Nabble - Calndr-L

Re: answer to Maya calendar enigma

2009-11-25T13:19:30Z

On Wed, Nov 25, 2009 at 11:12 AM, cliff <vgray@...> wrote:
> Dear Sepp, and Calendar People
>
> There are many instances where 260 day offsets may be found in astronomy,
> and is certainly a compelling reason why such a calendric base period should
> have been adopted together with the 360d, 365d, 584d periods to form a
> calendar with multiple base periods. However, the derivation of the 260d
> period cannot be discussed without recourse to the Long Count's History.

Is there a complete and detailed history of the long count? I'm aware
of only theories.

> The
> 260d offset relative to the Metonic cycle is really just another one of
> those many marvelous attributes of astronomy generally. Of the many 260d
> artifacts that persist which one could best be selected as the reason d'être
> for the calendar's construction? The Long Count originated in the narrow
> corridor of the Isthmus of Tehuantepec, with the Olmec region to the north,
> the Isthmian region in the middle and the Izapan region to the south, and it
> is in the context of this early history that this discussion must focus.

But it is also a significant leap that such geographic specificity is
relevant. That relevance must be demonstrated.

> Vincent Malmstrom has already shown the alignment of all the major Maya
> citadels to major nearby mountain peaks in terms of both the summer solstice
> sun alignment to those peaks, and the Aug 13th vertical sun transit as of
> paramount importance. Where does this penchant for such alignment arise?

Malstrom's book is online, but I have not yet read it completely. I
recall that my impression, though, was that some claims were suspect
(by me, anyway). Certainly, they would need to be verified before they
can be relied on.

> Izapa is at 14.8 N latitude which means the interval between the solar
> overhead transits is 105d approximately centered about summer solstice, and
> of course a corresponding 260d interval approximately centered about winter
> solstice.

Please see our conversation in September-October 2006 for an analysis
of times/locations where this interval works. It varies over time.

> It is much more likely the geographical location of Izapa forms
> the basis for the 260d calendar period, because the monuments are aligned
> accordingly. I can offer a compelling proof of this by defining something I
> call the TROPICAL LATITUDINAL ZONE EQUATION (TLZE), which is clearly visible
> in the constructions and alignments of monuments of many Mayan citadels at
> many different geographical locations. As you know the solar overhead
> transits at the equator are approximately at the equinoxes with an interval
> of about 183d, and as you move further north this interval decreases until
> at the tropic of Cancer (or Capricorn) the two overhead transits unit into a
> single annual event, where the interval between them has dropped to zero
> days. The tropical latitudinal zone equation is first and foremost a fixed
> calendric structure that does not change as one moves to different
> geographical locations. It's length changes but its structure remains fixed.
> The length of this structure is generally an integral tropical year span,
> and further the number of 360d tun calendar leap-days in this calibration
> interval defines the interval between the solar overhead transits centered
> about summer solstice, if the span is aligned to straddle between autumnal
> transits at its extremities. The embedded integral tun year span is shorter
> by the amount of tun leap-days and hence its terminus is at the spring over
> head transit. This structure is always the same no matter what latitude
> within the tropics is used (limiting the discussion to just integral
> tropical spans).

I have to say that I didn't follow any of this.

> For example at the equator an interval of 35y or 12783.5d exhibits 35*5.2422
> = ~183d tun leap-days, describing the interval between the overhead
> transits, and obviously the span length at the tropic of cancer is zero. At

Careful using 5.2422, which I guess comes from the difference between
a mean year and 360 days. However, besides the fact that year lengths
vary from year to year, they also vary with the time of year. The year
length thus determined at the equator will be different from the year
length determined at the Tropic of Cancer for the same reason that the
spring equinox year length is not the same as the summer solstice year
length. With tools available to generate actual modeled ephemerides,
why not use that instead of mean numbers?

> Izapa a 20y span of 7305d applies with 105 tun leap-days between the solar
> overhead transits approximately centered about summer solstice, This derives
> the 260d interval approximately centered about winter solstice. This 20y
> span straddles between Aug 13th solar transits and the embedded 20 tun span
> terminates at the Apr 30th transit. This I believe is the source of the
> preeminent 260d interval that best describes the 260d interval in astronomy,
> because the fixed calendric structure of the TLZE offers a generalized
> calendric basis for its selection.

But why is it any better than a Metonic cycle relationship?

> Edzna at 19.5 N. latitude is described by
> a 13y interval with 68 tun leap-days. The 13y span straddles between Jul
> 26th autumnal transits, and the embedded 13 tun span terminates at the May
> 19th zenithal transit. Tonina uses a 9y span to describe 47 tun leap-days,
> and is an example that uses a span 4d short of an integral tropical year
> span by design. Again elaborate calendric structures are described using
> Long Count dates involving several eclipses covering a long expanse of time.

I guess I should withhold further comment until I understand what
you're referring to by TLZE.

Victor

Re: answer to Maya calendar enigma

2009-11-25T09:12:46Z

Dear Sepp, and Calendar People

There are many instances where 260 day offsets may be found in astronomy,
and is certainly a compelling reason why such a calendric base period should
have been adopted together with the 360d, 365d, 584d periods to form a
calendar with multiple base periods. However, the derivation of the 260d
period cannot be discussed without recourse to the Long Count's History. The
260d offset relative to the Metonic cycle is really just another one of
those many marvelous attributes of astronomy generally. Of the many 260d
artifacts that persist which one could best be selected as the reason d'être
for the calendar's construction? The Long Count originated in the narrow
corridor of the Isthmus of Tehuantepec, with the Olmec region to the north,
the Isthmian region in the middle and the Izapan region to the south, and it
is in the context of this early history that this discussion must focus.
Vincent Malmstrom has already shown the alignment of all the major Maya
citadels to major nearby mountain peaks in terms of both the summer solstice
sun alignment to those peaks, and the Aug 13th vertical sun transit as of
paramount importance. Where does this penchant for such alignment arise?

Izapa is at 14.8 N latitude which means the interval between the solar
overhead transits is 105d approximately centered about summer solstice, and
of course a corresponding 260d interval approximately centered about winter
solstice. It is much more likely the geographical location of Izapa forms
the basis for the 260d calendar period, because the monuments are aligned
accordingly. I can offer a compelling proof of this by defining something I
call the TROPICAL LATITUDINAL ZONE EQUATION (TLZE), which is clearly visible
in the constructions and alignments of monuments of many Mayan citadels at
many different geographical locations. As you know the solar overhead
transits at the equator are approximately at the equinoxes with an interval
of about 183d, and as you move further north this interval decreases until
at the tropic of Cancer (or Capricorn) the two overhead transits unit into a
single annual event, where the interval between them has dropped to zero
days. The tropical latitudinal zone equation is first and foremost a fixed
calendric structure that does not change as one moves to different
geographical locations. It's length changes but its structure remains fixed.
The length of this structure is generally an integral tropical year span,
and further the number of 360d tun calendar leap-days in this calibration
interval defines the interval between the solar overhead transits centered
about summer solstice, if the span is aligned to straddle between autumnal
transits at its extremities. The embedded integral tun year span is shorter
by the amount of tun leap-days and hence its terminus is at the spring over
head transit. This structure is always the same no matter what latitude
within the tropics is used (limiting the discussion to just integral
tropical spans).

For example at the equator an interval of 35y or 12783.5d exhibits 35*5.2422
= ~183d tun leap-days, describing the interval between the overhead
transits, and obviously the span length at the tropic of cancer is zero. At
Izapa a 20y span of 7305d applies with 105 tun leap-days between the solar
overhead transits approximately centered about summer solstice, This derives
the 260d interval approximately centered about winter solstice. This 20y
span straddles between Aug 13th solar transits and the embedded 20 tun span
terminates at the Apr 30th transit. This I believe is the source of the
preeminent 260d interval that best describes the 260d interval in astronomy,
because the fixed calendric structure of the TLZE offers a generalized
calendric basis for its selection. Edzna at 19.5 N. latitude is described by
a 13y interval with 68 tun leap-days. The 13y span straddles between Jul
26th autumnal transits, and the embedded 13 tun span terminates at the May
19th zenithal transit. Tonina uses a 9y span to describe 47 tun leap-days,
and is an example that uses a span 4d short of an integral tropical year
span by design. Again elaborate calendric structures are described using
Long Count dates involving several eclipses covering a long expanse of time.

The Mayans cognized this tropical latitudinal zone equation structure and
used the 20y, 13y 9y, etc tropical spans needed to describe the vertical sun
transits at the various geographical locations, and what's more created
additional calendric structures based on this generalized TLZE structure,
that proves its existence. At Tonina a chin-strap head glyph form has been
identified with the 9y cycle. The Chinkultic disk ball court marker is
rooted in a an elaborate calendric structure involving eclipses and
planetary alignments, based on the Edzna 68d interval, and uses an
interesting series of 17d offsets in its structure. This tropical
latitudinal zone equation is much more likely to be the root of the tzolk'in
calendar period, using a 20y span solution in this TLZE structure.

The 260d offset associated with the Metonic cycle does not rise in
importance sufficiently to preempt the TLZE structure or the monument
alignments to summer solstice / mountain peak alignments and Aug 13th solar
overhead transits. The TLZE is ubiquitous in the archaeological record,
while the Metonic cycle is not. Discovery of the new Olmec Long Count has
also led to the means of deriving the tzolk'in epoch of the Long Count (uses
modulo arithmetic and Julian years in its derivation), which shows the
tzolk'in is intimately tied into the Long Count's design and dictated by its
internal structure (i.e. NOT based on a pre-existing tzolk'in calendar with
an arbitrary start date).

Again if a lunar span is to be discussed as the basis of a 260d astronomical
offset, it is imperative this is also done within the context of the
existing Mayan lunar calendar. They used 18 lunation segments that is 17d
short of 1.5 Years, and concatenated them.

There is evidence a Mayan lunar calendar added a lunar leap-day every double
tri-semester interval of 36 lunations, and one more lunar leap-day every 20
tri-semester intervals. Hence a total of 11 lunar leap days every 360
lunations. This is an interval of (3*29 + 3*30)*3*20 + 10 + 1 = 177*60 + 11
= 10631.012 days. A further 1d lunar leap-day correction will not be needed
for another 84 iterations of this 360 lunation interval or ~2445 years. Over
the course of the 13-baktun cycle only an additional 2 lunar leap days would
need to added, and the recent discovery of a new Olmec Long Count system
quite different to the existing Mayan and Epi-Olmec Long Counts suggests
that they did exactly that during the 3rd century BC. The interesting aspect
of this lunar calendar is lunar leap-days do not result in intercalated
lunar months, because leap-days are incorporated into the existing lunation
structure, by merely upgrading a 29d lunar month to 30d. Hence the number of
lunations within each tri-semester or 20 tri-semester interval is always
unchanged. It is a unique lunar calendar that uses the "wiggle room" within
a 29d lunar month to accommodate the addition of lunar leap-days, so that
over thousands of years intercalated lunar months are never needed. They
chose not to intercalate a lunar month after 3 years as is typical elsewhere
throughout the world, but preferred to deal in multiple semester intervals
and preferred even more to deal in tri-semester multiples.

