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Marian / Appendix B: Marian Calendar Tables

B - Marian Calendar Tables

Common and Leap Year Structures

B.1 Purpose

This appendix provides the principal structural tables for the Marian Calendar.

It shows the two regular annual templates, the twelve months, twenty-four minths, four quarters, six Sixths and the valid weekday positions at shortened terminal weeks. The tables are derived from the normative rules in Appendix A and are intended as a practical reference for readers, software implementers and future standards work.

Unless otherwise stated, ordinal sol numbers begin with Sol 1 on the first sol of the Marian year.

MY0 is excluded because it is a transitional epoch interval rather than a regular Marian year.

B.2 The two annual templates

Marian has only two regular year forms.

Table 1 in Appendix B: Marian Calendar Tables
PropertyCommon yearLeap year
Total sols668669
Months1212
Minths2424
Sixths66
Quarters44
Nominal week positions9696
56-sol months89
55-sol months43
28-sol minths2021
27-sol minths43
Six-position terminal civil weeks43

The common-year month pattern is:

56 – 56 – 55 | 56 – 56 – 55 | 56 – 56 – 55 | 56 – 56 – 55

The leap-year pattern differs only at the final position:

56 – 56 – 55 | 56 – 56 – 55 | 56 – 56 – 55 | 56 – 56 – 56

The additional leap sol is therefore the final sol of Month 12. Nothing earlier in the annual template changes.

B.3 The twelve months

The following table gives the complete month structure. Because Months 1 through 11 are identical in common and leap years, separate ordinal ranges are required only for the final endpoint of Month 12.

Table 2 in Appendix B: Marian Calendar Tables
MonthQuarterSixthMinthsCommon lengthLeap lengthOrdinal sols
1Q1S101–0256561–56
2Q1S103–04565657–112
3Q1S205–065555113–167
4Q2S207–085656168–223
5Q2S309–105656224–279
6Q2S311–125555280–334
7Q3S413–145656335–390
8Q3S415–165656391–446
9Q3S517–185555447–501
10Q4S519–205656502–557
11Q4S621–225656558–613
12Q4S623–245556614–668 / 614–669

The recurring common-year pattern can also be read quarter by quarter:

Table 3 in Appendix B: Marian Calendar Tables
QuarterMonth patternLength
Q156 – 56 – 55167
Q256 – 56 – 55167
Q356 – 56 – 55167
Q456 – 56 – 55167

In a leap year, Q4 becomes:

56 – 56 – 56 = 168 sols

B.4 The twenty-four minths

Each Marian month contains two minths. The first minth always contains 28 sols. The second contains 28 sols in a 56-sol month and 27 sols in a 55-sol month.

Table 4 in Appendix B: Marian Calendar Tables
MinthShorthandMonthLength: commonLength: leapOrdinal sols
01A128281–28
02B1282829–56
03C2282857–84
04D2282885–112
05E32828113–140
06F32727141–167
07G42828168–195
08H42828196–223
09I52828224–251
10J52828252–279
11K62828280–307
12L62727308–334
13M72828335–362
14N72828363–390
15O82828391–418
16P82828419–446
17Q92828447–474
18R92727475–501
19S102828502–529
20T102828530–557
21U112828558–585
22V112828586–613
23W122828614–641
24X122728642–668 / 642–669

The four shortened common-year minths are therefore:

Illustration: The Marian Calendar. Expanded text description follows.
The Marian Calendar
Detailed figure description

A printed-style annual calendar lays out twelve named Marian months in a multi-panel grid. The recurring seven weekday headings and numeric positions illustrate how months reuse stable weekly layouts. The 55-sol months terminate after the sixth weekday position in the final week, while longer months include the seventh. The exact integer year template is specified in Appendix B; the illustration is a visual reading aid.

Editorial note: this is a descriptive summary, not an independently verified transcription of every diagram label. Refer to the surrounding text and the Marian technical specification for authoritative numeric details where applicable.

06 · 12 · 18 · 24

In a leap year, Minth 24 gains the leap sol and contains 28 sols. The shortened leap-year minths are therefore:

06 · 12 · 18

Every minth begins at weekday position 1.

B.5 Quarters

The four Marian quarters divide the twelve-month annual frame into four groups of three months.

Table 5 in Appendix B: Marian Calendar Tables
QuarterNameMonthsMinthsCommon solsLeap solsOrdinal range
Q1Primiv1–301–061671671–167
Q2Secondiv4–607–12167167168–334
Q3Tertiv7–913–18167167335–501
Q4Quartiv10–1219–24167168502–668 / 502–669

Every common-year quarter therefore has the same internal month pattern:

56 + 56 + 55 = 167 sols

The leap sol belongs to Q4 only.

