# New Roman Lunisolar Calendar

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**New Roman Lunisolar Calendar** is a fictional calendar invented by Hellerick in 2008. The Calendar is inspired by the ancient 10-month Roman calendar and is an attempt to make it regular and suitable for long-term use.

## Structure of the year Edit

The “core” of the year consist of ten 30-day months. These months are adjusted in relation to the moon phase, and in theory the night between the first five months and the second five months of the core should be the new moon closest to the southern solstice (and therefore close to the new year in the Attic calendar). While the middle months are well adjusted, the peripheral months somewhat drift from the close correspondence between the day number and the moon phase (up to three day difference).

The rest of the year is the winter period known as *Brumiae* (“yules”) and is divided into two equal (or nearly equal) months. The Brumias can be either long (84 days) or short (54 or 55 days), and therefore their months can have either 42 or 27-28 days.

The beginning of the year is located between the two months of Brumias, and therefore falls on either new moon or full moon closest to the northern solstice. When the Brumias are short, the year begins on new moon; when the Brumias are long, the year begins on full moon.

The table below shows the month names and, their lengths, and the date span in Gregorian Calendar in which the first day of the month of the New Roman Lunisolar Calendar for recent years:

Februariae | 27 or 42 days | Dec. 12–Dec. 31 |

Martiae | 30 days | Jan. 8–Feb. 7 |

Apriliae | 30 days | Feb. 7–Mar. 9 |

Maiae | 30 days | Mar. 9–Apr. 8 |

Juniae | 30 days | Apr. 8–May. 8 |

Quintiliae | 30 days | May 8–June 7 |

Sextiliae | 30 days | June 7–July 7 |

Septembiae | 30 days | July 7–Aug. 6 |

Octobriae | 30 days | Aug. 6–Sep. 5 |

Novembriae | 30 days | Sep. 5–Oct. 5 |

Decembriae | 30 days | Oct. 5–Nov. 4 |

Januariae | 27, 28, or 42 days | Nov. 4–Dec. 4 |

### Naming conventions Edit

Six months’ names are derived from Latin numerals denoting the months’ position within the “core” of the year, e.g. *Sextiliae* is the sixth 30-day month, *Decembriae* the tenth etc. The month names look familiar, but in fact they are about 1.5 months fast in relation to the Gregorian calendar.

Strictly speaking, the months have no names of their own. Words like *Februariae* are in fact plurals, while a singular form *Februaria* means something like “a day of the first month of the year”; i.e. not the months but their days have special names denoting their position within the year. In English the month names are usually rendered as *Februarias*, *Martias*, *Aprilias* etc. (“The consuls’ term ends in the next Quintilias.”). The days of the month are named in the next style: “the first Maia, the second Maia, ... the 30th Maia”. To mention not the days of the month, but the month itself, you have to use an expression like *Apriliarum mensis* (“the month of Aprilias”), e.g. “every *Sextiliarum mensis* the Phrygians had to pay tribute”.

The terms like *calendae*, *nonae*, and *idae* are mostly discarded, and when used, denote the days of the actual moon phases, and aren't bound to some specified days of the months.

## Rules Edit

The calendar is based on 334-year cycle.

- 334 years = 4131 lunar months = 4008 calendarical months = 121991 days

It gives average year of 365.2425 days, and average lunar month of 29.53062 days. In theory once in ten cycles (i.e. once in 3340 years) one day should be dropped (which would give the values 365.2422 and 29.53060), but in practice no rules for it were developed.

The 334-year contains 123 long Brumias (corresponding to three lunar months) and 211 short Brumias (corresponding to two lunar months).

The next mathematical conditions determine the length of Brumias (in Pascal-style notation):

`Y mod 334 mod 19 mod 11 mod 3 = 0`: Januarias are long (42 days), otherwise they are short (27 or 28 days).`Y mod 334 mod 19 mod 11 mod 3 = 1`: Februarias are long (42 days), otherwise they are short (27 days).

Note: long Februarias always follow the long Januarias, and short Februarias always follow the short Januarias.