Of note 6 double tri-semester intervals of 36*6= 216 lunations incorporating
6 lunar days, leaves a 19 lunation shortfall from the Metonic cycle. I do
not believe the importance of the Metonic cycle preempted the importance of
the lunar calendar's structure as described above.

Cheers Cliff

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Sepp Rothwangl
Sent: Wednesday, November 25, 2009 12:49 AM
To: CALNDR-L@...
Subject: Re: answer to Maya calendar enigma

Hi Vic,

your argue is correct too, thus I said I do not want to mention
Venus, because this was in discussion already.
Your argue and mine are not concurrents, but rather fortify the
reason, why the tzolkin became so important for the Mayas.
But the Katun and 19-year relation with the gap of 260 days in
between was overseen so far.
And IMO the existence of the katun (a 20 multiple of 360), based on
the vigesimal system is one reason for the tzolikin's emergence,
because it created the 260 day gap to the 19-year Sun-Moon-
CONVERGENCE, (so to speak with a word of some Maya-esoterics)

Servus
Sepp

Am 24.11.2009 um 19:20 schrieb Victor Engel:

> Dear Sepp and Calendar People,
>
> I think you are essentially correct. But I think Venus plays an
> important part as well. Venus and Earth orbit in lock step with each
> other. One cycle is 2920 days. That is 8 periods of 360 days with 40
> left over, or 11 periods of 260 days with 60 left over. The difference
> between 60 and 40 is 20, one man.
>
> A few years ago I played around with all sorts of astronomical
> phenomena and was amazed how often the numbers 13 and 20 enter into
> alignments such as this. Each occurrence reinforces the significance
> of the numbers.
>
> Victor
>
> On Tue, Nov 24, 2009 at 11:42 AM, Sepp Rothwangl
> <calendersign@...> wrote:
>> Dear list,
>> I found the answer to a Mayan calendar enigma: the tzolkin.
>> The origin of the Mayan 260-day calendar, called tzolkin was
>> cyptic and many
>> argues occured, how it came about.
>>
>> The book "The End of Time: The Maya Mystery of 2012" by Anthony
>> Aveni gave
>> me incentive and ecouraged me, to consider once again an idea that
>> I had in
>> my mind already some time ago.
>> I have discussed this now with Ivan Sprajc and Anthony Aveni. Both
>> finds my
>> idea very interesting. Aveni wrote: "that the Maya may have known"
>> the facts
>> of theory "very likely"!
>> Sprajc wrote an article about: ASTRONOMICAL ALIGNMENTS AT
>> TEOTIHUACAN, LATIN
>> AMERICAN ANTIQUITY, Vol 11,4,2000), where he argues, that the
>> geographical
>> situation of Teotuhuacan caused an architectural design with the
>> reslut of
>> the 260 day count. (the sun pyramid aligned to (Aug 13 + 260 days
>> = apr 30 ;
>> feb 10 + 260 days = oct 30).
>> Thus I need not to cite more of his arguments, which sound
>> convincing, nor
>> im mention here other arguments of the 260 days, like the female
>> pregnancy
>> period, Venus' visibility, and maize ripening period.
>> Please allow me to explain now my theory:
>> No doubt, the Mayans wanted to keep time also with the moon and
>> not only
>> with the sun.
>> And here I think I found the missing link!
>> The Tzolkin itself IMO is the missing link between the Mayan Long
>> Count (LC)
>> and the best-matching luni-solar period: the Metonic cycle.
>> I found this, firstly because I am a bit legasthenic and always
>> consider
>> things from two sides (also from opposite, or inverted side, LOL)
>> and secondly, because I dived deep into the history of the 19-year
>> cycle,
>> which surely must be very old and global. Think of the 19-folded
>> Golden Hats
>> etc. (http://en.wikipedia.org/wiki/Golden_hat)
>> IMO also the Phenix period and the 216 year period of Pythagoras
>> is linked
>> to it. This "one day shift" in 216 years could also be the reason
>> for the
>> azimuthal difference between Sun Pyramid and the Ciudadela. (but
>> this still
>> needs to be checked closer).
>> Please consider with me the calendar at the hand of simple math:
>> 19 solar years and 235 lunar month differ by only 2 h, 6 min, 41 sec!
>> Or expressed in days:
>> 6939.68959 days for 235 lunar month
>> 6939.60161 days for 19 years.
>> If you round this up you arrive at 6940 days, the value of the
>> Metonic cycle
>> as known in antiquity.
>> This period is EXACTLY 260 days (!) shorter than the Mayan katun
>> with its
>> 7200 days.
>> I wonder, that this was not found by some Mayan calendar experts.
>> Or, was
>> this discussed already somewhere else? I could not find any citation.
>> IMO the tzolkin came about to due the vigesimal system, Mayas
>> using fingers
>> togehter with toes.
>> Counting in this way (with base 20) the days of the year result in
>> 20 times
>> 18 = 360 and some epagomenal days.
>> How could the Tzolkin have started?
>> If you want to find the average or true length of the year, you
>> need to
>> count as many as possible years and count all contained days.
>> In the Mayan vigesimal way of counting this was 20 times 18x20.
>> To do this you simply need to watch when the sun rises or sets
>> again at
>> always the same position of the horizon again and again.
>> When you observe also the moon at the same particular day of a
>> year you will
>> experience that always exactly after 19 years the moon is at the
>> same phase
>> as is the sun's position at the horizon. I need not to explain
>> you, that
>> this is the case after 19 years and repeats in the same way every
>> 19 years
>> over quite a long time.
>> By chance (or coincidence) this event is always 260 days shorter
>> than a
>> katun (20x18x20 = 7200)
>> Thus IMO these 260 days became ritually so important to expect the
>> end or
>> begin of the next katun.
>> By the "auxiliary" of the tzolkin, which was NOT a counting-system
>> with
>> numbers in our way, but rather a symbolic design of a value, it
>> was easily
>> to find the temporal distance to any date of the katun and to the
>> phases of
>> the moon and the cardinal or symmetric solar dates (260 days apart).
>> IMO the 260 day period is caused by the difference of the katun
>> and the
>> Metonic period.
>> Expressed in other words:
>> If you know E.g. a cardinal date of any katun, you only have to
>> subtract 260
>> days before the end of the next katun, to know the exact date of
>> moon and
>> sun.
>> the 260 days gives you always an orientation towards sun and moon,
>> similar
>> to the Golden Numbers of the Julian calendar.
>> After having having reallized that relation of Katun and the 19-
>> year period,
>> some ancient Mayan astronomer may have wanted to implement that
>> regularity
>> into the annual periods and found that fantastic symmetry and and
>> parallel
>> of risings and settings of the sun at horizon, mirroring the 260
>> days at
>> specific data (Aug 13 + 260 days = apr 30 ; feb 10 + 260 days =
>> oct 30)
>> Thus the tzolkin became so important for a ritual time keeping, as
>> well as
>> for architectural design.
>> It is a kind of countdown for the end of any katun, similar to the
>> Christian
>> advent calendar, which count days up to Christ's annual fictitious
>> birthday
>> (or as children counting down the days by the closed doors of
>> their Advent
>> calendar in anticipation Christmas)
>> Besides the article of Spraic, exist for the azimuthal orientation
>> of Mayan
>> buildings in the "260-days-design" lot of literature, e.g.:
>> Malmström, V. H. : A Reconstruction of the Chronology of Mesoamerican
>> Calendrical Systems; Journal for the History of Astronomy, Vol. 9,
>> Aveni A.: Archaeoastronomy in the Ancient Americas, Journal of
>> Archaeological Research Volume 11, Number 2 / Juni 2003
>> Milbrath, Susan: Star gods of the Maya: astronomy in art,
>> folklore, and
>> calendars
>> So far my further explanation on my Tzolkin theory.
>> If you want some more explanations, which I have not expressed
>> correctly or
>> incomprehensibly, please tell me.
>> But, because the Metonic cycle does match with sun and moon only
>> approximately, all calendrically fixed dates shift slowly due to the
>> deviance of the Metonic cycle: in average 1 day in 216 years.
>> This could be the reason for the 1-2 day difference at the azimuth
>> between
>> Sun pyramid and Cuidadela.
>> Here my explanation for this, which you could ascertain much
>> better with
>> your data:
>> If the mayans built a monument aligned to a date and a peculiar
>> sunrise, and
>> after some centuries the alignment did not match anymore with the
>> ("Metonic") date, they constructed a new monument, now aligned
>> with the date
>> again.
>> Thus this make sense for you?
>> In a buzz phrase: the tzolkin makes the Long Count "Metonic". or:
>> Tzolkin
>> and LC together are "METONIC"
>> What do you think about my theory?
>> Could it work to understand the Maya culture rituals and myth better?
>> Could it help to date monuments etc. better?
>> With best regards and hoping for your response
>> Sepp Rothwangl

Re: answer to Maya calendar enigma

2009-11-25T08:30:53Z

Dear Karl,

Thanks! Ok, I see.

But did they use for calculating tzolkins also the uinal-system (base 18)?

Servus

Sepp

Am 25.11.2009 um 17:22 schrieb Karl Palmen:

Dear Sepp

I’m using the same counting system as is used for the Long Count, within which the second digit from the right is base 18 rather than base 20.

From: East Carolina University Calendar discussion List [CALNDR-L@...] On Behalf Of Sepp Rothwangl
Sent: 25 November 2009 16:16
To: CALNDR-L@...
Subject: Re: answer to Maya calendar enigma

Am 25.11.2009 um 16:23 schrieb Karl Palmen:

Dear Karl,
I do not understand your kind of vigesimal system, because I get other resluts.
Please explain, or what I am doing wrong?
Servus
Sepp

The fact that 360-260=100 or 18-13=5 makes the 260 times table in long
count numbers a little easier to learn:
1 tzolkin = 13.0 days = 13*20 =260
correct

2 tzolkins = 1.8.0 days = 20*20+8*20 = 560 ;
2 tzolkins = 1.8.0 days = 20*18+8*20=520.

but 2*260 = 520

3 tzolkins = 2.3.0 days = 2*20*20 +3*20 = 860;
3 tzolkins = 2.3.0 days = 2*20*18+3*20=780.

but 3*260 = 780

4 tzolkins = 2.16.0 days
5 tzolkins = 3.11.0 days
6 tzolkins = 4.6.0 days
7 tzolkins = 5.1.0 days
8 tzolkins = 5.14.0 days
9 tzolkins = 6.9.0 days
10 tzolkins = 7.4.0 days
11 tzolkins = 7.17.0 days
12 tzolkins = 8.12.0 days
13 tzolkins = 9.7.0 days
14 tzolkins = 10.2.0 days
15 tzolkins = 10.15.0 days
16 tzolkins = 11.10.0 days
17 tzolkins = 12.5.0 days
18 tzolkins = 13.0.0 days. 13*18*20 = 18*260 = 4680

Karl

10(15(09

--
Scanned by iCritical.