B.6 Sixths

The six Marian Sixths divide the annual frame into six groups of two months.

Table 6 in Appendix B: Marian Calendar Tables
SixthNameMonthsMinthsCommon solsLeap solsOrdinal range
S1Primus1–201–041121121–112
S2Secundus3–405–08111111113–223
S3Tertius5–609–12111111224–334
S4Quartus7–813–16112112335–446
S5Quintus9–1017–20111111447–557
S6Sextus11–1221–24111112558–668 / 558–669

The common-year Sixth pattern is therefore:

112 – 111 – 111 – 112 – 111 – 111

The leap-year pattern is:

112 – 111 – 111 – 112 – 111 – 112

Quarters and Sixths are independent annual grids. Their boundaries coincide only where the month grouping happens to make them coincide.

B.7 Week structure within a month

Every Marian month contains eight nominal civil weeks.

A 56-sol month consists of eight complete seven-position weeks:

Table 7 in Appendix B: Marian Calendar Tables
WeekMonth solsValid weekday positions
11–71–7
28–141–7
315–211–7
422–281–7
529–351–7
636–421–7
743–491–7
850–561–7

A 55-sol month differs only in its final civil week:

Table 8 in Appendix B: Marian Calendar Tables
WeekMonth solsValid weekday positions
11–71–7
28–141–7
315–211–7
422–281–7
529–351–7
636–421–7
743–491–7
850–551–6

The seventh weekday position of Week 8 does not exist in a 55-sol month.

The following month nevertheless begins at:

Week 1 · Day 1

The physical sequence of sols remains continuous. Only the seventh weekday label is absent from the shortened terminal civil week.

B.8 Week structure within a minth

A 28-sol minth consists of four complete seven-position weeks:

7 + 7 + 7 + 7 = 28 sols

A 27-sol minth consists of:

7 + 7 + 7 + 6 = 27 sols

The final week of a 27-sol minth therefore contains weekday positions 1 through 6 only.

Table 9 in Appendix B: Marian Calendar Tables
Minth lengthWeeks 1–3Week 4
28 solsPositions 1–7Positions 1–7
27 solsPositions 1–7Positions 1–6

Because shortened minths occur only as the second minth of a shortened month, the missing seventh position is simultaneously:

Minth Week 4 · Day 7

and:

Month Week 8 · Day 7

It is one absent civil position described at two structural scales.

B.9 Terminal-week validity by month

For most dates, Marian validity is straightforward: Weeks 1 through 7 of every month contain all seven weekday positions. Only Week 8 · Day 7 can vary.

Table 10 in Appendix B: Marian Calendar Tables
MonthCommon year W8·D7Leap year W8·D7Result
1ValidValidMonth contains 56 sols
2ValidValidMonth contains 56 sols
3InvalidInvalidMonth ends at W8·D6
4ValidValidMonth contains 56 sols
5ValidValidMonth contains 56 sols
6InvalidInvalidMonth ends at W8·D6
7ValidValidMonth contains 56 sols
8ValidValidMonth contains 56 sols
9InvalidInvalidMonth ends at W8·D6
10ValidValidMonth contains 56 sols
11ValidValidMonth contains 56 sols
12InvalidValidLeap-sol position

The only civil date whose validity depends upon leap status is therefore:

Month 12 · Week 8 · Day 7

That position is the Marian leap sol.

B.10 Terminal transitions

The end of every 56-sol month is:

Month n · Week 8 · Day 7

followed by:

Month n+1 · Week 1 · Day 1

The end of every 55-sol month is:

Month n · Week 8 · Day 6

followed immediately by:

Month n+1 · Week 1 · Day 1

The physical sol following Day 6 therefore receives the first weekday label of the new month rather than the unused seventh label of the old one.

For the four common-year quarter boundaries:

Table 11 in Appendix B: Marian Calendar Tables
BoundaryFinal date before boundaryNext date
Q1 → Q2M3 · W8 · D6M4 · W1 · D1
Q2 → Q3M6 · W8 · D6M7 · W1 · D1
Q3 → Q4M9 · W8 · D6M10 · W1 · D1
Q4 → next yearM12 · W8 · D6Next MY · M1 · W1 · D1

In a leap year, the final transition differs:

M12 · W8 · D7 → next MY · M1 · W1 · D1

This is why every regular Marian year, month and minth begins at weekday position 1 despite the physical year containing 668 or 669 sols rather than an integer number of ordinary seven-sol weeks.