The short Januarias are leap, i.e. have 28 days instead of 27, when the next condition is true:

`(4 * (Y mod 334) - 2 * (int(Y mod 334) / 19) - 3 * (int(Y mod 334 mod 19) / 11) - 4 * (int(Y mod 334 mod 19 mod 11) / 3) - 4) mod 13 < 4`

The leap day is called *Brumia intercalaris*, and sometimes is not considered one of the Januarias, but a special “independent” day instead.

The table below shows the lengths of Januarias within 334 year cycle resulting from the formulas above:

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | |

0+ | 42 | 28 | 27 | 42 | 27 | 27 | 42 | 28 | 27 | 42 | 27 | 42 | 28 | 27 | 42 | 27 | 28 | 42 | 27 |

19+ | 42 | 27 | 28 | 42 | 27 | 27 | 42 | 27 | 28 | 42 | 27 | 42 | 27 | 28 | 42 | 27 | 27 | 42 | 28 |

38+ | 42 | 27 | 27 | 42 | 28 | 27 | 42 | 27 | 27 | 42 | 28 | 42 | 27 | 27 | 42 | 28 | 27 | 42 | 27 |

57+ | 42 | 28 | 27 | 42 | 27 | 28 | 42 | 27 | 27 | 42 | 27 | 42 | 28 | 27 | 42 | 27 | 28 | 42 | 27 |

76+ | 42 | 27 | 28 | 42 | 27 | 27 | 42 | 28 | 27 | 42 | 27 | 42 | 27 | 28 | 42 | 27 | 27 | 42 | 28 |

95+ | 42 | 27 | 27 | 42 | 28 | 27 | 42 | 27 | 28 | 42 | 27 | 42 | 27 | 27 | 42 | 28 | 27 | 42 | 27 |

114+ | 42 | 28 | 27 | 42 | 27 | 28 | 42 | 27 | 27 | 42 | 28 | 42 | 27 | 27 | 42 | 27 | 28 | 42 | 27 |

133+ | 42 | 27 | 28 | 42 | 27 | 27 | 42 | 28 | 27 | 42 | 27 | 42 | 28 | 27 | 42 | 27 | 27 | 42 | 28 |

152+ | 42 | 27 | 27 | 42 | 28 | 27 | 42 | 27 | 28 | 42 | 27 | 42 | 27 | 28 | 42 | 27 | 27 | 42 | 27 |

171+ | 42 | 28 | 27 | 42 | 27 | 28 | 42 | 27 | 27 | 42 | 28 | 42 | 27 | 27 | 42 | 28 | 27 | 42 | 27 |

190+ | 42 | 27 | 28 | 42 | 27 | 27 | 42 | 28 | 27 | 42 | 27 | 42 | 28 | 27 | 42 | 27 | 28 | 42 | 27 |

209+ | 42 | 27 | 27 | 42 | 28 | 27 | 42 | 27 | 28 | 42 | 27 | 42 | 27 | 28 | 42 | 27 | 27 | 42 | 28 |

228+ | 42 | 27 | 27 | 42 | 27 | 28 | 42 | 27 | 27 | 42 | 28 | 42 | 27 | 27 | 42 | 28 | 27 | 42 | 27 |

247+ | 42 | 28 | 27 | 42 | 27 | 27 | 42 | 28 | 27 | 42 | 27 | 42 | 28 | 27 | 42 | 27 | 28 | 42 | 27 |

266+ | 42 | 27 | 28 | 42 | 27 | 27 | 42 | 27 | 28 | 42 | 27 | 42 | 27 | 28 | 42 | 27 | 27 | 42 | 28 |

285+ | 42 | 27 | 27 | 42 | 28 | 27 | 42 | 27 | 27 | 42 | 28 | 42 | 27 | 27 | 42 | 28 | 27 | 42 | 27 |

304+ | 42 | 28 | 27 | 42 | 27 | 28 | 42 | 27 | 27 | 42 | 27 | 42 | 28 | 27 | 42 | 27 | 28 | 42 | 27 |

323+ | 42 | 27 | 28 | 42 | 27 | 27 | 42 | 28 | 27 | 42 | 27 |

Year length varies between 354 and 370 days. The 334-year cycle has:

- 61 years of 354 days (27+30×10+27)
- 27 years of 355 days (27+30×10+28)
- 208 years of 369 days (42+30×10+27 and 27+30×10+42)
- 38 years of 370 days (42+30×10+28)

## Epoch Edit

The calendar uses *ab urbe condita* (AUC) era. The first Februaria of the of the first year “after the founding of the city” is fixed on the full moon, January 1st, 752 BCE in Proleptic Julian calendar, or December 24th, 753 BCE in Proleptic Gregorian calendar.