Re: answer to Maya calendar enigma

2009-11-25T08:22:10Z

Dear Sepp

I’m using the same counting system as is used for the Long Count, within which the second digit from the right is base 18 rather than base 20.

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Sepp Rothwangl
Sent: 25 November 2009 16:16
To: CALNDR-L@...
Subject: Re: answer to Maya calendar enigma

Am 25.11.2009 um 16:23 schrieb Karl Palmen:

Dear Karl,

I do not understand your kind of vigesimal system, because I get other resluts.

Please explain, or what I am doing wrong?

Servus

Sepp

The fact that 360-260=100 or 18-13=5 makes the 260 times table in long

count numbers a little easier to learn:

1 tzolkin = 13.0 days = 13*20 =260

correct

2 tzolkins = 1.8.0 days = 20*20+8*20 = 560 ;

2 tzolkins = 1.8.0 days = 20*18+8*20=520.

but 2*260 = 520

3 tzolkins = 2.3.0 days = 2*20*20 +3*20 = 860;

3 tzolkins = 2.3.0 days = 2*20*18+3*20=780.

but 3*260 = 780

4 tzolkins = 2.16.0 days

5 tzolkins = 3.11.0 days

6 tzolkins = 4.6.0 days

7 tzolkins = 5.1.0 days

8 tzolkins = 5.14.0 days

9 tzolkins = 6.9.0 days

10 tzolkins = 7.4.0 days

11 tzolkins = 7.17.0 days

12 tzolkins = 8.12.0 days

13 tzolkins = 9.7.0 days

14 tzolkins = 10.2.0 days

15 tzolkins = 10.15.0 days

16 tzolkins = 11.10.0 days

17 tzolkins = 12.5.0 days

18 tzolkins = 13.0.0 days. 13*18*20 = 18*260 = 4680

Karl

10(15(09

--
Scanned by iCritical.

Re: answer to Maya calendar enigma

2009-11-25T08:15:44Z

Am 25.11.2009 um 16:23 schrieb Karl Palmen:

Dear Karl,

I do not understand your kind of vigesimal system, because I get other resluts.

Please explain, or what I am doing wrong?

Servus

Sepp

The fact that 360-260=100 or 18-13=5 makes the 260 times table in long
count numbers a little easier to learn:
1 tzolkin = 13.0 days = 13*20 =260

correct

2 tzolkins = 1.8.0 days = 20*20+8*20 = 560 ;

but 2*260 = 520

3 tzolkins = 2.3.0 days = 2*20*20 +3*20 = 860;

but 3*260 = 780

4 tzolkins = 2.16.0 days
5 tzolkins = 3.11.0 days
6 tzolkins = 4.6.0 days
7 tzolkins = 5.1.0 days
8 tzolkins = 5.14.0 days
9 tzolkins = 6.9.0 days
10 tzolkins = 7.4.0 days
11 tzolkins = 7.17.0 days
12 tzolkins = 8.12.0 days
13 tzolkins = 9.7.0 days
14 tzolkins = 10.2.0 days
15 tzolkins = 10.15.0 days
16 tzolkins = 11.10.0 days
17 tzolkins = 12.5.0 days
18 tzolkins = 13.0.0 days. 13*20*20*20 = 104,000

18*260 = 4680

Re: answer to Maya calendar enigma

2009-11-25T07:23:20Z

Dear Victor, Sepp and Calendar People

More about the 260-day Tzolkin cycle with respect to the lunar month and
the long count:

I find that two 73-yerm cycles of 1193 months each have exactly 271
tzolkins. The mean month is 29.530595138... days.
Previously mentioned to this list, is a much less accurate cycle of 405
months of 46 tzolkins, which can be constructed from five 81-month cycle
of five yerms of 17+15+17+15+17 months. The mean month is 29.530864...
days.
If one subtracts the second cycle from the first, you get a 121-yerm
cycle of 1981 months which has 225 tzolkins and so a mean month of
29.530540131... days. This 121-yerm cycle is made up of seven eras of
16+19+16+19+16+19+16 yerms.

The double 73-year cycle and the 121-year cycle form a pair of mixer
cycles for lunar cycles of a whole number of tzolkins and so every such
cycle with a mean month in between their mean months can be formed by
mixing a whole number of each and so must be considerably longer.

The fact that 360-260=100 or 18-13=5 makes the 260 times table in long
count numbers a little easier to learn:
1 tzolkin = 13.0 days
2 tzolkins = 1.8.0 days
3 tzolkins = 2.3.0 days
4 tzolkins = 2.16.0 days
5 tzolkins = 3.11.0 days
6 tzolkins = 4.6.0 days
7 tzolkins = 5.1.0 days
8 tzolkins = 5.14.0 days
9 tzolkins = 6.9.0 days
10 tzolkins = 7.4.0 days
11 tzolkins = 7.17.0 days
12 tzolkins = 8.12.0 days
13 tzolkins = 9.7.0 days
14 tzolkins = 10.2.0 days
15 tzolkins = 10.15.0 days
16 tzolkins = 11.10.0 days
17 tzolkins = 12.5.0 days
18 tzolkins = 13.0.0 days.

Karl

10(15(09

PS: To determine whether a cycle A1 a-units and B1 b-units and a cycle
of A2 a-units and B2 b-units form a pair of mixer cycles, calculate
A1*B2-A2*B1 and if this value is either +1 or -1, then they are mixer
cycles for a-units and b-units.

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Sepp Rothwangl
Sent: 25 November 2009 08:49
To: CALNDR-L@...
Subject: Re: answer to Maya calendar enigma

Hi Vic,

your argue is correct too, thus I said I do not want to mention
Venus, because this was in discussion already.
Your argue and mine are not concurrents, but rather fortify the
reason, why the tzolkin became so important for the Mayas.
But the Katun and 19-year relation with the gap of 260 days in
between was overseen so far.
And IMO the existence of the katun (a 20 multiple of 360), based on
the vigesimal system is one reason for the tzolikin's emergence,
because it created the 260 day gap to the 19-year Sun-Moon-
CONVERGENCE, (so to speak with a word of some Maya-esoterics)

Servus
Sepp

--
Scanned by iCritical.

Re: answer to Maya calendar enigma

2009-11-25T05:00:31Z

Dear Victor, Sepp and Calendar People

In long count numbers the 6940 days of the Metonic cycle is 19.5.0 which would be seen to by 13.0 (=260) days short of 20.0.0.
The period five Venus cycles or 8 haab (365-day) cycles is 8.2.0 days, which is obviously 8 periods of 360 days plus 40, but not obviously 11 periods of 260 days and 60 days.

What strikes me about the 19.5.0 days of the Metonic cycle is the 5 in it suggesting it could be divided by 5. If I do so, I get 3.15.8 days for 47 lunar months, which is 2.12 (=4*13) days short of 4.0.0 days.

This 47-month cycle suggests to me the more accurate 49-month cycle of 4.0.7 days, which I discovered when inventing the Yerm Calendar. This is 13 days short of 4.1.0 days, which is equal to four haab cycles of 1.0.5 days.
The double 49-month cycle, which is much more noticeable than a single 49-month cycle because it has nearly a whole number (7) of full moon cycles, has 8.0.14 days and so is 1.6 (=26) days short of 8 haab cycles or 5 Venus cycles as mentioned by Victor (8.2.0 days).

So 20 cycles of 49 lunar months have 4.0.7.0 days which is 13.0 (=260) days short of 80 haab cycles or 50 Venus cycles. It is also 111 periods of 260 days with 80 days left over.

I discovered these facts about the 49-month cycle while writing this note, which suggests that such coincidences are easy to find.

NB: The '.' in all the numbers of days mentioned is always the digit separator for long count numbers and never a decimal point.

Karl

10(15(09

-----Original Message-----
From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Sepp Rothwangl
Sent: 25 November 2009 08:49
To: CALNDR-L@...
Subject: Re: answer to Maya calendar enigma

Hi Vic,

your argue is correct too, thus I said I do not want to mention
Venus, because this was in discussion already.
Your argue and mine are not concurrents, but rather fortify the
reason, why the tzolkin became so important for the Mayas.
But the Katun and 19-year relation with the gap of 260 days in
between was overseen so far.
And IMO the existence of the katun (a 20 multiple of 360), based on
the vigesimal system is one reason for the tzolikin's emergence,
because it created the 260 day gap to the 19-year Sun-Moon-
CONVERGENCE, (so to speak with a word of some Maya-esoterics)

Servus
Sepp

Am 24.11.2009 um 19:20 schrieb Victor Engel:

--
Scanned by iCritical.

Re: Harappan calendar RE: answer to Maya calendar enigma

2009-11-25T00:55:53Z

Hi Brij,

I understand your argue, but IMO that has nothing to do with the reason why the Maya came up with a ritual 260 day count, except that in both the Metonic cycle was involved.

Servus

Sepp

Am 24.11.2009 um 19:10 schrieb Brij Bhushan Vij:

Sepp, Derek sirs:
You might recall our 'discussions' and E-mail echchange regarding my ideas & linking the Harappan "Phase/Tithi" value of ONE Lunation =29 1/2 Tithi. Please see: http://www.brijvij.com/bb1920_caL-harappa.pdf
Wherefrom, I build the possible calendar that Harappan/Indus civilisation usedduring their flourishing days!
It certainly has been long time when I had your blessing on my various inputs on Calndr-L. The date 21 December, 2012 happen to be 13th - a Friday. My son was born on a 13th, the Friday of 1963 December 13. My input on The 'alternate' World Calendar is placed at: http://www.brijvij.com/bb_alt-wrldCal.pdf
It would be encouraging to hear you comments/views.
Regards,
Brij Bhushan Vij

Re: answer to Maya calendar enigma

2009-11-25T00:48:47Z

Hi Vic,

your argue is correct too, thus I said I do not want to mention
Venus, because this was in discussion already.
Your argue and mine are not concurrents, but rather fortify the
reason, why the tzolkin became so important for the Mayas.
But the Katun and 19-year relation with the gap of 260 days in
between was overseen so far.
And IMO the existence of the katun (a 20 multiple of 360), based on
the vigesimal system is one reason for the tzolikin's emergence,
because it created the 260 day gap to the 19-year Sun-Moon-
CONVERGENCE, (so to speak with a word of some Maya-esoterics)

Servus
Sepp

Am 24.11.2009 um 19:20 schrieb Victor Engel:

Re: answer to Maya calendar enigma

2009-11-24T18:48:56Z

Dear Sepp,

It is very interesting.

Where I can read the article “ASTRONOMICAL ALIGNMENTS AT TEOTIHUACAN”?

Give me the link, please.

Best regards,

Vladimir Pakhomov

http://pakhomov.com/

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Sepp Rothwangl
Sent: Tuesday, November 24, 2009 8:42 PM
To: CALNDR-L@...
Subject: answer to Maya calendar enigma

…

Sprajc wrote an article about: ASTRONOMICAL ALIGNMENTS AT TEOTIHUACAN…

Re: answer to Maya calendar enigma

2009-11-24T10:20:58Z

Dear Sepp and Calendar People,

I think you are essentially correct. But I think Venus plays an
important part as well. Venus and Earth orbit in lock step with each
other. One cycle is 2920 days. That is 8 periods of 360 days with 40
left over, or 11 periods of 260 days with 60 left over. The difference
between 60 and 40 is 20, one man.

