# Finally Made My Runic Calendar

2024-09-21 - [53] 7:5

Update 2025-07-23: After calculating Moon and Sun positions for "L" Golden Years (..., 2006, 2025, 2044, 2063, ...), I have decided to capitalize the "l" at October 6th and uncapitalize the "L" at November 5th of the Runic calendar. The rest of the post has been updated to account for this change.

I'll start off by showing the calendar.

## The Calendar

    Perpetual Full Moon Calendar
    ...|0000000001111111111222222222233
    ...|1234567890123456789012345678901
    ---+-------------------------------
    Jan|e-mb-j-rg-od-l-ai-qf-nc-ks-hp-e
    Feb|m-bj-rg-od-l-ai-qf-nc-k-sh-p
    Mar|e-mb-j-rg-od-l-ai-qf-nc-ks-hp-e
    Apr|m-bj-rg-od-l-ai-qf-nc-k-sh-pe-
    May|mb-j-rg-od-l-ai-qf-nc-ks-hp-em-
    Jun|bj-rg-od-l-ai-qf-nc-k-sh-pe-mb
    Jul|-j-rg-od-l-ai-qf-nc-ks-hp-em-bj
    Aug|-rg-od-l-ai-qf-nc-k-sh-pe-mb-j-
    Sep|rg-od-l-ai-qf-nc-ks-hp-em-bj-r
    Oct|g-od-L-AI-QF-NC-K-SH-PE-MB-J-RG
    Nov|-OD-l-ai-qf-nc-ks-hp-em-bj-rg-
    Dec|od-l-ai-qf-nc-k-sh-pe-mb-j-rg-o

This calendar is accurate to about +/- 1 day.

For a little over 3 years now, I have been working on creating a Runic Calendar, a perpetual lunar calendar that takes advantage of the 19 year Metonic cycle of the moon. Runic calendars tended to specify the new moon phase, but I wanted my runic calendar to specify the full moon phases, as Yule, Winternights, and Sigrblot are celebrated on the full moon. More info about Runic calendars can be found at the following Wikipedia article.

Runic Calendar Wikipedia article [HTTPS]

## My Methodology

To start out, I needed to figure out an average baseline for when full moons occur. The following is what I started with.

- Find Winter Solstice for each year
- Estimate when the first sliver of the moon is visible after the first new moon since the Winter Solstice
- Find the full moon after that estimated sliver of the moon point, this is the Yule full moon
- Find the full moon 3 full moons before the Yule full moon, this is the Winter Nights full moon
- Get the "Golden Number" of the metonic (19 year) cycle by taking the remainder of the year divided by 19 and adding 1 to the result
- Add the result to a running total for the golden number, having 19 total running totals
- Average the results

I wanted the Winter Nights full moons because the religious time reckoning I use considers Winter Nights to be the start of the year. Winter Nights is always 3 full moons before Yule, and Yule is the first full moon after the first new moon (first visible sliver of the moon, as opposed to the "dark/black" moon that people use "new moon" to mean nowadays) after the Winter Solstice, so I found the Winter Nights full moons based on the Winter Solstice.

The rounded results I got were the following in order from golden number 1 to 19:

- [1] Oct 8
- [2] Oct 26
- [3] Oct 15
- [4] Nov 3
- [5] Oct 23
- [6] Oct 12
- [7] Oct 31
- [8] Oct 20
- [9] Oct 9
- [10] Oct 28
- [11] Oct 17
- [12] Nov 5
- [13] Oct 25
- [14] Oct 14
- [15] Oct 6
- [16] Oct 22
- [17] Oct 11
- [18] Oct 30
- [19] Oct 19

While Runic calendars would use the Younger Futhark runes (+3 extra runes for 17, 18, and 19) "ᚠᚢᚦᚬᚱᚴᚼᚾᛁᛅᛋᛏᛒᛚᛘᛦᛮᛯᛰ" instead of 1 through 19, I'll use A-S.

Using A-S, the order starting from October 6th using a hyphen for skipped days is "L-AI-QF-NC-K-SH-PE-MB-J-RG-OD". Without the hyphens, the pattern is "LAIQFNCKSHPEMBJRGODL", or with runes "ᛏᚠᛁᛮᚴᛚᚦᛋᛰᚾᛦᚱᛒᚢᛅᛯᚼᛘᚬ". This pattern with the hyphens will pop up again shortly.

A full lunar cycle (the time between 2 consecutive full moons) is about 29.5 days long. In many lunar calendars, this is represented by having about half of the months be 30 days long and half of the months be 29 days long. Because of this, I need to divide 29 and 30 both evenly by 19. This will tell me how to split up the "LAIQFNCKSHPEMBJGOD" pattern. The results I get are:

- For 29: 1, 3, 4, 6, 7, 9, 10, 12, 13, 15, 16, 18, 19, 21, 22, 24, 25, 27, 28
- For 30: 1, 3, 4, 6, 7, 9, 10, 12, 14, 15, 17, 18, 20, 21, 23, 25, 26, 28, 29

Matching to the pattern like before with hyphens, 29 gives "L-AI-QF-NC-KS-HP-EM-BJ-RG-OD-" and 30 gives "L-AI-QF-NC-K-SH-PE-MB-J-RG-OD-". 30 matches that Winter Nights pattern from before, just with a hyphen added at the end. The way I remember the patterns is 1-2-2-2-2-2-2-2-2-2 for 29 and 1-2-2-2-1-2-2-2-1-2-2 for 30.

Because of the 29.5 day cycles, I just need to have a repeating pattern of 29-30-29-30. That full pattern of 29-30 would be "L-AI-QF-NC-KS-HP-EM-BJ-RG-OD-L-AI-QF-NC-K-SH-PE-MB-J-RG-OD-". I can also slot in the Winter Nights set of golden numbers on the calendar and extend that 29-30-29-30 pattern to the rest of the calendar. I also ignore February 29th entirely. Because February 29th only happens every 4 years and the metonic cycle is 19 years long, you can safely just assume a full moon isn't happening on February 29th often enough to mess things up. And besides, the full moon days in this calendar can be off by about a day in either direction anyways, so just deciding that February 29th is a hyphen day is fine.

You might notice the misalignment of letter order from the end of December to the beginning of January. The reason the pattern is out of order is because the change in year means the golden number jumps up 1, so instead of "O" being followed by "D", it's followed by "E". This extends the 30 day pattern though, but this doesn't really impact the accuracy of the calendar by much. Essentially the error in the calendar is crammed into January and February and accumulates to 1 day after 4 years, which then gets fixed by February 29th happening and resetting that error. As I mentioned earlier, the full moon days in this calendar can be off by about a day in either direction.

In the calendar at the top of this post, I use lowercase letters for every golden number day with the exception of the Winter Nights days. That is mostly for myself so I can visually reckon the beginning of the year by taking the day before the golden number day (Winter Nights is 3 nights long, about as long as the moon appears full, so the day before and after the full moon and the full moon).

## Contact/Reply

If you would like to reply to this post, feel free to send me an email.

Email: vi@vigrey.com [Email]
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