IVY MIKE CALENDAR

[Helios]

In previous post, I have favored a 17-fold-division calendar. Now I have the equations that do the job. The Ivy Mike calendar is based on the 33-year cycle. It's very simple.
-------------------------------------------------------------------------------
Here are the formulas;
C = JD - 2434315.5
T = FLOOR[ ( 33*C + 692 ) / 709 ]
D = C - 21*( T - 1 ) - FLOOR[ 16*T / 33 ]
Where JD = Julian date, C = Day Count, T = Term or 17th-of-year, D = day-of-term
-------------------------------------------------------------------------------
I use Mayan ( Haab ) names for convenience. The similarity to the Haab is in name only. There is the ommision of "Uo" and "Uayeb" from a Haab set of 19 names.

01) Pop ( 9th = Autumn Mid-quarter* )
02) Zip
03) Zotz ( 9th = Winter Solstice )
04) Tzec
05) Xul ( 9th = Winter Mid-quarter )
06) Yaxkin
07) Mol ( 13th = Spring Equinox )
08) Chen
09) Yax ( 16th = Spring Mid-quarter )
10) Zac
11) Ceh ( 19th Summer Solstice )
12) Mac
13) Kankin
14) Muan ( 1st = Summer Mid-quarter )
15) Pax
16) Kayab ( 6th = Autumn Equinox )
17) Cumku

*Mid-quarters are based on a solar declination = ( + or - ) 16.694°
-------------------------------------------------------------------------------
Here are 17 "solar glyphs" I am fond of.


-------------------------------------------------------------------------------
So let's input JD = 2455008.5 ( JUN 26, 2009 )
C = 20693
T = 964
D = 3
that is, Mac 3 of year 57

[Karl Palmen]

Dear Helios and Calendar People

The calendar structure is not obvious from the formulae given and is considerably more simple than these formulae.

This arises from the facts that 709=21+16*(22+21) and (33 + 692) mod 709 = 16 = (33-1)/2.

The calendar is an example of a calendar Helios suggested several years ago.

The terms start with day C=1 and alternate between 21 and 22 days for a 33-term cycle (a term-yerm) of 709 days.
The first day C of each term has ( ( 33*C + 692 ) mod 709 ) < 33. For a 22-day term the value of this expression is less than 17 so that adding 33*21=693 makes it less than 709. For a 21-day term adding 33*21=693 makes it more than 709. For each 33-term cycle (term-yerm), the value of this expression for the first day of each term is
16, 00, 17, 01, 18, 02, 19, 03, ... 29, 13, 30, 14, 31, 15, 32.

Seventeen of these 709-day cycles have 12053 days, which is very close to 33 years and gives a mean year of 365.2424242424... days. So Helios defines a year to be equal the 17 terms. A year has 365 days if it either begins with a 21-day term or contains the first term of the 709-day cycle (term-yerm) else it has 366 days (by having a 22-day term at both the beginning and end).
The 33-term cycle is a Helios cycle, therefore these years form a Helios Cycle, and so the 366-day years are 3, 7, 11, 15, 19, 23, 27 and 31 of each 33-year cycle.

I take it that JD is the JD at the start of the day. Calendar conversion algorithms usually use the JD at noon, which is an integer. Lance Latham did this, so does Calendrica (explicitly)
http://emr.cs.iit.edu/home/reingold/calendar-book/Calendrica.htm .
This leads to day C=1, being the day that begins JD 2434316.5 and so be JD 2434317, which I make to be 31 October 1952.
See http://isotropic.org/cgi-bin/date.pl?date=31+Oct+1952 .

Helios also needs to work out formulae to convert T and D back to C or JD.
Also needed are the simple formulae to convert T to Y (year) and S (term of year) and back.


If each day of the term is replaced by a 17-day period (which I call a dove). Each term expands to form a year and the 709-day term-yerm becomes a 33-year cycle. This idea I put forward as the Dove calendar
http://www.the-light.com/cal/kp_Dove.html 
Helios's formulae can be modified to find the Dove calendar date for a given day.
I set the Dove calendar epoch so that the last Dove of each year nearly always has the northward equinox (especially in US EST).
Today (26 June 2009) is Ff 2009 in the Dove calendar (6th day of 6th Dove).