A few years ago I played around with all sorts of astronomical
phenomena and was amazed how often the numbers 13 and 20 enter into
alignments such as this. Each occurrence reinforces the significance
of the numbers.

Victor

On Tue, Nov 24, 2009 at 11:42 AM, Sepp Rothwangl <calendersign@...> wrote:

> Dear list,
> I found the answer to a Mayan calendar enigma: the tzolkin.
> The origin of the Mayan 260-day calendar, called tzolkin was cyptic and many
> argues occured, how it came about.
>
> The book "The End of Time: The Maya Mystery of 2012" by Anthony Aveni gave
> me incentive and ecouraged me, to consider once again an idea that I had in
> my mind already some time ago.
> I have discussed this now with Ivan Sprajc and Anthony Aveni. Both finds my
> idea very interesting. Aveni wrote: "that the Maya may have known" the facts
> of theory "very likely"!
> Sprajc wrote an article about: ASTRONOMICAL ALIGNMENTS AT TEOTIHUACAN, LATIN
> AMERICAN ANTIQUITY, Vol 11,4,2000), where he argues, that the geographical
> situation of Teotuhuacan caused an architectural design with the reslut of
> the 260 day count. (the sun pyramid aligned to (Aug 13 + 260 days = apr 30 ;
> feb 10 + 260 days = oct 30).
> Thus I need not to cite more of his arguments, which sound convincing, nor
> im mention here other arguments of the 260 days, like the female pregnancy
> period, Venus' visibility, and maize ripening period.
> Please allow me to explain now my theory:
> No doubt, the Mayans wanted to keep time also with the moon and not only
> with the sun.
> And here I think I found the missing link!
> The Tzolkin itself IMO is the missing link between the Mayan Long Count (LC)
> and the best-matching luni-solar period: the Metonic cycle.
> I found this, firstly because I am a bit legasthenic and always consider
> things from two sides (also from opposite, or inverted side, LOL)
> and secondly, because I dived deep into the history of the 19-year cycle,
> which surely must be very old and global. Think of the 19-folded Golden Hats
> etc. (http://en.wikipedia.org/wiki/Golden_hat)
> IMO also the Phenix period and the 216 year period of Pythagoras is linked
> to it. This "one day shift" in 216 years could also be the reason for the
> azimuthal difference between Sun Pyramid and the Ciudadela. (but this still
> needs to be checked closer).
> Please consider with me the calendar at the hand of simple math:
> 19 solar years and 235 lunar month differ by only 2 h, 6 min, 41 sec!
> Or expressed in days:
> 6939.68959 days for 235 lunar month
> 6939.60161 days for 19 years.
> If you round this up you arrive at 6940 days, the value of the Metonic cycle
> as known in antiquity.
> This period is EXACTLY 260 days (!) shorter than the Mayan katun with its
> 7200 days.
> I wonder, that this was not found by some Mayan calendar experts. Or, was
> this discussed already somewhere else? I could not find any citation.
> IMO the tzolkin came about to due the vigesimal system, Mayas using fingers
> togehter with toes.
> Counting in this way (with base 20) the days of the year result in 20 times
> 18 = 360 and some epagomenal days.
> How could the Tzolkin have started?
> If you want to find the average or true length of the year, you need to
> count as many as possible years and count all contained days.
> In the Mayan vigesimal way of counting this was 20 times 18x20.
> To do this you simply need to watch when the sun rises or sets again at
> always the same position of the horizon again and again.
> When you observe also the moon at the same particular day of a year you will
> experience that always exactly after 19 years the moon is at the same phase
> as is the sun's position at the horizon. I need not to explain you, that
> this is the case after 19 years and repeats in the same way every 19 years
> over quite a long time.
> By chance (or coincidence) this event is always 260 days shorter than a
> katun (20x18x20 = 7200)
> Thus IMO these 260 days became ritually so important to expect the end or
> begin of the next katun.
> By the "auxiliary" of the tzolkin, which was NOT a counting-system with
> numbers in our way, but rather a symbolic design of a value, it was easily
> to find the temporal distance to any date of the katun and to the phases of
> the moon and the cardinal or symmetric solar dates (260 days apart).
> IMO the 260 day period is caused by the difference of the katun and the
> Metonic period.
> Expressed in other words:
> If you know E.g. a cardinal date of any katun, you only have to subtract 260
> days before the end of the next katun, to know the exact date of moon and
> sun.
> the 260 days gives you always an orientation towards sun and moon, similar
> to the Golden Numbers of the Julian calendar.
> After having having reallized that relation of Katun and the 19-year period,
> some ancient Mayan astronomer may have wanted to implement that regularity
> into the annual periods and found that fantastic symmetry and and parallel
> of risings and settings of the sun at horizon, mirroring the 260 days at
> specific data (Aug 13 + 260 days = apr 30 ; feb 10 + 260 days = oct 30)
> Thus the tzolkin became so important for a ritual time keeping, as well as
> for architectural design.
> It is a kind of countdown for the end of any katun, similar to the Christian
> advent calendar, which count days up to Christ's annual fictitious birthday
> (or as children counting down the days by the closed doors of their Advent
> calendar in anticipation Christmas)
> Besides the article of Spraic, exist for the azimuthal orientation of Mayan
> buildings in the "260-days-design" lot of literature, e.g.:
> Malmström, V. H. : A Reconstruction of the Chronology of Mesoamerican
> Calendrical Systems; Journal for the History of Astronomy, Vol. 9,
> Aveni A.: Archaeoastronomy in the Ancient Americas, Journal of
> Archaeological Research Volume 11, Number 2 / Juni 2003
> Milbrath, Susan: Star gods of the Maya: astronomy in art, folklore, and
> calendars
> So far my further explanation on my Tzolkin theory.
> If you want some more explanations, which I have not expressed correctly or
> incomprehensibly, please tell me.
> But, because the Metonic cycle does match with sun and moon only
> approximately, all calendrically fixed dates shift slowly due to the
> deviance of the Metonic cycle: in average 1 day in 216 years.
> This could be the reason for the 1-2 day difference at the azimuth between
> Sun pyramid and Cuidadela.
> Here my explanation for this, which you could ascertain much better with
> your data:
> If the mayans built a monument aligned to a date and a peculiar sunrise, and
> after some centuries the alignment did not match anymore with the
> ("Metonic") date, they constructed a new monument, now aligned with the date
> again.
> Thus this make sense for you?
> In a buzz phrase: the tzolkin makes the Long Count "Metonic". or: Tzolkin
> and LC together are "METONIC"
> What do you think about my theory?
> Could it work to understand the Maya culture rituals and myth better?
> Could it help to date monuments etc. better?
> With best regards and hoping for your response
> Sepp Rothwangl

Harappan calendar RE: answer to Maya calendar enigma

2009-11-24T10:10:39Z

Sepp, Derek sirs:
You might recall our 'discussions' and E-mail echchange regarding my ideas & linking the Harappan "Phase/Tithi" value of ONE Lunation =29 1/2 Tithi. Please see: http://www.brijvij.com/bb1920_caL-harappa.pdf
Wherefrom, I build the possible calendar that Harappan/Indus civilisation usedduring their flourishing days!
It certainly has been long time when I had your blessing on my various inputs on Calndr-L. The date 21 December, 2012 happen to be 13th - a Friday. My son was born on a 13th, the Friday of 1963 December 13. My input on The 'alternate' World Calendar is placed at: http://www.brijvij.com/bb_alt-wrldCal.pdf
It would be encouraging to hear you comments/views.
Regards,
Brij Bhushan Vij
(MJD 2455160)/1361+D-336W48-02 (G. Tuesday, 2009 November 24H13:7(decimal) EST
Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda
Jan:31; Feb:29; Mar:31; Apr:30; May:31; Jun:30
Jul:30; Aug:31; Sep:30; Oct:31; Nov:30; Dec:30
(365th day of Year is World Day)
My Profile:http://www.brijvij.com/bbv_2col-vipBrief.pdf
HOME PAGE: http://www.brijvij.com/
******As per Kali V-GRhymeCalendaar*****
"Koi bhi cheshtha vayarth nahin hoti, purshaarth karne mein hai"
Contact # 001 (201) 675-8548

Date: Tue, 24 Nov 2009 18:42:10 +0100
From: calendersign@...
Subject: answer to Maya calendar enigma
To: CALNDR-L@...

Dear list,

I found the answer to a Mayan calendar enigma: the tzolkin.

The origin of the Mayan 260-day calendar, called tzolkin was cyptic and many argues occured, how it came about.

The book "The End of Time: The Maya Mystery of 2012" by Anthony Aveni gave me incentive and ecouraged me, to consider once again an idea that I had in my mind already some time ago.

I have discussed this now with Ivan Sprajc and Anthony Aveni. Both finds my idea very interesting. Aveni wrote: "that the Maya may have known" the facts of theory "very likely"!

Sprajc wrote an article about: ASTRONOMICAL ALIGNMENTS AT TEOTIHUACAN, LATIN AMERICAN ANTIQUITY, Vol 11,4,2000), where he argues, that the geographical situation of Teotuhuacan caused an architectural design with the reslut of the 260 day count. (the sun pyramid aligned to (Aug 13 + 260 days = apr 30 ; feb 10 + 260 days = oct 30).

Thus I need not to cite more of his arguments, which sound convincing, nor im mention here other arguments of the 260 days, like the female pregnancy period, Venus' visibility, and maize ripening period.

Please allow me to explain now my theory:

No doubt, the Mayans wanted to keep time also with the moon and not only with the sun.

And here I think I found the missing link!

The Tzolkin itself IMO is the missing link between the Mayan Long Count (LC) and the best-matching luni-solar period: the Metonic cycle.

I found this, firstly because I am a bit legasthenic and always consider things from two sides (also from opposite, or inverted side, LOL)

and secondly, because I dived deep into the history of the 19-year cycle, which surely must be very old and global. Think of the 19-folded Golden Hats etc. (http://en.wikipedia.org/wiki/Golden_hat)

IMO also the Phenix period and the 216 year period of Pythagoras is linked to it. This "one day shift" in 216 years could also be the reason for the azimuthal difference between Sun Pyramid and the Ciudadela. (but this still needs to be checked closer).

Please consider with me the calendar at the hand of simple math:

19 solar years and 235 lunar month differ by only 2 h, 6 min, 41 sec!

Or expressed in days:

6939.68959 days for 235 lunar month

6939.60161 days for 19 years.

If you round this up you arrive at 6940 days, the value of the Metonic cycle as known in antiquity.

This period is EXACTLY 260 days (!) shorter than the Mayan katun with its 7200 days.

I wonder, that this was not found by some Mayan calendar experts. Or, was this discussed already somewhere else? I could not find any citation.

IMO the tzolkin came about to due the vigesimal system, Mayas using fingers togehter with toes.