B.11 Common-year terminal positions

The four shortened terminal civil weeks in a common year occur at:

Table 12 in Appendix B: Marian Calendar Tables
LocationOrdinal sols in terminal weekLast valid positionMissing position
Month 3, Week 8162–167Day 6 = Sol 167Day 7
Month 6, Week 8329–334Day 6 = Sol 334Day 7
Month 9, Week 8496–501Day 6 = Sol 501Day 7
Month 12, Week 8663–668Day 6 = Sol 668Day 7

The corresponding shortened minths are:

Table 13 in Appendix B: Marian Calendar Tables
MinthOrdinal rangeFinal valid position
06141–167Week 4 · Day 6
12308–334Week 4 · Day 6
18475–501Week 4 · Day 6
24642–668Week 4 · Day 6

B.12 Leap-year terminal positions

A leap year restores the final weekday position of Month 12 only.

The shortened terminal civil weeks are therefore:

Table 14 in Appendix B: Marian Calendar Tables
LocationOrdinal sols in terminal weekLast valid positionMissing position
Month 3, Week 8162–167Day 6 = Sol 167Day 7
Month 6, Week 8329–334Day 6 = Sol 334Day 7
Month 9, Week 8496–501Day 6 = Sol 501Day 7
Month 12, Week 8663–669Day 7 = Sol 669None

The final minth changes accordingly:

Table 15 in Appendix B: Marian Calendar Tables
MinthCommon yearLeap year
2427 sols; ends W4·D628 sols; ends W4·D7

Thus:

MY leap sol = Month 12 · Minth 24 · Month Week 8 · Minth Week 4 · Day 7 · Ordinal Sol 669

These are different coordinate descriptions of the same physical sol.

B.13 Common-year structure at a glance

The complete common-year annual frame is:

Table 16 in Appendix B: Marian Calendar Tables
QuarterMonthsMonth lengthsSixths crossing regionMinthsOrdinal sols
Q11–356 · 56 · 55S1, part of S201–061–167
Q24–656 · 56 · 55part of S2, S307–12168–334
Q37–956 · 56 · 55S4, part of S513–18335–501
Q410–1256 · 56 · 55part of S5, S619–24502–668

In compact form:

12 months:
56 – 56 – 55 | 56 – 56 – 55 | 56 – 56 – 55 | 56 – 56 – 55

24 minths:
28 – 28 · 28 – 28 · 28 – 27 |
28 – 28 · 28 – 28 · 28 – 27 |
28 – 28 · 28 – 28 · 28 – 27 |
28 – 28 · 28 – 28 · 28 – 27

6 Sixths:
112 – 111 – 111 – 112 – 111 – 111

4 quarters:
167 – 167 – 167 – 167

Total:
668 sols

B.14 Leap-year structure at a glance

The leap-year annual frame is identical until the final civil position:

Table 17 in Appendix B: Marian Calendar Tables
QuarterMonthsMonth lengthsMinthsOrdinal sols
Q11–356 · 56 · 5501–061–167
Q24–656 · 56 · 5507–12168–334
Q37–956 · 56 · 5513–18335–501
Q410–1256 · 56 · 5619–24502–669

In compact form:

12 months:
56 – 56 – 55 | 56 – 56 – 55 | 56 – 56 – 55 | 56 – 56 – 56

24 minths:
28 – 28 · 28 – 28 · 28 – 27 |
28 – 28 · 28 – 28 · 28 – 27 |
28 – 28 · 28 – 28 · 28 – 27 |
28 – 28 · 28 – 28 · 28 – 28

6 Sixths:
112 – 111 – 111 – 112 – 111 – 112

4 quarters:
167 – 167 – 167 – 168

Total:
669 sols

B.15 Date-validity quick reference

A regular Marian date is structurally valid if all of the following are true:

Table 18 in Appendix B: Marian Calendar Tables
ComponentValid range / rule
Month1–12
Month week1–8
Weekday position1–7, subject to terminal-week rule
Minth01–24
Minth within month1 or 2
Minth week1–4
QuarterQ1–Q4
SixthS1–S6
Ordinal sol1–668 common; 1–669 leap

For Month Week 8 · Day 7, apply one additional test:

Equivalently, for a minth date:

No other weekday position changes validity between the two regular annual templates.

B.16 The whole architecture in one line

For reference, the common Marian year can be reconstructed from a remarkably small set of relationships:

A common year has 668 sols, arranged as 12 months (56–56–55 ×4), 24 minths, 6 Sixths and 4 quarters.

and the leap year by one additional instruction:

restore the final Day 7 of Month 12 → 669 sols

Everything else in these tables follows from those two statements.