# Golden number

After 19 years, the phases of the Moon repeat themselves (albeit, with a small degree of inaccuracy) on the same calendar dates.
In this 19-year lunar cycle (Latin: *cyclus decemnevennalis*), 235 phases of the Moon alternate near-perfectly.
The Golden number (*numerus aurus*), is a number that lets us know the ordinal position (i.e., first, second, third, etc.) in this 19-year cycle that any year in question occurs.

When calculating the date for Easter Sunday, an improved Metónic cycle is used (in fact, it’s exactly one quarter of the Callippic cycle),
and this allows the Julian solar year to align with the lunar year.
This improved cycle has twelve synodic months (i.e, the phases of the moon have cycled 12 times).
Of these 12 months, six have 30 days (even, or “full” months of the mensis plenus) and six have 29 days (odd, or “empty” months of the mensis cavus).
This adds up to a total of 354 days, and averages out to about 29.5 days per month.
In order to balance the 19 lunar years (6,726 days) and the 19 solar years (6,939 ¾ days),
the addition of leap months (mensis embolismalis) were inserted on the 3rd, 6th, 8th, 11th, 14th, 17th, and 19th year in the nineteen-year cycle.
Each of these leap months were 30 days in length, which caused their corresponding lunar year (annus embolismalis) to then have 384 days.
With this addition, this then put the total length of a 19-year cycle at 6,936 days (354 × 12 + 384 × 7).
In each nineteen-year cycle, 4 ¾ leap days (*dies embolismales*), which originate from the Julian calendar, were also added.
19 lunar years then added up to a total of 6940 ¾ days.
However, in order to equal 19 solar years, a month had to be shortened by one day (lunar leap, saltus lunae) in the last year of the 19-year cycle.
For the first year of the nineteen-year cycle, a year was chosen where January’s new moon began with the new moon of 24 December of the previous year.
This then caused the first new moon of the cycle to begin on 23 January.
This first year is considered to be 532 AD, the first year of the Dionysian tables, and just as predicted, on the 24th of December, 531, there was a new moon.

Some researchers claim that this cycle was inscribed in the Athenian temple of the goddess Minerva in golden letters on black marble. Others think that the name comes from the monks' custom of writing these numbers in gold on their calendars.

**golden_number = (year + 1) % 19**

if the result is 0, golden_number is 19

Which can be shortened to

**golden_number = year % 19 + 1**

Only whole numbers are to be counted, with the '%' character (the modulo) indicating that the remainder is to be used. The year 532 is sometimes considered to be the initial year of the first cycle of the Golden Number, and sometimes the year 1 BC is considered to be the beginning, because it also happens to meet the condition of having December’s new moon in the previous year.

The Golden number is of Western origin, but there is a Byzantine nineteen-year-old lunar cycle that begins its cycle three years later. In some sources, the Latin term cyclus lunaris can represent either the Golden Number or the Byzantine lunar cycle.

Below is a table of Golden Numbers from year 0 (according to astronomical years) all the way up to the year 5,699, and it is quite simple to use. Simply find the century in the column and the year in the row. The Golden Number you are looking for will be at the intersection. For example, if we are interested in the year 1348’s Golden Number, we would locate 1300 in the column and then line up with 48 in the row. At the intersection, we get the number 19, which is the Golden Number for the year 1348.

years | 0 1900 3800 | 100 2000 3900 | 200 2100 4000 | 300 2200 4100 | 400 2300 4200 | 500 2400 4300 | 600 2500 4400 | 700 2600 4500 | 800 2700 4600 | 900 2800 4700 | 1000 2900 4800 | 1100 3000 4900 | 1200 3100 5000 | 1300 3200 5100 | 1400 3300 5200 | 1500 3400 5300 | 1600 3500 5400 | 1700 3600 5500 | 1800 3700 5600 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0 19 38 57 76 95 | 1 | 6 | 11 | 16 | 2 | 7 | 12 | 17 | 3 | 8 | 13 | 18 | 4 | 9 | 14 | 19 | 5 | 10 | 15 |