Counting in this way (with base 20) the days of the year result in 20 times 18 = 360 and some epagomenal days.

How could the Tzolkin have started?

If you want to find the average or true length of the year, you need to count as many as possible years and count all contained days.

In the Mayan vigesimal way of counting this was 20 times 18x20.

To do this you simply need to watch when the sun rises or sets again at always the same position of the horizon again and again.

When you observe also the moon at the same particular day of a year you will experience that always exactly after 19 years the moon is at the same phase as is the sun's position at the horizon. I need not to explain you, that this is the case after 19 years and repeats in the same way every 19 years over quite a long time.

By chance (or coincidence) this event is always 260 days shorter than a katun (20x18x20 = 7200)

Thus IMO these 260 days became ritually so important to expect the end or begin of the next katun.

By the "auxiliary" of the tzolkin, which was NOT a counting-system with numbers in our way, but rather a symbolic design of a value, it was easily to find the temporal distance to any date of the katun and to the phases of the moon and the cardinal or symmetric solar dates (260 days apart).

IMO the 260 day period is caused by the difference of the katun and the Metonic period.

Expressed in other words:

If you know E.g. a cardinal date of any katun, you only have to subtract 260 days before the end of the next katun, to know the exact date of moon and sun.

the 260 days gives you always an orientation towards sun and moon, similar to the Golden Numbers of the Julian calendar.

After having having reallized that relation of Katun and the 19-year period, some ancient Mayan astronomer may have wanted to implement that regularity into the annual periods and found that fantastic symmetry and and parallel of risings and settings of the sun at horizon, mirroring the 260 days at specific data (Aug 13 + 260 days = apr 30 ; feb 10 + 260 days = oct 30)

Thus the tzolkin became so important for a ritual time keeping, as well as for architectural design.

It is a kind of countdown for the end of any katun, similar to the Christian advent calendar, which count days up to Christ's annual fictitious birthday (or as children counting down the days by the closed doors of their Advent calendar in anticipation Christmas)

Besides the article of Spraic, exist for the azimuthal orientation of Mayan buildings in the "260-days-design" lot of literature, e.g.:

Malmström, V. H. : A Reconstruction of the Chronology of Mesoamerican Calendrical Systems; Journal for the History of Astronomy, Vol. 9,

Aveni A.: Archaeoastronomy in the Ancient Americas, Journal of Archaeological Research Volume 11, Number 2 / Juni 2003

Milbrath, Susan: Star gods of the Maya: astronomy in art, folklore, and calendars

So far my further explanation on my Tzolkin theory.

If you want some more explanations, which I have not expressed correctly or incomprehensibly, please tell me.

But, because the Metonic cycle does match with sun and moon only approximately, all calendrically fixed dates shift slowly due to the deviance of the Metonic cycle: in average 1 day in 216 years.

This could be the reason for the 1-2 day difference at the azimuth between Sun pyramid and Cuidadela.

Here my explanation for this, which you could ascertain much better with your data:

If the mayans built a monument aligned to a date and a peculiar sunrise, and after some centuries the alignment did not match anymore with the ("Metonic") date, they constructed a new monument, now aligned with the date again.

Thus this make sense for you?

In a buzz phrase: the tzolkin makes the Long Count "Metonic". or: Tzolkin and LC together are "METONIC"

What do you think about my theory?

Could it work to understand the Maya culture rituals and myth better?

Could it help to date monuments etc. better?

With best regards and hoping for your response

Sepp Rothwangl

Windows 7: It works the way you want. Learn more.

answer to Maya calendar enigma

2009-11-24T09:42:10Z

Dear list,

I found the answer to a Mayan calendar enigma: the tzolkin.

The origin of the Mayan 260-day calendar, called tzolkin was cyptic and many argues occured, how it came about.

The book "The End of Time: The Maya Mystery of 2012" by Anthony Aveni gave me incentive and ecouraged me, to consider once again an idea that I had in my mind already some time ago.

I have discussed this now with Ivan Sprajc and Anthony Aveni. Both finds my idea very interesting. Aveni wrote: "that the Maya may have known" the facts of theory "very likely"!

Please allow me to explain now my theory:

No doubt, the Mayans wanted to keep time also with the moon and not only with the sun.

And here I think I found the missing link!

The Tzolkin itself IMO is the missing link between the Mayan Long Count (LC) and the best-matching luni-solar period: the Metonic cycle.

I found this, firstly because I am a bit legasthenic and always consider things from two sides (also from opposite, or inverted side, LOL)

and secondly, because I dived deep into the history of the 19-year cycle, which surely must be very old and global. Think of the 19-folded Golden Hats etc. (http://en.wikipedia.org/wiki/Golden_hat)

Please consider with me the calendar at the hand of simple math:

19 solar years and 235 lunar month differ by only 2 h, 6 min, 41 sec!

Or expressed in days:

6939.68959 days for 235 lunar month

6939.60161 days for 19 years.

If you round this up you arrive at 6940 days, the value of the Metonic cycle as known in antiquity.

This period is EXACTLY 260 days (!) shorter than the Mayan katun with its 7200 days.

I wonder, that this was not found by some Mayan calendar experts. Or, was this discussed already somewhere else? I could not find any citation.

IMO the tzolkin came about to due the vigesimal system, Mayas using fingers togehter with toes.

Counting in this way (with base 20) the days of the year result in 20 times 18 = 360 and some epagomenal days.

How could the Tzolkin have started?

If you want to find the average or true length of the year, you need to count as many as possible years and count all contained days.

In the Mayan vigesimal way of counting this was 20 times 18x20.

To do this you simply need to watch when the sun rises or sets again at always the same position of the horizon again and again.

By chance (or coincidence) this event is always 260 days shorter than a katun (20x18x20 = 7200)

Thus IMO these 260 days became ritually so important to expect the end or begin of the next katun.

IMO the 260 day period is caused by the difference of the katun and the Metonic period.

Expressed in other words:

If you know E.g. a cardinal date of any katun, you only have to subtract 260 days before the end of the next katun, to know the exact date of moon and sun.

the 260 days gives you always an orientation towards sun and moon, similar to the Golden Numbers of the Julian calendar.

Thus the tzolkin became so important for a ritual time keeping, as well as for architectural design.

Besides the article of Spraic, exist for the azimuthal orientation of Mayan buildings in the "260-days-design" lot of literature, e.g.:

Malmström, V. H. : A Reconstruction of the Chronology of Mesoamerican Calendrical Systems; Journal for the History of Astronomy, Vol. 9,

Aveni A.: Archaeoastronomy in the Ancient Americas, Journal of Archaeological Research Volume 11, Number 2 / Juni 2003

Milbrath, Susan: Star gods of the Maya: astronomy in art, folklore, and calendars

So far my further explanation on my Tzolkin theory.

If you want some more explanations, which I have not expressed correctly or incomprehensibly, please tell me.

But, because the Metonic cycle does match with sun and moon only approximately, all calendrically fixed dates shift slowly due to the deviance of the Metonic cycle: in average 1 day in 216 years.

This could be the reason for the 1-2 day difference at the azimuth between Sun pyramid and Cuidadela.

Here my explanation for this, which you could ascertain much better with your data:

Thus this make sense for you?

In a buzz phrase: the tzolkin makes the Long Count "Metonic". or: Tzolkin and LC together are "METONIC"

What do you think about my theory?

Could it work to understand the Maya culture rituals and myth better?

Could it help to date monuments etc. better?

With best regards and hoping for your response

Sepp Rothwangl

Brij Calendar the alternate RE: Assyrian 364-day Calendar - more about it.

2009-11-23T11:21:10Z

Wilfered Akhas, sirs:
I have been discussing my ideas on Reform of Gregorian calendar, since 1971... through Indian media and later through USMA & Calndr-L lists. I post you a link expressing some 'developments of my thoughts' that lead me to 9*1730-yrs/192574 lunation cycle that give, almost current value for Mean Year & Mean lunation. Please see: http://www.brijvij.com/bb_alt-wrldCal.pdf
Yur views on my approach are welcome. Thanks for your time.
Brij Bhushan Vij
(MJD 2455159)/1361+D-335W48-01 (G. Monday, 2009 November 23H14:34 (decimal) EST
Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda
Jan:31; Feb:29; Mar:31; Apr:30; May:31; Jun:30
Jul:30; Aug:31; Sep:30; Oct:31; Nov:30; Dec:30
(365th day of Year is World Day)
My Profile:http://www.brijvij.com/bbv_2col-vipBrief.pdf
HOME PAGE: http://www.brijvij.com/
******As per Kali V-GRhymeCalendaar*****
"Koi bhi cheshtha vayarth nahin hoti, purshaarth karne mein hai"
Contact # 001 (201) 675-8548

Date: Mon, 23 Nov 2009 14:16:21 +0000
From: karl.palmen@...
Subject: Assyrian 364-day Calendar - more about it.
To: CALNDR-L@...

Dear Calendar People

This calendar resembles the Iranian/Persian calendar, but has 30 instead of 31 days in the sixth month and there is no mention of a leap day, but a leap month is mentioned.

The only reference provided by the article is http://www.nineveh.com/Assyrian%20Calendar.html by Wilfred Alkhas , which does not appear to back up any assertions concerning the number of days in the months or usage of the calendar from the 1950s.

Karl

10(15(07

_____________________________________________
From: Palmen, Karl (STFC,RAL,CICT)
Sent: 20 November 2009 14:17
To: CALNDR-L@...
Subject: Assyrian 364-day Calendar

Dear Calendar People

A Wikipedia article claims the existence of a modern Assyrian calendar introduced in the 1950s that has 364 days in a year.

The article is http://en.wikipedia.org/wiki/Assyrian_calendar

Has this calendar been used and is it correctly described in the article?

Karl

10(15(04

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Re: Gear/Chain Lunisolar Device

2009-11-23T09:04:16Z

Dear Karl and Calendar People,

On Mon, Nov 23, 2009 at 7:06 AM, Karl Palmen <karl.palmen@...> wrote:
> Dear Victor and Calendar People
>
> I can't quite grasp Victor's scheme.

I wonder. What follows seems to indicate that Karl does, indeed, grasp
the scheme or at least guesses correctly.

> I guess that the 7 and 13 tooth wheels correct the approximation of the
> 1/19 lunar month to 14/9 days by the first wheel and chain.

Yes.

> If uncorrected, the mean month would be 266/9 = 29.555555... days. If I
> subtract a mean of 29.530593 days from it and take the reciprocal I get
> 40.06 to an astonishing accuracy. This suggests that the correction rate
> is very close to one day per 40.06 lunar months. If find that 40.06
> lunar months of 29.530593 days is very close to 1183 days. I vaguely
> recall this 1183 days. This 1183 is 7*13*13 so the 7 and 13 tooth wheels
> are a way of counting 1183 days. One every 1183 days two hooks are moved
> instead of the usual one hook.

Exactly. And here I'd like to interject that 7 is the number of days
in a week, and 7*13 is the number of days in a normal quarter, thus
making wheels of these sizes very convenient.

