# How to arrange the Werewolf Auspices to the days of a lunar month?

There are 5 Werewolf auspices, each with a "phase":

• Ragabash, New Moon
• Theurge, Crescent Moon
• Philodox, Half Moon
• Galliard, Gibbous Moon
• Ahroun, Full Moon

How can I sort a full moon phase to each one somewhat equally?

Note: The calculation in normal text is based on a lunation. The corrected numbers for a sidereal month are found in the supertext. Note that approach has an in-built self-correction: When pinning the full moons to the known dates of a lunar calendar, there is a scaling process included. This compensates the 51-hour error between synodic and sidereal month.

# Pretext

This is mainly a question of mathematics. A moon in 27.3/29.5 days long. Divided upon 5 Auspices, this is 5.46/5,9 days per Auspice. But how to distribute these? We can't place them all one after another in the listed order, as then the new moon follows the full moon, and those should be half a month apart! We need to distribute a little...

# Graphical Method

## Generating the 'bar'

Let's start in the middle of a full moon phase, as we can't cut that apart but for marking the center - the absolute full - of it. And now we draw out 2.73/2.95 days, as that is half the phase's length...

Now, we repeat these for the Gibbous (allmost full), Half and crescent Moon, stacking them...

Next comes the new moon, which again can't be divided into a first or second half of the month, so it will be a full 5.46/5.9 days. Then again the phases with 2.73/2.95 day in backward order.

## Calender dating

Note the gap at the end to the 28 day/4 week display - this is responsible for the shifting of the phases. But taking this bar and a moon calendar, it is easy to place each day towards one of the phases, and with more math, one could decide exactly when in the night/day the auspices shift.

Example: Tuesday 3rd July 2012 was a full moon, the 18th a new moon and 2nd of August a full moon again according to my moon calendar. Using a properly scaled bar like the one before (with a full, 5.465.9 days full moon at the end) the lunar month looks like this:

# Full Math Approach

Taking a Sidereal Month as a base we know that an Auspice is supposed to be 5.9 days or 141.6 hours or 141 hours and 36 minutes.

Let's get the full moon moment of the 3rd July 2012: according to lunaf.com that is 18:52, as the center of the Time. WA says this time has 99.92%, so close enough.

2 days, 22 Hours, 48 Minutes later we should change from full moon to Gibbous Moon. That is 6th of July 2012, 17:40 UTC. 2.95 days till each new phase starts - of in the case of the New and Full moon, reaches its zenith. That can be easily taken to excel or another spreadsheet program! Fill in one date for a full moon in B2 and in the field below add =B2+2.95the 2.95 is assuming average moon length - an error! - then pull it down to fill the column. The categories are to be in the following order: Full Zenith, Gibbous Start, Half Start, Crescent Start, New Start, New Zenith, Crescent Start, Half Start, Gibbous Start, Full Start, Full Zenith. The last entry is again the first entry of the next lunar month, so we get a repetitive pattern, and don't even need to scale anything1.

## Compensation for variable moon lengths

Our calculation gives 2nd of August 6:52 UTC as full moon zenith, lunaf.com gives 03:27 UTC. The error of 3 hours comes from the variance the synodic month has, ranging from 29.18 to 29.93 days, resulting in Auspiece-lengths of 2.918 to 2.993 days. The chosen month in the example is mathematically 29.358 days long.

Because of this it is advisable to look up the dates of full moons in the years played and then calculate the correct sidereal lengths to correct for this error. The formula gets considerably more complex though. So take a look at this spreadsheet that fixes the sidereal month's length by taking input in the shape of a start and end date for a month.

# Illumination + lunar calender method

Another variant would be to look up the illumination of a moon for certain days. The Full moon of course has 100% illumination, the new moon 0%. The swing from full moon to new moon and back to full moon thus swings twice over the scale, a total of 200 percentage points. Each phase thus should cover 200/5=40 percentage points, 20 of these on the waning and 20 on the waxing side. These illuminations can be looked up at some online tools, and then easily compared to a simple chart that does not care for which half in the lunar month one is in, as it mirrors around the 0 and 100 point to swing back:

• 80-100% - Full
• 60-80% - Gibbous
• 40-60% - Half
• 20-40% - Crescent
• 0-20% - New

Note though that illumination does not exactly follow a perfect distribution over the month and visible illuminated area varies depending on the position on the globe. Check where your calendar is dated for, or use Wolfram Alpha to a local position!

