Dear Calendar People,
Years ago, I came up with a calendar that used a simple alternation of 1 and 2 day months. I was thinking about this again, and I think I'd prefer to use different terms.
I now call the basic unit a day, just like any calendar.
The next unit I call a turn. Previously I called it a month, but that can be confusing because it is so short compared to what we normally think of as months.
There are short turns and long turns. A short turn is 1 day. A long turn is 2 days.
A block is 161 turns, alternating between short and long turns and both starting and ending with a short turn.
The basic cycle of the calendar consists of these blocks concatenated end to end without interruption.
Each block of 161 turns has 80 long turns and 81 short turns. We may wish to group these into two groups. I call these demiblocks. Each demiblock starts with a short turn.
A year is conveniently divided into quarters by simply defining a quarter as 61 turns.
If we wish to use a period like a month of about 30 days, I note that a quarter would have 2 20 turn months and one 21 turn month. It would be nice if the 21 turn months were those that had two days in a row. There would be others, but we'd want to make
all the ones with two short turns in a row to be 21 turn months to make the month lengths as even as possible. That's where it's helpful to have demiblocks. If we made a month a 21 turn month iff it contained the first day of a demiblock, I think that would
make the scheme welldefined. Perhaps to make it welldefined we would have to also specify that a month cannot end in two short turns.
Victor

Dear Victor and Calendar People
I remember joining every two consecutive turns to make a period normally of 3 days. I'll call them miniweeks. The resulting block is twice as long and has 161 miniweeks consisting of 160 3day miniweeks and one 2day miniweek, so lasting 482 days. Each year has 122 miniweeks.
Victor's scheme has the advantage that the year can be divided into quarters of 61 turns with months of 20, 20 & 21 turns not necessarily in that order.
For miniweeks, we'd need 10 months of 10 miniweeks and 2 months of 11 miniweeks in each year.
I see Victor wants every pair of consecutive 1day turns to occur in a 21turn month. This would cause the month to have 31 days. This would also occur for any 21turn month beginning with an oddnumbered turn of the block.
I also see that Victor suggest achieving that by making any month that contains the 1st or 81st turn of a block (without using his concept of a demiblock) have 21 turns. This would break the requirement that every 3rd month has 21turns so there must either be some additional 21turn months or some exceptions.
Also Victor's scheme is not well defined. What if a month were to begin 20 turns before the start of a demiblock? Would the first turn of the next demiblock belong to this month or the next month? A rule to specify this would also be needed.
Victor's scheme is equivalent to giving each month 20 turns, not counting the 1st and 81st turn of each block. These each have 1 day and occur once every 121.5 days on average. This is less often than the 4 per year needed so some additional 21turn months would be needed about one per year.
Within each block, the 21turn months must alternate between 31 & 32 days no matter how they are placed within a block, but any that straddle two blocks will have 31 days.
So in each year we can choose the order of the 20, 20 & 21 turn months of each quarter so that one of the 21turn months straddles two blocks. Some years will give you a choice of two, then choose a straddling month beginning on an evennumbered turn of the block, if possible.
Each block has 241 days and so contains the starts of either two or three 21turn months.
Karl
Monday Alpha March 2020

Dear Victor and Calendar People
I had more thoughts about Victors turn & block calendar. I realise that every 365day year must have at least one month of 32 days and every 366day year must have at least two months of 32days.
I now think what Victor wants is to ensure no 20turn month has 29 days. This occurs if and only if it straddles two blocks and begins with an oddturn of the block. This is would minimise the occurrence of 32day months.
So one must give 21 turns to any month that begins with the 143rd, 145th, .... 161st turn of the block. One could have a quarterly 3month cycle in any year that has only one block start. If a year has two block starts, one may have to interrupt the 3month cycle to ensure a 21turn month straddles both block starts, but only if those months begin with an oddnumber month of the block. The block within the year would have two other nonstraddling 21turn months hence, either both or neither of the block starts need a 21turn month.
Karl
Monday Alpha March 2020