> The exact value of the mean month is then (266/9)*(1183/1184) =
> 29.5305930930 with 930 recurring = 29 2827/5328.
> So the equivalent lunar calendar would have a period of 5328 months,
> three of which form the period of Victor's mechanism.
> The 5328-month cycle has 326 yerms grouped into 5 eras, which can have
> 64+67+64+67+64 yerms.
> The short repetition period of the decimal fraction arises from the fact
> that 5382 is 37 times a number with no prime divisor greater than 3.
> This also applies to 1184 = 37 * 2^5, which is 1/3 of 5382.
>
> (1183/1184) = (7/4)*(13/8)*(13/37) so can be realised by gears of these
> ratios.

I hadn't thought of directly using gears like this, but I like the
idea. Four teeth is rather few for a gear, though, so the first gear
would probably be (14/8) instead.

Victor

Assyrian 364-day Calendar - more about it.

2009-11-23T06:16:21Z

Assyrian 364-day Calendar - more about it.

Dear Calendar People

This calendar resembles the Iranian/Persian calendar, but has 30 instead of 31 days in the sixth month and there is no mention of a leap day, but a leap month is mentioned.

Karl

10(15(07

_____________________________________________
From: Palmen, Karl (STFC,RAL,CICT)
Sent: 20 November 2009 14:17
To: CALNDR-L@...
Subject: Assyrian 364-day Calendar

Dear Calendar People

A Wikipedia article claims the existence of a modern Assyrian calendar introduced in the 1950s that has 364 days in a year.

The article is http://en.wikipedia.org/wiki/Assyrian_calendar

Has this calendar been used and is it correctly described in the article?

Karl

10(15(04

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Re: Gear/Chain Lunisolar Device

2009-11-23T05:06:14Z

Dear Victor and Calendar People

I can't quite grasp Victor's scheme.

I guess that the 7 and 13 tooth wheels correct the approximation of the
1/19 lunar month to 14/9 days by the first wheel and chain.

If uncorrected, the mean month would be 266/9 = 29.555555... days. If I
subtract a mean of 29.530593 days from it and take the reciprocal I get
40.06 to an astonishing accuracy. This suggests that the correction rate
is very close to one day per 40.06 lunar months. If find that 40.06
lunar months of 29.530593 days is very close to 1183 days. I vaguely
recall this 1183 days. This 1183 is 7*13*13 so the 7 and 13 tooth wheels
are a way of counting 1183 days. One every 1183 days two hooks are moved
instead of the usual one hook.

The exact value of the mean month is then (266/9)*(1183/1184) =
29.5305930930 with 930 recurring = 29 2827/5328.
So the equivalent lunar calendar would have a period of 5328 months,
three of which form the period of Victor's mechanism.
The 5328-month cycle has 326 yerms grouped into 5 eras, which can have
64+67+64+67+64 yerms.
The short repetition period of the decimal fraction arises from the fact
that 5382 is 37 times a number with no prime divisor greater than 3.
This also applies to 1184 = 37 * 2^5, which is 1/3 of 5382.

(1183/1184) = (7/4)*(13/8)*(13/37) so can be realised by gears of these
ratios.

Victor's 14/9 wheel and chain system can be in calendar terms be
realised by a 14-day cycle of nine cells of one or two days arranged as
a simple alternating Helios cycle (2,1,2,1,2,1,2,1,2). There are 19 cell
per lunar month and usually 235 cells per year.
Correcting this by a one day (once every 1183 days) would add
considerable jitter to the lunar months. However this cycle can be
corrected by any multiple of 1/14 day. 1183 divides by 7, so this
suggests correcting by 1/7=2/14 day once every 1183/7=169 days.
Hence once every 169 days the current 14-day cycle is corrected by
inserting four cells following the same alternating pattern (so lasting
six days). These inserted cells count as part of the 169 days, so 163
days are counted besides those of the four inserted cells.
This can be done by means of an accumulator of limit 163 and increment
14 for each fortnight of either 9 cells of 14 days or 13 cells of 20
days. The accumulator indicates who many days before the end of its
fortnight the most recent correction was completed. This gives rise to a
cycle of 163 fortnights of which 14 have been extended to 20 days, which
lasts twice 1183 days.

Karl

10(15(07

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Victor Engel
Sent: 20 November 2009 17:35
To: CALNDR-L@...
Subject: Gear/Chain Lunisolar Device

Dear Karl and Calendar People,

Some time ago I described a device arranged as follows:

* A lower wheel has a gear with 9 teeth and 14 hooks.
* A chain with 235 teeth is driven by this gear.
* The chain drives a lunar wheel having 19 teeth.

Normally, the device is manipulated one hook per day. Previously, I
described adjusting the device every time there is a lunar eclipse.
This occasionally will result in a hook being moved a day earlier than
it normally would have.

I thought of another procedure that doesn't rely on observing the moon.

Two wheels, having 13 and 7 teeth respectively, work together, being
aligned at the same spot on the chain. Each wheel has one tooth
specially marked. They line up once every 13*7=91 days, or once a
quarter. The 13 toothed wheel has another marker. Each time an
alignment marks a new quarter, this second marker is moved one tooth.
When this manipulation results in the two markers lining up, an extra
hook is moved.

This results in a mean lunation of 29.530593 days. Thus described, the
mean year would be 365.2468 days.

Previously, I described an adjustment of the year using two pegs on
the 19 tooth lunar wheel. Since it operates independently, the device
could thus track two years, one of 365.2468 days and the other of
365.2422 or 365.2425 days.

Victor

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Re: New version of my Java calendar packa

2009-11-22T22:41:15Z

On Fri, Nov 20, 2009 at 11:28:45PM +0100, Tom Peters wrote:
> http://joyds1.joensuu.fi/calendar/calendar-0.12.zip
> Not Found

Oops! Now the files are where they should be.

I hope. (-:

Re: Gregorian Easter question

2009-11-22T22:12:13Z

On 2009 Nov 22, at 06:18 , Tom Peters wrote:

The question remains: does the molad match a conjunction, or a first visibility?
The molad interval is pretty accurate, and has accumulated an error with respect to our "true" mean Moon of only 6 hours or so since they started using it. Difference between conjunction and first visibility is at least a day. So it should be possible to discriminate between the two definitions used.

Irv replies:

The molad moment is nowhere near (well before) first visibility.

Its variance from the mean conjunction moment is less than the variance of the actual conjunction moments from the actual mean conjunction moments.

The molad calculation was started long before 359 AD -- I reckoned it to have been started in the era of Hipparchus, as that was the era when the traditional calculation was closest to the actual mean conjunction moments, as I have explained at <http://www.sym454.org/hebrew/molad.htm>. Note that there was a near mid-day total solar eclipse that crossed central Israel from west to east not long before the calculation seems to have been started, perhaps that eclipse was the inspiration for developing the molad calculation? On the other hand, the traditional molad calculation is not a good approximation for that eclipse moment.

Today the accumulated error since the era of Hipparchus is actually just under 2 mean solar hours.

There can be no doubt that the molad was intended as a mean conjunction moment, but it is an approximation whose inaccuracy is growing ~ quadratically. In the present era for the month of Tishrei, which is the only month that is directly affected by the molad moment, the molad is on average 5+2/3 hours late, if Jerusalem is taken as the intended meridian, although there is no primary traditional source that I know of that specified Jerusalem as the original meridian. The first molad at the Hebrew calendar epoch was implicitly reckoned for the Garden of Eden. Today the molad moments correspond closely to the mean lunar conjunction moments at the meridian of Qandahar, Afghanistan, but due to the progressively excessive length of the traditional molad interval the meridian that correlates best is continuing to drift eastward at an accelerating rate.

So if the molad calculation was already in use, and the 19-year Metonic cycle was already known for centuries, then what happened to the Hebrew calendar in 359 AD? The Romans banned the calendar messengers from announcing the start of each month, so the Sanhedrin discontinued the observational calendar and established fixed month lengths, fixed leap cycle (probably skipping one octaeteris as I have explained at <http://www.sym454.org/hebrew/drift.htm>), use of the molad to provisionally reckon the first day of Tishrei, and the Rosh HaShanah postponement rules (formalizing what had been the de facto practice for avoiding starting Rosh HaShanah on ritually inconvenient weekdays). This fixed arithmetic design is rather complex and therefore could not have been worked out in only a month -- somebody must have developed it many years earlier and then the Sanhedrin must have had it available for internal verification purposes long before its release.

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/hebrew/>

Re: Gregorian Easter question

2009-11-22T18:11:47Z

Tom Peters wrote:
> The question remains: does the molad match a conjunction, or a first visibility?

http://www.biu.ac.il/JH/Parasha/eng/vahet/lev.html

Quoting from Yaakov Lewinger at Bar-Ilan University:

<<Therefore, to find astronomical verification that our calendar was founded in 359 (CE) we must examine whether the spring equinox actually coincided with the appearance of the new moon in Nisan in the first year of the cycle then being followed.>>

<<The year 359, which is 4119 by the Jewish calendar, fell in the 217th lunar month of our calendar. In the first year of this cycle, namely 4105 by the Jewish calendar, both the actual spring equinox and the "mean" appearance of the new moon of Nisan fell on the 29th of Adar, corresponding to March 20, 345, with only about a six-hour difference between the two. Therefore, in terms of astronomy, the tradition that our calendar was founded near this time appears quite reasonable.>>

End of quote.

Wednesday, March 20 of 345 AD was the day of the True New Moon (conjunction) and the Mean New Moon (conjunction) and the True Vernal Equinox and the Tekufah (Hebrew Calendar Nominal Equinox) all in one. A fine occasion for re-calibrating a Lunar Calendar. The Hebrew Molad was at 8 hours and 642 parts on that day (a "calendric echo" of Hebrew Year 1 when the Molad of Nissan was at 9 hours and 642 parts). Six Months later the Molad of Tishrei was at 13 hours 0 parts (a "calendric echo" of the beginning of Hebrew Year 2, marking the Creation of Adam at the moment of the Molad, 14 hours and 0 parts).

That Molad of Tishrei in 345 AD was on Friday September 13 julian. The True New Moon (conjunction) was about 16:13 GMT on September 12th. Adding 2 hrs 21 minutes for Jerusalem Time makes 18:34, which is after 6 PM (approximate Sunset near time of the Equinox), therefore the True New Moon was shortly after the beginning of September 13 by Hebrew Reckoning... the same day as the Molad.

The True New Moon of March 20 was about 14 hours 24 minutes LATER than the Molad. The True New Moon of September 12th or 13th was about 12 hours 26 minutes EARLIER than the Molad. If Mean New Moons were to average out this difference, we see that the Molad was within a couple of hours from the Mean New Moon (conjunction) at the time of the Hebrew Calendar Reform of about 359 AD (and possibly calibrated to these observations at the beginning of the Metonic Cycle in 345 AD.