1 20 39 58 77 96 | 2 | 7 | 12 | 17 | 3 | 8 | 13 | 18 | 4 | 9 | 14 | 19 | 5 | 10 | 15 | 1 | 6 | 11 | 16 |

2 21 40 59 78 97 | 3 | 8 | 13 | 18 | 4 | 9 | 14 | 19 | 5 | 10 | 15 | 1 | 6 | 11 | 16 | 2 | 7 | 12 | 17 |

3 22 41 60 79 98 | 4 | 9 | 14 | 19 | 5 | 10 | 15 | 1 | 6 | 11 | 16 | 2 | 7 | 12 | 17 | 3 | 8 | 13 | 18 |

4 23 42 61 80 99 | 5 | 10 | 15 | 1 | 6 | 11 | 16 | 2 | 7 | 12 | 17 | 3 | 8 | 13 | 18 | 4 | 9 | 14 | 19 |

5 24 43 62 81 | 6 | 11 | 16 | 2 | 7 | 12 | 17 | 3 | 8 | 13 | 18 | 4 | 9 | 14 | 19 | 5 | 10 | 15 | 1 |

6 25 44 63 82 | 7 | 12 | 17 | 3 | 8 | 13 | 18 | 4 | 9 | 14 | 19 | 5 | 10 | 15 | 1 | 6 | 11 | 16 | 2 |

7 26 45 64 83 | 8 | 13 | 18 | 4 | 9 | 14 | 19 | 5 | 10 | 15 | 1 | 6 | 11 | 16 | 2 | 7 | 12 | 17 | 3 |

8 27 46 65 84 | 9 | 14 | 19 | 5 | 10 | 15 | 1 | 6 | 11 | 16 | 2 | 7 | 12 | 17 | 3 | 8 | 13 | 18 | 4 |

9 28 47 66 85 | 10 | 15 | 1 | 6 | 11 | 16 | 2 | 7 | 12 | 17 | 3 | 8 | 13 | 18 | 4 | 9 | 14 | 19 | 5 |

10 29 48 67 86 | 11 | 16 | 2 | 7 | 12 | 17 | 3 | 8 | 13 | 18 | 4 | 9 | 14 | 19 | 5 | 10 | 15 | 1 | 6 |

11 30 49 68 87 | 12 | 17 | 3 | 8 | 13 | 18 | 4 | 9 | 14 | 19 | 5 | 10 | 15 | 1 | 6 | 11 | 16 | 2 | 7 |

12 31 50 69 88 | 13 | 18 | 4 | 9 | 14 | 19 | 5 | 10 | 15 | 1 | 6 | 11 | 16 | 2 | 7 | 12 | 17 | 3 | 8 |

13 32 51 70 89 | 14 | 19 | 5 | 10 | 15 | 1 | 6 | 11 | 16 | 2 | 7 | 12 | 17 | 3 | 8 | 13 | 18 | 4 | 9 |

14 33 52 71 90 | 15 | 1 | 6 | 11 | 16 | 2 | 7 | 12 | 17 | 3 | 8 | 13 | 18 | 4 | 9 | 14 | 19 | 5 | 10 |

15 34 53 72 91 | 16 | 2 | 7 | 12 | 17 | 3 | 8 | 13 | 18 | 4 | 9 | 14 | 19 | 5 | 10 | 15 | 1 | 6 | 11 |

16 35 54 73 92 | 17 | 3 | 8 | 13 | 18 | 4 | 9 | 14 | 19 | 5 | 10 | 15 | 1 | 6 | 11 | 16 | 2 | 7 | 12 |

17 36 55 74 93 | 18 | 4 | 9 | 14 | 19 | 5 | 10 | 15 | 1 | 6 | 11 | 16 | 2 | 7 | 12 | 17 | 3 | 8 | 13 |

18 37 56 75 94 | 19 | 5 | 10 | 15 | 1 | 6 | 11 | 16 | 2 | 7 | 12 | 17 | 3 | 8 | 13 | 18 | 4 | 9 | 14 |