161-year calendar etc. RE: Phantom Day Ratios

Dear Victor and Calendar People

My suggested calendar where most of the months have three days and some have two days, could be realised by having a year of 366 dates, where every 483^rd date is omitted. The months would then have 3 dates. This causes every 161^st month to be short. This does not work with Victor’s months of 1 or 2 days. One could time months alternating between 1 and 2 dates, so that only a 2-date month has a date omitted, but this would produce three consecutive 1-day months, rather than two as in Victor’s calendar.

One could instead have months alternating between 30 and 31 dates, in this cases a date would be omitted in months of either length, so some months would have 29 days.

One can get an accurate lunar calendar cycle by omitting 11 dates every 703 dates from months of 30 dates.

I also note that the 482-day cycle of date omission in the solar calendar is approximately one mean yerm long. So one could have a lunar calendar where months alternate between 29 and 30 dates,  except after each omission of a date in the solar calendar when an additional month of 30 days is inserted. The mean lunar month would be (59*482)/(2*482-1) = 29.530633 days.

Also I invented a lunisolar calendar where each solar year has 372 dates, but a date is omitted at the end of each 29-day lunar month and another date is omitted once every 13^th lunar month. See http://www.hermetic.ch/cal_stud/palmen/lunar13.htm .

Karl

10(03(13

Dear Karl and Calendar People,

My favorite calendar involving the number 161 is the one I mentioned a few years ago that has alternating months of 1 and 2 days. This pattern of alternating months repeats for 161 days, then starts over. Each year has 244 months.

Karl then modified this calendar, making months generally twice as long, having usually 3 days each, and occasionally 2.

These are discussed in the document http://the-light.com/cal/ve244.txt

Additionally, I came up with a lunisolar scheme of some sort. I’ve lost my notes, so I’ll have to reconstruct it, unless someone has a copy of the conversation where I mentioned it originally.

If you arrange the 1 and 2 day months described, above, into groups of 20, you have what I’ll call now a standard lunation. A lunation consists of 20 of these very short months.

The average length of a lunation with no adjustment, is 241/161*20 = 29.938 days. However, in http://the-light.com/cal/ve161m.txt I show how the pattern can be shifted either every 3 or every 4 lunations to get a better value for the mean lunation length. I don’t recall what the pattern of shifts was. With some rough calculations, it looks like a shift should occur approximately every 11/3 lunations.

I’ll see if I can find the original emails where I discussed this.

I also crocheted a Metonic cycle using this scheme. See http://the-light.com/cal/vecrochet0.jpg for an illustration. The crochet pattern consists of these 1 and 2 day months. A 1 day month is simply a double crochet. A 2 day month is two double crochets placed in the same spot, with the top loop being drawn through both stitches. The color changes every 161 days. Each row is a new year, so the Metonic cycle is given by 19 rows.

Victor