-- Robert H. Douglass

Re: Gregorian Easter question

2009-11-22T03:18:10Z

Op 22-nov-2009, om 0:47 heeft Irv Bromberg het volgende geschreven:

> On 2009 Nov 20, at 10:54 , RDoug wrote:
>> Traditional Jewish Calendar (First Century) used observed crescents.
>> Calculated Jewish Calendar (since 359 AD) uses calculated mean
>> conjunction.
>
> Irv replies:
>
> Actually, the fixed arithmetic Hebrew calendar used since 359 AD
> employs the "molad", which if intended to be a mean conjunction is
> a rather crude approximation that is growing progressively more
> erroneous at an accelerating rate due to the increasingly excessive
> length of the traditional molad interval = 29d 12h 44+1/18m
> relative to the astronomical mean synodic month.
>
> The traditional molad moment is calculated as HebrewEpoch +
> 467/2160 of a day + [the traditional molad interval x the number of
> months elapsed since the epoch].

The question remains: does the molad match a conjunction, or a first
visibility?
The molad interval is pretty accurate, and has accumulated an error
with respect to our "true" mean Moon of only 6 hours or so since they
started using it. Difference between conjunction and first
visibility is at least a day. So it should be possible to
discriminate between the two definitions used.

--
Tom Peters

Re: Gregorian Easter question

2009-11-21T15:47:51Z

On 2009 Nov 20, at 10:54 , RDoug wrote:

Traditional Jewish Calendar (First Century) used observed crescents.
Calculated Jewish Calendar (since 359 AD) uses calculated mean conjunction.

Irv replies:

Actually, the fixed arithmetic Hebrew calendar used since 359 AD employs the "molad", which if intended to be a mean conjunction is a rather crude approximation that is growing progressively more erroneous at an accelerating rate due to the increasingly excessive length of the traditional molad interval = 29d 12h 44+1/18m relative to the astronomical mean synodic month.

The traditional molad moment is calculated as HebrewEpoch + 467/2160 of a day + [the traditional molad interval x the number of months elapsed since the epoch].

In the context of this thread, the above comment would seem to imply that the molad has something to do with the start of each Hebrew month, but that is not the case at all.

The molad only determines, provisionally, the first day of the Hebrew month of Tishrei (Rosh HaShanah), but the actual day is subject to Rosh HaShanah postponement rules that can delay it by 0, 1 or 2 days. For other calendar months, even though the moment of the molad is publicly announced on the Sabbath prior the start of the month, the announced moment in no way affects when the month will start.

For more information, please see: <http://www.sym454.org/hebrew/molad.htm> and <http://www.sym454.org/hebrew/postpone.htm>.

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/hebrew/>

Re: New version of my Java calendar packa

2009-11-20T14:28:45Z

Op 20-nov-2009, om 8:17 heeft Hannu Väisänen het volgende geschreven:

> I have released a new version of my Java calendar package.
>
> http://joyds1.joensuu.fi/calendar/index.html

Thanx, but:

http://joyds1.joensuu.fi/calendar/calendar-0.12.zip
Not Found

The requested URL /calendar/calendar-0.12.zip was not found on this
server.

--
Tom Peters

Bessilian Y2007 RE: New moon closest to new year, and solar year/lunation patterns closest to mean lunation/tropical year

2009-11-20T12:06:52Z

Karl, CC sirs:
>.....what year when the new moon was closest to the new Besselian*/Rotation-adjusted/Mean orbitial year?

*(Sun Longitude 280.00°)

New Moon on Wednesday, 2014 Jan 1 11:14 correspond to (2000 + (2456658 -2451544.533 ¸ 365.242189669781)=2014.00020902466 BY

Full Moon on Monday, 2007 January 01 05:29 =(2000 + (2454101.228328-2451544.533 ¸ 365.242189669781)

=2007.000000000853 BY with its Sun Longitude is close to 280-degree. This event, shall slightly be earlier on Wednesday, 2007 Jan 3 13:57 (Full Moon), can be the serious candidate, if astronomers, deem fit that fall in line with [(Y2000 - 80)+/- 128] at Y1920 plus 87, as the 1st Keplers Leap Week of Y2007; to remain in continuation of Era start at YEAR ZERO '0000' AD/BCE.
Regards,
Brij Bhushan Vij
(MJD 2455156)/1361+D-332W47-05 (G. Friday, 2009 November 20H15:08 (decimal) EST

Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda
Jan:31; Feb:29; Mar:31; Apr:30; May:31; Jun:30
Jul:30; Aug:31; Sep:30; Oct:31; Nov:30; Dec:30
(365th day of Year is World Day)
My Profile:http://www.brijvij.com/bbv_2col-vipBrief.pdf
HOME PAGE: http://www.brijvij.com/
******As per Kali V-GRhymeCalendaar*****
"Koi bhi cheshtha vayarth nahin hoti, purshaarth karne mein hai"
Contact # 001 (201) 675-8548

Date: Thu, 19 Nov 2009 16:10:52 +0000
From: karl.palmen@...
Subject: Re: New moon closest to new year, and solar year/lunation patterns closest to mean lunation/tropical year
To: CALNDR-L@...

Dear Ryan and Calendar People

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of ELITE 3000
Sent: 19 November 2009 05:56
To: CALNDR-L@...
Subject: New moon closest to new year, and solar year/lunation patterns closest to mean lunation/tropical year

Hello. I want to know what year when the new moon was closest to the new Besselian*/Rotation-adjusted/Mean orbitial year?

*(Sun Longitude 280.00°)

The Wikipedia page about the new moon has information that could be helpful for this.

See http://en.wikipedia.org/wiki/New_moon

And is there any solar/lunar patterns that is closest to the mean lunation/tropical year?

It depends on what kind of pattern you are looking for.

For example, the leap-term calendar, in which the mean lunation is 29+503/948 days (in which out of 948 lunations, there will be 503 30-day months and 445 29-day months) and the mean year is 365+327/1349 days (resulting in 327 solar leap years per 1k349-year period)

One has the Year, Lunar month and Day. One could introduce another period such as term to with a simpler relationship with the other three than they have with each other. Helios has introduced a term of 8/11 lunar month, just under 21.5 days and also just under 1/17 year.

I suggested the 5181-year and 8635-year cycles. They both have the property that 1 year is exactly 17 + 1/157 terms. They have a slightly different number of days to a term. The 5181-year cycle is a multiple of 80 lunar cycles of 801-months , which has a simple lunar calendar (mean month 29+426/801 days). One can use it, to regulate the number of days in a term and hence (via 1 year = 17 1/157 terms) the number of days in a year.

Also I suggest you look at the various lunisolar cycles in my lunisolar spreadsheets at

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

you may even download a spreadsheet and try your own cycle on it.

Karl

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Re: Gregorian Easter question

2009-11-20T11:43:53Z

-----Original Message-----
>From: RDoug <rdouglass001@...>
>Sent: Nov 20, 2009 10:54 AM
...
>Christian Computus uses tables, eg those of Alexandria, which can be shown
>to represent calculated mean conjunction.

>Gregorian Reform shifted
>everything by one day, so "Luna XIV" now falls approximately on the day of
>the Full Moon... which was not the case when the Alexandrian Tables were
>new.

Simon queries:
If I remember correctly, Irv and I went through this for the Dionysian
Julian computus (origin in 6th.century) and found that LUNA XIV fit the
full moon quite well at that time.

The Gregorian computus was intended as a reform and update of the Dionysian
Julian computus and adheres to its assumptions about LUNA XIV despite its
technical failures (mistaken effective average month length and anomalous
lunations with 1 day, 28 days, 31 days etc. in the Gregorian lunar calendar).

Dee's Years,
Simon Cassidy

Cheers from Simon

Gear/Chain Lunisolar Device

2009-11-20T09:35:06Z

Dear Karl and Calendar People,

Some time ago I described a device arranged as follows:

* A lower wheel has a gear with 9 teeth and 14 hooks.
* A chain with 235 teeth is driven by this gear.
* The chain drives a lunar wheel having 19 teeth.

Normally, the device is manipulated one hook per day. Previously, I
described adjusting the device every time there is a lunar eclipse.
This occasionally will result in a hook being moved a day earlier than
it normally would have.

I thought of another procedure that doesn't rely on observing the moon.

Two wheels, having 13 and 7 teeth respectively, work together, being
aligned at the same spot on the chain. Each wheel has one tooth
specially marked. They line up once every 13*7=91 days, or once a
quarter. The 13 toothed wheel has another marker. Each time an
alignment marks a new quarter, this second marker is moved one tooth.
When this manipulation results in the two markers lining up, an extra
hook is moved.

This results in a mean lunation of 29.530593 days. Thus described, the
mean year would be 365.2468 days.

Previously, I described an adjustment of the year using two pegs on
the 19 tooth lunar wheel. Since it operates independently, the device
could thus track two years, one of 365.2468 days and the other of
365.2422 or 365.2425 days.

Victor

Re: Gregorian Easter question

2009-11-20T07:54:52Z

Tom Peters wrote:

> The conjunction, "Dark Moon", is not the same as the traditional "New
> Moon" which is the first visible crescent, one to many days later:
> that's the one used in Jewish and Islamic calendars, and also in the
> Christian computus.

Traditional Jewish Calendar (First Century) used observed crescents. Calculated Jewish Calendar (since 359 AD) uses calculated mean conjunction.

Christian Computus uses tables, eg those of Alexandria, which can be shown to represent calculated mean conjunction. Gregorian Reform shifted everything by one day, so "Luna XIV" now falls approximately on the day of the Full Moon... which was not the case when the Alexandrian Tables were new.

-- Robert Douglass

Assyrian 364-day Calendar

2009-11-20T06:16:54Z

Assyrian 364-day Calendar

Dear Calendar People

A Wikipedia article claims the existence of a modern Assyrian calendar introduced in the 1950s that has 364 days in a year.

The article is http://en.wikipedia.org/wiki/Assyrian_calendar

Has this calendar been used and is it correctly described in the article?

Karl

10(15(04

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Re: Gregorian Easter question

2009-11-20T05:09:02Z

Dear Calendar People

Many years ago I made a list of epacts for 1995 to 2014 inclusive, which
I compared with the age of the moon (time since conjunction) at Jan 1,
00:00 UT and the yerm calendar date of Jan 1, 00:00 and so produced the
following list:

Year NY Begins Epact Age of Moon at NY

1995 51(09(29 29 29d 00h
1996 52(07(10 10 09d 22h
1997 01(02(21 21 21d 07h
1998 01(15(03 02 02d 07h
1999 02(10(13 13 13d 01h
2000 03(05(24 24 24d 01h
2001 04(03(06 05 06d 07h
2002 04(15(17 16 17d 03h
2003 05(10(27 27 27d 16h
2004 06(06(08 08 08d 14h
2005 07(03(20 19 19d 22h
2006 07(16(01 00 00d 09h
2007 08(11(12 11 11d 10h
2008 09(06(22 22 22d 06h
2009 10(04(04 03 04d 12h
2010 10(16(15 14 15d 12h
2011 11(11(26 25 26d 06h
2012 12(07(07 06 07d 06h
2013 13(04(18 17 18d 15h
2014 13(16(29 29 29d 00h
NY Yerm Cal Epact Age of moon

I see that the Epact is quite close to the age of the moon but gradually
becomes less later on until corrected by the saltus lunae in 2014
(2014=19*106). If the age of the were reckoned from Jan 1, 12:00 Rome or
Jerusalem time, the epact would be decisively less than the age of the
moon.