Karl

10(10(04


-----Original Message-----
From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Helios
Sent: 26 June 2009 03:48
To: CALNDR-L@...
Subject: IVY MIKE CALENDAR

In previous post, I have favored a 17-fold-division calendar. Now I have the
equations that do the job. The Ivy Mike calendar is based on the 33-year
cycle. It's very simple.
-------------------------------------------------------------------------------
Here are the formulas;
C = JD - 2434315.5
T = FLOOR[ ( 33*C + 692 ) / 709 ]
D = C - 21*( T - 1 ) - FLOOR[ 16*T / 33 ]
Where JD = Julian date, C = Day Count, T = Term or 17th-of-year, D =
day-of-term
-------------------------------------------------------------------------------
I use Mayan ( Haab ) names for convenience. The similarity to the Haab is in
name only. There is the ommision of "Uo" and "Uayeb" from a Haab set of 19
names.

01) Pop ( 9th = Autumn Mid-quarter* )
02) Zip
03) Zotz ( 9th = Winter Solstice )
04) Tzec
05) Xul ( 9th = Winter Mid-quarter )
06) Yaxkin
07) Mol ( 13th = Spring Equinox )
08) Chen
09) Yax ( 16th = Spring Mid-quarter )
10) Zac
11) Ceh ( 19th Summer Solstice )
12) Mac
13) Kankin
14) Muan ( 1st = Summer Mid-quarter )
15) Pax
16) Kayab ( 6th = Autumn Equinox )
17) Cumku

*Mid-quarters are based on a solar declination = ( + or - ) 16.694°
-------------------------------------------------------------------------------
Here are 17 "solar glyphs" I am fond of.

http://www.nabble.com/file/p24214208/17glyph.jpg 
-------------------------------------------------------------------------------
So let's input JD = 2455008.5 ( JUN 26, 2009 )
C = 20693
T = 964
D = 3
that is, Mac 3 of year 56

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[Helios]

The 3663 luni-solar year cycle is listed on Karl P's

http://www.the-light.com/cal/Lunisolar33.html

Many of the values for these datums are divisible by 17. It tells us that a good estimation for a term-month relationship is,

3663 terms = 2665 months

1 term = 2665 / 3663 months = 8 / 11 months + 1 / 3663 months

and noting that 1 / 11 = 333 / 3663 tells us that the elevenths part is incremented every 333 terms ( about 19.6 years ).

So I'll set the initial value of the Brown Lunation Number "L" for the first term

L = 369 & 1522 / 3663 months

and create the formula

L = (  2665*T + 1350504 )/ 3663

to give the Lunation Number for all terms thereafter

[Karl Palmen]

Dear Helios and Calendar People

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Helios
Sent: 27 June 2009 23:37
To: CALNDR-L@...
Subject: 3663 luni-solar year cycle

The 3663 luni-solar year cycle is listed on Karl P's

http://www.the-light.com/cal/Lunisolar33.html 

Many of the values for these datums are divisible by 17. It tells us
that a
good estimation for a term-month relationship is,

3663 terms = 2665 months

KARL SAYS: Helios has discovered that the number of months (45305) in
the 3663-year cycle is divisible by 17. 45305/17 = 2665 hence this cycle
approximates 2665 lunar months to 3663 terms. It has a mean month of
29.5305816... days.

HELIOS CONTINUES:
1 term = 2665 / 3663 months = 8 / 11 months + 1 / 3663 months

and noting that 1 / 11 = 333 / 3663 tells us that the elevenths part is
incremented every 333 terms ( about 19.6 years ).

KARL SAYS: I recall that Helios has previously suggested the idea of
dividing each term into 8 cells (of 2 or 3 days) and counting 11 cells
to each lunar month. 333 terms would then have 2664 cells. So this
suggests having a 9-cell term once every 333 terms, to bring it up to
2665 cells.

Suppose instead we have 9-cell term once every 334 terms. The 334 terms
have 2673 cells, which is exactly 243 months and so it approximates 334
terms to 243 months. Seventeen of these 243-month cycles make a 334-year
cycle of years and months. The complete cycle is 33*334=11022 years and
has a mean month of 29.5306179... days.