The table below shows correspondence between the first days of the months of the New Roman Lunisolar Calendar, and the dates in Gregorian Calendar for recent years:

AUC | CE | 1, Febr. | 2, Mart. | 3, Apr. | 4, Mai. | 5, Jun. | 6, Quin. | 7, Sext. | 8, Sept. | 9, Oct. | 10, Nov. | 11, Dec. | 12, Jan. | LF | LJ | LY |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

2742 | 1990 | 12/28 | 1/24 | 2/23 | 3/25 | 4/24 | 5/24 | 6/23 | 7/23 | 8/22 | 9/21 | 10/21 | 11/20 | 27 | 27 | 354 |

2743 | 1991 | 12/17 | 1/13 | 2/12 | 3/14 | 4/13 | 5/13 | 6/12 | 7/12 | 8/11 | 9/10 | 10/10 | 11/09 | 27 | 42 | 369 |

2744 | 1992 | 12/21 | 2/01 | 3/02 | 4/01 | 5/01 | 5/31 | 6/30 | 7/30 | 8/29 | 9/28 | 10/28 | 11/27 | 42 | 27 | 369 |

2745 | 1993 | 12/24 | 1/20 | 2/19 | 3/21 | 4/20 | 5/20 | 6/19 | 7/19 | 8/18 | 9/17 | 10/17 | 11/16 | 27 | 28 | 355 |

2746 | 1994 | 12/14 | 1/10 | 2/09 | 3/11 | 4/10 | 5/10 | 6/09 | 7/09 | 8/08 | 9/07 | 10/07 | 11/06 | 27 | 42 | 369 |

2747 | 1995 | 12/18 | 1/29 | 2/28 | 3/30 | 4/29 | 5/29 | 6/28 | 7/28 | 8/27 | 9/26 | 10/26 | 11/25 | 42 | 27 | 369 |

2748 | 1996 | 12/22 | 1/18 | 2/17 | 3/18 | 4/17 | 5/17 | 6/16 | 7/16 | 8/15 | 9/14 | 10/14 | 11/13 | 27 | 42 | 369 |

2749 | 1997 | 12/25 | 2/05 | 3/07 | 4/06 | 5/06 | 6/05 | 7/05 | 8/04 | 9/03 | 10/03 | 11/02 | 12/02 | 42 | 27 | 369 |

2750 | 1998 | 12/29 | 1/25 | 2/24 | 3/26 | 4/25 | 5/25 | 6/24 | 7/24 | 8/23 | 9/22 | 10/22 | 11/21 | 27 | 28 | 355 |

2751 | 1999 | 12/19 | 1/15 | 2/14 | 3/16 | 4/15 | 5/15 | 6/14 | 7/14 | 8/13 | 9/12 | 10/12 | 11/11 | 27 | 42 | 369 |

2752 | 2000 | 12/23 | 2/03 | 3/04 | 4/03 | 5/03 | 6/02 | 7/02 | 8/01 | 8/31 | 9/30 | 10/30 | 11/29 | 42 | 27 | 369 |

2753 | 2001 | 12/26 | 1/22 | 2/21 | 3/23 | 4/22 | 5/22 | 6/21 | 7/21 | 8/20 | 9/19 | 10/19 | 11/18 | 27 | 27 | 354 |

2754 | 2002 | 12/15 | 1/11 | 2/10 | 3/12 | 4/11 | 5/11 | 6/10 | 7/10 | 8/09 | 9/08 | 10/08 | 11/07 | 27 | 42 | 369 |

2755 | 2003 | 12/19 | 1/30 | 3/01 | 3/31 | 4/30 | 5/30 | 6/29 | 7/29 | 8/28 | 9/27 | 10/27 | 11/26 | 42 | 28 | 370 |

