In the Double-Month Calendar or, more precisely, Double-Month Week Calendar (DMWC), the year is divided into 6 sesters, alias sextals, bimesters or double-months, each of which contains a whole number of weeks in a pattern of 9:9:8, i.e. there are either 56 or 63 days in a bim.

## Notation

The ISO-like date format is `±YYYY-S-W-D`. The calendar is compatible with that standard as far as possible, e.g. weeks begin on Monday. For example, today is 2024-4-2-5, the same as 2024-W28-5 or, less obviously, 2024-07-12.

If disambiguation with similar schemes is required, e.g. from Octalendar’s `±YYYY-M-W-D` with 6–7-week months, the sester number may be prefixed by a single-letter marker `B` for bimonth, e.g. 2024-B4-2-5. The more intuitive choice `S` was avoided because it may more readily be associated with a quarter-year season, as in the International Calendar, or a 6-month, half-year semester. The hyphen separators are optional then, 2024B425. With just three digits, this notation is more efficient than most commonly used ones that use at least 4 digits.

## Leap week

The leap week is appended to the last sextal at the end of the year; that means only the third sester has just 8 weeks then, all the others have 9 weeks. This avoids a 10-week bim and is the reason for choosing the pattern 9:9:8 over 9:8:9 or 8:9:9.

This happens in exactly the same years that have a W53 by ISO rules. Unfortunately this is a very complex and seemingly irregular pattern with no simple algorithm.

## Subdivision variants

Each sextal can be matched by two months of 4 or 5 weeks exactly. The possible patterns for half a year, i.e. three consecutive sextals, are

• 5:4 : 5:4 : 4:4,
• 5:4 : 4:5 : 4:4,
• 4:5 : 5:4 : 4:4 and
• 4:5 : 4:5 : 4:4.

The last one could be dubbed “4:5*” and is harmonic for the second half of the leap year. The second one, on the other hand, is equivalent to the 5:4:4 pattern, ensuring that there are never 3 consecutive short months with just 4 weeks each. Both of these preferable patterns align well with 13-week quarters. The “symmetric” week-month pattern 4:5:4 would yield a different pattern for sextals, 9:8:9, and 4:4:5 would result in another, 8:9:9.

Relation to other leap week calendars
Week 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
13mon Janon Febron Marchon Apron Mayon Junion Extron Julon Augon Septon Octon Novon Decon †
5:4:4 Janaire Febraire Marchose Aprilose Mayose Junal Julial Augial Septidor Octidor Novidor Decaire †
4:5:4 Janose Febrose Aprial Mayal Julidor Augidor Octaire Novaire
4:4:5 Febral Marchal Maydor Junidor Augaire Septaire Novose Decose †
Quarter quart 1 quart 2 quart 3 quart 4
7:6 Bol Sar Tan Lit Nas Mon Sam Yul †
4:5* Janose Febrose Marchose Aprilose Mayose Junal Julidor Augidor Septidor Octidor Novidor Decaire †
9:9:8 sester 1 sester 2 sester 3 sester 4 sester 5 sester 6
5:5:6:5 Primoth Secoth Tertoth Quaroth Quintoth Sixtoth Septoth Octoth Novoth Decoth †
10:11 quinter 1 quinter 2 quinter 3 quinter 4 quinter 5
8:7 Monmonth Tuesmonth Wednesmonth Thursmonth Frimonth Saturmonth Sunmonth †
Terms Spring semester Summer break Fall semester
Winter semester Spring break Summer semester Fall break Winter semester
Epiphany/Hilary trimester Trinity trimester Summer break Michaelmas trimester