of a division.

The reading

Two weeks make a third

Five of the ten wheels just cycle. But the one-day, two-day and ten-day weeks are not cycles at all — they are computed, out of the five-day and seven-day wheels, using each day's urip, its ritual value. Add the urip of the five-day name to the urip of the seven-day name, add one, and fold over ten. The result picks the ten-day week by value, and its parity picks the two-day and one-day weeks: even is Pepet and Luang, odd is Menga and no day at all.

The ten wheels

Here is the machine's own table, the days around the picked one. Every wheel turns on its own; the thirty seven-day weeks are the wuku, named like chapters.

The stutter days

210 refuses to divide by 4, 8 or 9 — so those three wheels would drift out of step every cycle. The pawukon's fix is to repeat a day. Where the repeats fall, and what they cost, is the most elegant thing in the machine:

The thirty weeks

The seven-day wheel is special: its thirty turns are named, one name per week of seven days — the wuku. When certain five-day and seven-day names coincide, the day is urip in the other sense: a day with weight. Five conjunctions matter, and each returns six times per cycle.

Galungan, every 210 days

The wuku names matter because Bali's biggest celebration is anchored to them. Galungan — when ancestral spirits visit, marked by the bent bamboo penjor poles lining every road — is the Buda-Keliwon of the wuku Dunggulan. Ten days later comes Kuningan, when the spirits return. Every 210 days, forever: some solar years get two Galungans, some only one.

Why 210?

Because 210 is what you get when you refuse to wait. Ten wheels of 1 to 10 days, left to cycle freely, all align again only after LCM(1, 2, …, 10) = 2,520 days — a seven-year "week of weeks". The pawukon does not wait. It builds the cycle on 2 × 3 × 5 × 7 = 210, which every wheel except the 4-, 8- and 9-day ones divides exactly — and for those three it pays a small correction: two borrowed days for the four-day wheel, two for the eight-day, three for the nine-day. Seven borrowed days in total fold 2,520 down to 210. The thirty-five-day pairing of the five- and seven-day wheels — the Javanese call one turn of it a weton — divides 210 exactly six times, which is why the same weekday-and-market pairing comes back like clockwork. The calendar is not a compromise between the wheels; it is a schedule of small payments that keeps them synchronized anyway.

The week that never left

Look at the seven-day wheel's names: Redite, Soma, Anggara, Buda, Wraspati, Sukra, Saniscara — the Sunday-to-Saturday week, carried to Indonesia with Hinduism well over a thousand years ago and never displaced since. Redite is Sunday: on any date you like, the seventh wheel and the Gregorian weekday agree. That agreement is not a convention this page chose; it is a theorem of the machine, and it doubles as the built-in sanity check the Balinese themselves use — if the seventh name is wrong, the counting slipped somewhere.

No year at all

The pawukon has no epoch and no cycle numbers: it is a wheel, not a timeline. To put it on a page at all, someone must choose where cycle day 1 lands. The standard choice, from Dershowitz and Reingold's Calendrical Calculations, is the first cycle starting on a positive Julian Day Number: JDN 146, April 18 in the year 4713 BCE proleptic Gregorian. From there the mapping is one subtraction and one remainder. It sounds arbitrary — and it is — but it is not loose: the machine built on that anchor puts Galungan on every one of the recorded holiday dates for 2018 through 2030, twenty-two out of twenty-two, so the scholarly anchor and the living practice agree to the day. Balinese families even mark the wheel personally: a baby's first complete turn of the cycle, at 210 days, is the oton, a small rite of passage measured in pawukon weeks rather than months.

The other calendar in the room

The pawukon's partner is the Balinese Saka calendar, a lunisolar system whose twelve months are named Kasa, Karo, Katiga — plain ordinals, one to twelve, in Old Balinese and Sanskrit dress. Each month runs from new moon to new moon, with days numbered 1 to 15 waxing and 15 to 1 waning, and a solar day that quietly carries two lunar days every nine weeks (ngunalatri, "minus one night") to keep the months honest. An intercalary month is slipped in after the eleventh or twelfth month whenever the last day of the seventh month would otherwise drift into December. Its years run 78 behind the Gregorian count, and it begins — like the Indian Śaka — with the era of an Indian king. The two calendars divide the work between them: the Saka says where in the year you are, the pawukon says what kind of day it is. The year's quietest day belongs to the Saka: Nyepi, the day of silence, opening the Saka year, when the whole island stops. Everything festive belongs to the pawukon.

A short family tree

The ten-week system is Balinese, but the family is Javanese too: the thirty wuku names and the five-day market week run through Javanese almanacs as well, where the pairing of five-day and seven-day names (the weton) is still consulted for everything from weddings to market days. The thirty names are tradition's own cast list: they begin with Sinta and end with Watugunung — a queen and the king she belongs to, in the story the almanacs tell — and each wuku has its guardian deity, tree and animal in the Javanese books. Where the pawukon came from originally nobody can say precisely; a 210-day cycle with ten interleaved weeks is the kind of machine that could only have been assembled by people who found the seven-day week indispensable and wanted nine more wheels to play with.

Honest limits

The cycle is unnumbered in practice, so the JDN 146 anchor is a scholarly convention — a phase, not a date Balinese tradition records. The mapping below that anchor is arithmetic and needs no convention; above it, this page projects the cycle backward and forward without apology, and the picker is capped at 1583–2500 to keep the arithmetic in territory that has been checked. The day-name table is one reconstruction — the one published in Dershowitz and Reingold and reproduced on the calendar's page — spelled as that source spells it; Balinese and Javanese almanacs differ in small details, and some name a week or a day differently (the eight-day week appears as both Astawara and Asatawara). The Galungan/Kuningan cross-check covers 2018–2030 because that is what the recorded holiday list covers; further out, the machine is exact arithmetic, but practice is anchored by living tradition, not by this page. The wuku's guardian lore and the fortune-telling use of the weton are real and are not attempted here — that is a different kind of knowledge, recorded elsewhere by people who hold it properly.