2756 | 2004 | 12/24 | 1/20 | 2/19 | 3/20 | 4/19 | 5/19 | 6/18 | 7/18 | 8/17 | 9/16 | 10/16 | 11/15 | 27 | 27 | 354 |

2757 | 2005 | 12/12 | 1/08 | 2/07 | 3/09 | 4/08 | 5/08 | 6/07 | 7/07 | 8/06 | 9/05 | 10/05 | 11/04 | 27 | 42 | 369 |

2758 | 2006 | 12/16 | 1/27 | 2/26 | 3/28 | 4/27 | 5/27 | 6/26 | 7/26 | 8/25 | 9/24 | 10/24 | 11/23 | 42 | 27 | 369 |

2759 | 2007 | 12/20 | 1/16 | 2/15 | 3/17 | 4/16 | 5/16 | 6/15 | 7/15 | 8/14 | 9/13 | 10/13 | 11/12 | 27 | 42 | 369 |

2760 | 2008 | 12/24 | 2/04 | 3/05 | 4/04 | 5/04 | 6/03 | 7/03 | 8/02 | 9/01 | 10/01 | 10/31 | 11/30 | 42 | 27 | 369 |

2761 | 2009 | 12/27 | 1/23 | 2/22 | 3/24 | 4/23 | 5/23 | 6/22 | 7/22 | 8/21 | 9/20 | 10/20 | 11/19 | 27 | 28 | 355 |

2762 | 2010 | 12/17 | 1/13 | 2/12 | 3/14 | 4/13 | 5/13 | 6/12 | 7/12 | 8/11 | 9/10 | 10/10 | 11/09 | 27 | 42 | 369 |

2763 | 2011 | 12/21 | 2/01 | 3/03 | 4/02 | 5/02 | 6/01 | 7/01 | 7/31 | 8/30 | 9/29 | 10/29 | 11/28 | 42 | 27 | 369 |

2764 | 2012 | 12/25 | 1/21 | 2/20 | 3/21 | 4/20 | 5/20 | 6/19 | 7/19 | 8/18 | 9/17 | 10/17 | 11/16 | 27 | 27 | 354 |

2765 | 2013 | 12/13 | 1/09 | 2/08 | 3/10 | 4/09 | 5/09 | 6/08 | 7/08 | 8/07 | 9/06 | 10/06 | 11/05 | 27 | 42 | 369 |

2766 | 2014 | 12/17 | 1/28 | 2/27 | 3/29 | 4/28 | 5/28 | 6/27 | 7/27 | 8/26 | 9/25 | 10/25 | 11/24 | 42 | 28 | 370 |

2767 | 2015 | 12/22 | 1/18 | 2/17 | 3/19 | 4/18 | 5/18 | 6/17 | 7/17 | 8/16 | 9/15 | 10/15 | 11/14 | 27 | 42 | 369 |

2768 | 2016 | 12/26 | 2/06 | 3/07 | 4/06 | 5/06 | 6/05 | 7/05 | 8/04 | 9/03 | 10/03 | 11/02 | 12/02 | 42 | 27 | 369 |

2769 | 2017 | 12/29 | 1/25 | 2/24 | 3/26 | 4/25 | 5/25 | 6/24 | 7/24 | 8/23 | 9/22 | 10/22 | 11/21 | 27 | 27 | 354 |

2770 | 2018 | 12/18 | 1/14 | 2/13 | 3/15 | 4/14 | 5/14 | 6/13 | 7/13 | 8/12 | 9/11 | 10/11 | 11/10 | 27 | 42 | 369 |

2771 | 2019 | 12/22 | 2/02 | 3/04 | 4/03 | 5/03 | 6/02 | 7/02 | 8/01 | 8/31 | 9/30 | 10/30 | 11/29 | 42 | 28 | 370 |

2772 | 2020 | 12/27 | 1/23 | 2/22 | 3/23 | 4/22 | 5/22 | 6/21 | 7/21 | 8/20 | 9/19 | 10/19 | 11/18 | 27 | 27 | 354 |

The first two columns are year numbers in *ab urbe condita* and Common eras (please note that New Roman year begins in December of the previous Gregorian year, e.g. 2760 AUC starts on 2007-12-24 CE and not in 2008). The next twelve columns show the months/days of the Gregorian calendar, on which the New Roman months begin. *LF* and *LJ* columns show the length of that year's Februarias and Januarias (all the other months are 30 days long). The last column shows the length of the New Roman year.