Dear Victor and Calendar People
I thought about the quarters and how to avoid 29day months from occurring in them.
I see 4 types of quarters (of 61 turns):
Type A begins with an oddnumbered turn, has one block in it, so ends with another oddnumbered turn and so has 91 days. Its long month has 31 days.
Type B begins with an evennumbered turn, has one block in it, so ends with another evennumbered turn and so has 92 days. Its long month has 32 days.
Type C begins with an oddnumbered turn, has two blocks in it, so ends with an evennumbered turn and has 91 days.
Type D begins with an evennumbered turn has two blocks in it, so ends with an oddnumbered turn and has 91 days.
To avoid any 29month from occurring, a type C quarter must have a long month straddling the blocks or in the first block and a type D quarter must have a long month straddling the blocks or in the second block.
Karl
Monday Alpha March 2020

Dear Victor and Calendar People
I found out that these 4 types of quarters give rise to 10 types of year, with the year type determined by which turn of the block the year begins.
I thought about Victor's idea about which of the three months of the quarter is long. It can be either the month that contains the first turn of a demiblock or if the quarter has no such month, then the middle month of the quarter.
I'd prefer the middle month of the quarter, except for any quarter that would have a 29day month, then that month is the long month of the quarter. I expect this would apply to about 1 in 6 type C or D quarters.
Karl
Monday Alpha March 2020

In reply to this post by k.palmen@btinternet.com
Dear Karl and Calendar People,
I remember your 3.....2 scheme as well. For those who weren't part of the original conversation, this set of calendars is interesting because the mean year length is 244 * 241 / 161 = ~ 365.24224 days, the cycle that repeats every 161 years in 58,804 days.
This desire is in order to attempt to minimize jitter.
That is why I added the rule that a month cannot end in two short turns. However, I did not think that through carefully.
I'm not sure I follow. A block is always 3*80+1 = 241 days. Each block starts and ends with a short turn, so the average frequency of these turns is 241/2 = 120.5 days. If this was just an arithmetical error, the main point still remains:
Yes. In this case, my first inclination is to consider quarters. In the case the above is true, there will be an entire quarter with no instance of consecutive short turns. I would suggest making the middle month of such quarter a long month (which could
potentially extend the last month of the quarter over a pair of consecutive short turns).
Yes.
Months, unfortunately, do not evenly divide the quarters. I consider any scheme to set up months approximating Gregorian months somewhat of a kludge. I suspect any such calendar actually adopted (not likely) to actually divide the months by weeks rather
than turns, but I haven't thought through that exercise yet.
Victor

Dear Victor and Calendar People
Thank you Victor for your reply. I reply below.
KARL REPLIES: I take it Victor means variation of month lengths. 32day months are inevitable, but 29day months can be eliminated and Victor's scheme does that and in so doing minimises the number of 32day months. I mentioned this later notes. Making the months that straddle two blocks long is sufficient to do this, but not always necessary. In explain a necessary condition in my 3rd note, in which I define 4 types of quarters.
KARL REPLIES: Sorry if didn't note that. KARL REPLIES: Yes the 121.5 was an error. It should be 120.5.
KARL REPLIES: I thought of this and mentioned it in my last note along with my preference, which is to make the middle month long, except in any quarter that would have a 29day month, in which case the month that would have 29 days becomes the long month.
KARL REPLIES: I was here referring to blocks not quarters. Each block is just slightly shorter than 8 months. 8 months average 8*61/3 = 162 2/3 turns. Each block has 161 turns.
Karl
Tuesday Alpha March 2020

In reply to this post by k.palmen@btinternet.com
Dear Victor and Calendar People
I found three more types of year each of which occurs only once every 161 years. Each has a block beginning on the same day as a quarter other than the first quarter, so has two consecutive type A quarters.
Karl
Wednesday Alpha March 2020

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