# Comparison & Verification

Let's run a test: looking up the 27th July of 2012

The Illumination+Calender method shows at lunaf.com or Wolfram-Alpha that at noon it was a 62.01% illumination, which is a Gibbous moon in the waxing half of the lunar cycle.

Comparing this to the other methods we see that the moon just changed into this phase on the 27th (graphical Method) and did so at 9:16with long-term median length / 6:32corrected for month length AM. Close enough, aye? All three methods came to a workable result for the example day!

Careful checking on WA shows, that the actual 60% point was at 7:43 AM in Greenwich at 51°28′40″N 0°00′05″W. This error is relative minuscule and is to a good degree derived from different full moon times.

## TL:DR;

  Percent
Illuminated     Auspice
-----------------------
0.0% - 12.5%   Ragabash
12.5% - 37.5%   Theurge
37.5% - 62.5%   Philodox
62.5% - 87.5%   Galliard
87.5% - 100%    Ahroun


### How we got that result.

A lunar month is (aka lunation, aka synodic month) is approximately 29.5 days long. This is the time it takes to return to the same place with respect to the sun, and consequently to the same phase, e.g. from new moon to new moon. The exact length of time varies somewhat because the orbits of the moon around the Earth and the Earth around the sun are elliptical and not circular. From https://en.wikipedia.org/wiki/Lunar_month:

Because of these variations in angular rate, the actual time between lunations may vary from about 29.18 to about 29.93 days. The long-term average duration is 29.530587981 days (29 d 12 h 44 min 2.8016 s).

The often referenced 27.3 day period is the sidereal month, which is the amount of time it takes the moon to return to a similar place in the sky with respect to the background stars; thought of another way, it's the time it takes the moon to move 360° through its orbit.

The synodic month is longer (by about 51 hours) because the Earth moves along its own orbit, so the moon has to travel more than 360° along its orbit before it returns to the same phase. This animation shows it quite nicely: http://www.sumanasinc.com/webcontent/animations/content/sidereal.html

In any case, despite the incorrect times, the approach outlined by Trish is the correct one.

Here is the answer with respect to percentage of the moon illuminated, which is easily found for any date on many different websites, such as Wolfram Alpha.

  Percent
Illuminated     Auspice
-----------------------
0.0% - 12.5%   Ragabash
12.5% - 37.5%   Theurge
37.5% - 62.5%   Philodox
62.5% - 87.5%   Galliard
87.5% - 100%    Ahroun


For example, the moon phase for 11 January 1976 was 66.2% and waxing, making this Garou a Galliard. (Remember that whether the moon is waxing or waning can play a role in fine-tuning the Garou's auspical personality; the specifics are covered in the core rulebooks.)

Note that while Theurge, Philodox and Galliard each have 25% of the moon's cycle, at first glance it seems that Ragabash and Ahroun only have 12.5% slices of the pie; but remember that they extend another 12.5% into the previous and next lunations as well.

How to handle those Garou born exactly at the cusp between auspices is up to you and your Storyteller.

• This is not an answer of the original question but an addendum/comment on the previous answer. Please either put it as a comment on the previous post or edit to make it a full answer on the question – Dinomaster Nov 22 '18 at 8:25
• I would have, but I can't due to lack of reputation. – cunninglinguine Nov 22 '18 at 8:31
• Thanks for the note - I have added the corrected numbers and incorporated it. If you have a different, maybe even better, approach, I suggest to outline it here! – Trish Nov 22 '18 at 9:33
• Your light addition is kinda wrong in your reasoning and calculation: a full lunar cycle is 100% to 0% to 100% illumination, so each auspice shows up once on the Waning and once on the Waxing side. You get to place 20% illumination for each on each swing: 0-20/20-40/40-60/60-80/80-100-80/80-60/60-40/40-20/20-0 – Trish Nov 22 '18 at 11:07
• your calculation method of assigning 12.5% for the Ahroun and Ragabash of a half moon phase gives them 25 percentage points on a moon while the others gain 50 percentage points on the full swing - TWICE the ammount of the two phases. – Trish Nov 22 '18 at 11:26