## Market week Edit

The calendar is designed to be used with 6-day market week. The days of the week are identified by a letter of the Latin Alphabet (A through F). There are no “days off” in the market week, but different kinds of activity and legal actions are assigned to its days. This assignment is flexible, and the government, every city, organization etc. may decide what these activities are. The Day F is usually considered the market day. A particular market may decide on a different day to operate though.

The *Brumia intercalaris* (the 28th Januaria of short Brumias), which occurs roughly once in five years, is not considered part of any week, and no weekday is assigned to it.

Every month except short Februarias begins on Day A; short Februarias begin on Day D. Most months consist of 5 weeks, long months consist of 7 weeks, short months consist of 4.5 weeks, i.e. the middle week of short Brumias is divided between the two years: three days (A, B, C) are left in the previous year, and three days (D, E, F) go to the next.

**Legend:**

The blue days are found in long Brumias only.

The red day is the possible position of the *Brumia intercalaris*, which occus in leap short Januarias.

The gray disks are the nights of new moons.

The yellow disks are the nights of full moons.

The quartered disks are the nights that can be either full moons or new moons, depending on whether the Brumias are long or short.

Note: the Februarias are shown as they are long; when they are short they should be shifted three days rightward (the top line “d e f a b c” shows the weekdays assigned to the short Februarias).

There is a version of the calendar with different lengths of months designed for the 8-day Nundinal cycle.

## Algorithms Edit

The next algorithms can be used to convert the dates between New Roman Lunisolar Calendar and Microsoft Excel day number.

Note: The next expressions bind the Microsoft Excel day number with Rata Die and Julian day number:

- MEDN = RD – 693594
- MEDN = JDN – 2415018.5

### In Visual Basic / OpenOffice.org Basic Edit

The code below defines functions for conversation between the calendars that can be used in spreadsheets of Microsoft Excel and OpenOffice.org Calc.

Function Newroman2excelDate(Y As Integer, M As Integer, D As Integer) Rem 2008-04-25 Dim a As Long Dim b As Long a = Y Mod 334 a = a - 7 * Int((Y Mod 334 + 18) / 19) + 14 a = a - 4 * Int(((Y Mod 334 + 18) Mod 19) / 11) a = a - Int(((Y Mod 334 + 18) Mod 19 Mod 11) / 3) b = 4 * Int(a / 13) b = b + 3 * Int((a Mod 13) / 12) b = b + Int((a Mod 13 Mod 12) / 3) b = b + 121991 * Int(Y / 334) b = b + 6936 * Int((Y Mod 334) / 19) b = b + 4014 * Int((Y Mod 334 Mod 19) / 11) b = b + 1092 * Int((Y Mod 334 Mod 19 Mod 11) / 3) b = b + 369 * (Y Mod 334 Mod 19 Mod 11 Mod 3) b = b + 30 * M + D If M > 1 Then b = b + 15 * (Y Mod 334 Mod 19 Mod 11 Mod 3 Mod 2) - 3 b = b - 968665 Newroman2excelDate = b End Function Function excelDate2newroman(excelDate As Long) As String Rem 2008-04-25 Dim c As Integer ' Number of 334-year cylces Dim D As Long ' Days within 334-year cycle Dim Y As Integer ' Years within 334-year cycle Dim g As Integer ' Correction for number of long winters Dim h As Integer ' Correction for 28-day Januarias Dim i As Long ' Days within 334-year cycle, adjusted Dim j As Integer ' Counter Dim k As Long ' Day of 334-year cycle on which this year begun Dim l As Integer ' 42-day Februarias indicator Dim M As Integer ' Month number within year Dim O As Integer ' Day number within month Dim S As String ' Output string D = excelDate + 968632 c = Int(D / 121991) D = D Mod 121991 i = D For j = 1 To 2 Y = 19 * Int(i / 6936) Y = Y + 11 * Int((i Mod 6936) / 4014) Y = Y + 3 * Int((i Mod 6936 Mod 4014) / 1092) Y = Y + Int((i Mod 6936 Mod 4014 Mod 1092) / 369) g = Y - 7 * Int((Y + 18) / 19) g = g - 4 * Int(((Y + 18) Mod 19) / 11) g = g - Int(((Y + 18) Mod 19 Mod 11) / 3) h = 4 * Int((g + 1) / 13) + 2 h = h + 3 * Int(((g + 1) Mod 13) / 12) h = h + Int(((g + 1) Mod 13 Mod 12) / 3) i = D - h Next j k = 6936 * Int(Y / 19) k = k + 4014 * Int((Y Mod 19) / 11) k = k + 1092 * Int((Y Mod 19 Mod 11) / 3) k = k + 369 * Int(Y Mod 19 Mod 11 Mod 3) k = k + h l = 3 - 15 * (Y Mod 19 Mod 11 Mod 3 Mod 2) M = Int((D - k + l) / 30) + 1 If M = 0 Then M = 1 If M = 13 Then M = 12 O = D - k + 1 If M > 1 Then O = O + 30 * (1 - M) + l S = Format(Y + 334 * c, "0000") S = S & "-" & Format(M, "00") S = S & "-" & Format(O, "00") excelDate2newroman = S End Function