HELIOS CONTINUES:
So I'll set the initial value of the Brown Lunation Number "L" for the
first
term

L = 369 & 1522 / 3663 months

and create the formula

L = (  2665*T + 1350504 )/ 3663

to give the Lunation Number for all terms thereafter

KARL SAYS: This gives only an estimate of the lunation number and not
the moon phase

Karl

10(10(07
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[Helios]

One more thing on this. By the parameters of the 3663y luni-solar cycle, which is 111 33y cycles, the mean year of the 11-year luni-solar cycle evidently drifts through the seasons every 2664 years.

Therefore

= 1 drift cycle
= 2664 solar years
= 2665 luni-solar years ( 11y-cycle )

I have now made a web-page for the IM calender
http://www.helios.netne.net/ivymike.htm

[Karl Palmen]

Dear Helios and Calendar People

I recall responding to one of Helios's E-mails, by suggesting 11 cells
(or 2 or 3 days each) in each lunar month and 136 cells in each year,
but not counting every 2665th cell in the 136 cells of a year.

Then 2664 years have 136 cells that are not counted making up a total of
2665*136 cells, which is 2665 years with all cells counted.

Karl

10(10(29

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Helios
Sent: 20 July 2009 10:49
To: CALNDR-L@...
Subject: Re: 3663 lunisolar year cycle

One more thing on this. By the parameters of the 3663y luni-solar cycle,
which is 111 33y cycles, the mean year of the 11-year luni-solar cycle
evidently drifts through the seasons every 2664 years.

Therefore

= 1 drift cycle
= 2664 solar years
= 2665 luni-solar years ( 11y-cycle )

I have now made a web-page for the IM calender
http://www.helios.netne.net/ivymike.htm
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[Karl Palmen]

Dear Helios and Calendar People

Helios has reckoned the drift cycle for a year of exactly 136/11
lunations, which arises from an 11-year cycle.

This has got me thinking of the drift cycle for a year of exactly 371/30
lunations, which arises from a 30-year cycle.

I then realised that a lunisolar cycle whose length is equal to one of
these drift cycles would have 371 saltus lunae corrections. I list such
cycles below:

Years Leap Months Year/Month
Years/Truncations
7679 2828 12.368277 365.667
(exactly 365 2/3)
7709     2839 12.368271 350.409
7739        2850              12.368265 336.478
7769        2861 12.368258 323.708

Note that the number of days in the cycle does not affect the number of
saltus lunae, so is not shown or even calculated.

I've shown the number of years per truncation of the 19-year cycle to 11
years to enable comparison with the 334-year and 353-year cycles. For a
given mean month, the 7739-year cycle has a slightly longer mean year
than the 334-year cycle and the 7709-year cycle has a slightly shorter
mean year than the 353-year cycle.

So if we use the 7709-year cycle as the drift cycle we have
= 1 drift cycle
= 7709 solar years
= 7710 years of the 30-year cycle (of 371/30 lunations).

This fits in with there being 7710*371/30 = 95347 = 12*7709 + 2839 lunar
months in the cycle.

A 30 year cycle can be generated by dividing each lunar month into 30
tithis and each year into 371 tithis.
Each tithi can be set equal to a day except for six tithis every common
year or five tithis every leap year, which have no duration (I expect
Charles Moyer has been cleaning up after his most recent uruz bull
sacrifice).
This 30-year cycle is corrected by occasionally adding a tithi to a
year, which gives rise to a saltus lunae.
Then the number of 'leap' years (with five tithis of zero duration)
needs to be reduced by the number of these saltus lunae corrections to
become equal to the number of abundant years as in column C in my
lunisolar spreadsheets
http://www.the-light.com/cal/kp_Lunisolar_xls.html .

Karl

10(11(01

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Helios
Sent: 20 July 2009 10:49
To: CALNDR-L@...
Subject: Re: 3663 lunisolar year cycle

One more thing on this. By the parameters of the 3663y luni-solar cycle,
which is 111 33y cycles, the mean year of the 11-year luni-solar cycle
evidently drifts through the seasons every 2664 years.

Therefore

= 1 drift cycle
= 2664 solar years
= 2665 luni-solar years ( 11y-cycle )

I have now made a web-page for the IM calender
http://www.helios.netne.net/ivymike.htm 
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