### In Python Edit

def newRomanValue(year, month, day): """Converts New Roman date to MS Excel day number.""" A = year % 334 + 14 A -= (year % 334 + 18) / 19 * 7 A -= (year % 334 + 18) % 19 / 11 * 4 A -= (year % 334 + 18) % 19 % 11 / 3 B = A / 13 * 4 B += A % 13 / 12 * 3 B += A % 13 % 12 / 3 B += year / 334 * 121991 B += year % 334 / 19 * 6936 B += year % 334 % 19 / 11 * 4014 B += year % 334 % 19 % 11 / 3 * 1092 B += year % 334 % 19 % 11 % 3 * 369 B += 30 * month + day - 968665 if month > 1: B += year % 334 % 19 % 11 % 3 % 2 * 15 - 3 return B def newRomanDate(excelDate): """Converts MS Excel day number to the New Roman Calendar.""" D = int(excelDate + 968632) C = D / 121991 I = D = D % 121991 for J in range(2): Y = I / 6936 * 19 Y += I % 6936 / 4014 * 11 Y += I % 6936 % 4014 / 1092 * 3 Y += I % 6936 % 4014 % 1092 / 369 G = Y - (Y + 18) / 19 * 7 G -= (Y + 18) % 19 / 11 * 4 G -= (Y + 18) % 19 % 11 / 3 H = (G + 1) / 13 * 4 + 2 H += (G + 1) % 13 / 12 * 3 H += (G + 1) % 13 % 12 / 3 I = D - H H += Y / 19 * 6936 H += Y % 19 / 11 * 4014 H += Y % 19 % 11 / 3 * 1092 H += Y % 19 % 11 % 3 * 369 L = 3 - Y % 19 % 11 % 3 % 2 * 15 M = (D - H + L) / 30 + 1 if M == 0: M = 1 if M == 13: M = 12 D += 1 - H if M > 1: D += 30 * (1 - M) + L Y += 334 * C return Y, M, D

## Trivia Edit

In period between 1982 and 2064 CE, the New Roman Lunisolar Calendar can be used to determine the date of the Western Easter. The rule is the next: when `YEAR mod 19` is 2 or 13, the Easter falls on the Sunday between 18th and 24th Aprilia, otherwise it falls on the Sunday between 18th and 24th Maia.

The months of the New Roman Lunisolar Calendar sometimes coincide with the months of the Gregorian Calendar. E.g.:

- 2008-09-01 CE = 2760-09-01 AUC
- 2008-10-01 CE = 2760-10-01 AUC
- 2011-02-01 CE = 2763-02-01 AUC
- 2011-06-01 CE = 2763-06-01 AUC
- 2011-07-01 CE = 2763-07-01 AUC etc.

The last time the new years of the New Roman and the Julian calendars did coincide was in 32 CE / 784 AUC. The first time the beginnings of the New Roman and the Gregorian calendars will coincide will be in 7904 CE / 8656 AUC.