I recall Ryan asking which year has the closest new year to a new moon.
From this list 2006 is the closest. This could be compared with other
years a small multiple of 19 years different such as 1949, 1968, 1987,
2025, 2044 & 2063.

My yerm calendar is defined at
http://www.hermetic.ch/cal_stud/palmen/yerm1.htm
and has a converter at
http://the-light.com/cal/converter/ , which is valid for times after
12:00 noon.

Karl

10(15(04

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Tom Peters
Sent: 19 November 2009 21:12
To: CALNDR-L@...
Subject: Re: Gregorian Easter question

Wikipedia is your friend:

http://en.wikipedia.org/wiki/Epact

The conjunction, "Dark Moon", is not the same as the traditional "New
Moon" which is the first visible crescent, one to many days later:
that's the one used in Jewish and Islamic calendars, and also in the
Christian computus.

--
Tom Peters

--
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New version of my Java calendar packa

2009-11-19T23:17:24Z

I have released a new version of my Java calendar package.

http://joyds1.joensuu.fi/calendar/index.html

The package is free software distributed under the terms of the GNU
General Public License.

Re: Gregorian Easter question

2009-11-19T13:11:41Z

Op 19-nov-2009, om 16:59 heeft Mark J. Reed het volgende geschreven:

> Right. The epact is defined as the difference between the solar year
> and the lunar year, or equivalently as the age of the moon on 1 Jan.
>
> The traditional technique for *using* the epact does use descending
> numbers, however those numbers are not themselves "epacts". They are
> just labels for calculation - starting with 30 (or 0 or "*") on 1 Jan,
> descending modulo 30 except that every second day labeled "25" (except
> the last one of the year) is also labeled "24", to achieve the
> alternation between 29- and 30-day months. With this labeling, any
> date whose label matches the epact for the year has an ecclesiastical
> new moon.
>
> Which is of course another indication that counting back to 0 rather
> than 1 would yield the ecclesiastical new moon preceding the new year.
> I shoulda just done the math. :)

Wikipedia is your friend:

http://en.wikipedia.org/wiki/Epact
http://en.wikipedia.org/wiki/Epact

The conjunction, "Dark Moon", is not the same as the traditional "New
Moon" which is the first visible crescent, one to many days later:
that's the one used in Jewish and Islamic calendars, and also in the
Christian computus.

--
Tom Peters

Re: New moon closest to new year, and solar year/lunation patterns closest to mean lunation/tropical year

2009-11-19T08:10:52Z

Dear Ryan and Calendar People

Hello. I want to know what year when the new moon was closest to the new Besselian*/Rotation-adjusted/Mean orbitial year?

*(Sun Longitude 280.00°)

The Wikipedia page about the new moon has information that could be helpful for this.

See http://en.wikipedia.org/wiki/New_moon

And is there any solar/lunar patterns that is closest to the mean lunation/tropical year?

It depends on what kind of pattern you are looking for.

Also I suggest you look at the various lunisolar cycles in my lunisolar spreadsheets at

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

you may even download a spreadsheet and try your own cycle on it.

Karl

--
Scanned by iCritical.

Re: leap-term calendar

2009-11-19T08:09:16Z

Dear Ryan and Calendar people

Ryan has neglected the other two cycles that Helios mentions (5181-years
and 6835-years).

Helios has chosen these cycles mainly because of the simple leap term
rule of once every 157 years,
which would also make it easier to calculate the mean year from the mean
term
( mean_year = (17 + 1/157) * mean_term ).

Karl

10(15(03

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of ELITE 3000
Sent: 19 November 2009 05:26
To: CALNDR-L@...
Subject: Re: leap-term calendar

So, the lunation of that is
29 & 503 / 948 days = 29.53059071729957805907172995780591 days,
and the mean year of that is
365 & 327 / 1349 days = 365.2424017790956263899184581171238 days?

The average of the lunation of the leap-term calendar is longer than the

average lunation (29.530589 days) and the average year of the leap-term
calendar is longer than the mean tropical year (365.24218967 days),
although
shorter than the average Gregorian year (265.2425 days).

--------------------------------------------------
From: "Helios" <suntheorem@...>
Sent: Wednesday, November 18, 2009 8:49 PM
To: <CALNDR-L@...>
Subject: leap-term calendar

> Dear Karl et al.
>
> The leap-term calendar began when I first wanted to see what terms of
8 /
> 11
> months looked like. I then found the concise value of 21 & 113 / 237
days
> for a term and the pattern of 11 term-yerms in 5090 days. This led
> directly
> to the short lunar calendar cycle of months = 29 & 503 / 948 days and

> this
> led to the 6745 year luni-solar cycle when the leap-term idea occurred
to
> me.
>
> Karl has shown some alternate versions of the leap-term calendar and
has
> shown that a straight 157-year leap-term rule works very well. Karl
> notified
> me of the 5181-year and 8635-year cycles which are divisable by 157. I

> share
> the enthusiasm for the straight 157-year leap-term rule because the
> simplicity is irresistible. I consider it to be the preferable form of

> this
> calendar.
>
> values for the "octomonth" could be
>
> 236 & 196 / 801 days ( 5181-year cycle )
> 236 & 1089 / 4450 days ( 8635-year cycle )
>
> "1089" reminded me of number 1069 and that once about thirty years ago

> there
> was a fellow who wanted to change his name to "1069".
>
> --
> View this message in context:
>
http://old.nabble.com/Calendar-using-6745-year-luni-solar-cycle-tp263739
46p26419073.html
> Sent from the Calndr-L mailing list archive at Nabble.com.
>
>

--
Scanned by iCritical.

Re: Gregorian Easter question

2009-11-19T07:59:48Z

Right. The epact is defined as the difference between the solar year
and the lunar year, or equivalently as the age of the moon on 1 Jan.

The traditional technique for *using* the epact does use descending
numbers, however those numbers are not themselves "epacts". They are
just labels for calculation - starting with 30 (or 0 or "*") on 1 Jan,
descending modulo 30 except that every second day labeled "25" (except
the last one of the year) is also labeled "24", to achieve the
alternation between 29- and 30-day months. With this labeling, any
date whose label matches the epact for the year has an ecclesiastical
new moon.

Which is of course another indication that counting back to 0 rather
than 1 would yield the ecclesiastical new moon preceding the new year.
I shoulda just done the math. :)

On Thu, Nov 19, 2009 at 10:44 AM, HR-CALNDR-L <CALNDR-L@...> wrote:

> Epact is in fact the difference between a solar year (365 days) and a lunar
> year (354 days).
> "epact" comes from greek "epaktai hemerai" = added days.
> It is the number of days to be added to the moon year to get back to the solar
> year.
> Normally, the epact is incremented by 11 each year, subtracting 30 whenever
> possible.
>
> So it is not decreasing by 1 each day.
>
> Christof Clavius (together with Lilius THE designer of the Gregorian
> computus) has published many many tables, in which the new moon intervals ar
> more or less an alteration of 29 and 30 days.
> see http://www.henk-reints.nl/cal/gc-nl/explicatio.htm (please use MSIE or
> Chrome, it does not yet correctly work in firefox)
>
> Another thing is the question "what is a new moon", as interpreted by the
> astronomers of the 16th century. is it the same as what we now call new moon,
> i.e. a zero longitudinal elongation, or is is simply the first visibility of
> the moon, which I think is the original (ages old) meaning of "new moon".
> It normally is at least 1 day difference, as I guess most of you know.
>
>
> _________________________________________________
> Kind regards / met vriendelijke groeten,
>
> Henk Reints
>
>
>
> Oorspronkelijke tekst Karl Palmen
>> Dear Mark and Calendar People
>>
>> I recall that new moons are reckoned by assigning epacts to each day of the
>> day of the year (except leap day), normally decreasing by 1 each day. Then a
>> new moon occurs on each day whose epact matches the epact of the year.
>>
>> This does not ensure that the epact is always the number of days that January
>> 1 occurs after the preceding new moon day, but this does apply to January 1 of
>> any year whose number is not divisible by either 19 or 100.
>>
>> This method may sometimes cause a new moon to be missed out or occur twice by
>> a new year, so is slightly amended to prevent that from happening. It may also
>> sometimes cause lunar months of 28 or 31 days to occur across a new year.
>>
>> Helios has done likewise with Golden numbers instead of epacts.
>>
>> Karl
>>
>> 10(15(03
>>
>> -----Original Message-----
>> From: East Carolina University Calendar discussion List
>> [mailto:CALNDR-L@...] On Behalf Of Mark J. Reed
>> Sent: 19 November 2009 14:08
>> To: CALNDR-L@...
>> Subject: Gregorian Easter question
>>
>> The epact of a year is the nominal age of the moon on January 1. Does
>> an epact of 1 or 0 ("*") mean a nominal new moon on that date?
>>
>> --
>> Mark J. Reed <markjreed@...>
>>
>>
>
>

--
Mark J. Reed <markjreed@...>

Re: Gregorian Easter question

2009-11-19T07:44:50Z

Epact is in fact the difference between a solar year (365 days) and a lunar
year (354 days).
"epact" comes from greek "epaktai hemerai" = added days.
It is the number of days to be added to the moon year to get back to the solar
year.
Normally, the epact is incremented by 11 each year, subtracting 30 whenever
possible.

So it is not decreasing by 1 each day.

Christof Clavius (together with Lilius THE designer of the Gregorian
computus) has published many many tables, in which the new moon intervals ar
more or less an alteration of 29 and 30 days.
see http://www.henk-reints.nl/cal/gc-nl/explicatio.htm (please use MSIE or
Chrome, it does not yet correctly work in firefox)

Another thing is the question "what is a new moon", as interpreted by the
astronomers of the 16th century. is it the same as what we now call new moon,
i.e. a zero longitudinal elongation, or is is simply the first visibility of
the moon, which I think is the original (ages old) meaning of "new moon".
It normally is at least 1 day difference, as I guess most of you know.

_________________________________________________
Kind regards / met vriendelijke groeten,

Henk Reints

Oorspronkelijke tekst Karl Palmen

> Dear Mark and Calendar People
>
> I recall that new moons are reckoned by assigning epacts to each day of the
> day of the year (except leap day), normally decreasing by 1 each day. Then a
> new moon occurs on each day whose epact matches the epact of the year.
>
> This does not ensure that the epact is always the number of days that January
> 1 occurs after the preceding new moon day, but this does apply to January 1 of
> any year whose number is not divisible by either 19 or 100.
>
> This method may sometimes cause a new moon to be missed out or occur twice by
> a new year, so is slightly amended to prevent that from happening. It may also
> sometimes cause lunar months of 28 or 31 days to occur across a new year.
>
> Helios has done likewise with Golden numbers instead of epacts.
>
> Karl
>
> 10(15(03
>
> -----Original Message-----
> From: East Carolina University Calendar discussion List
> [mailto:CALNDR-L@...] On Behalf Of Mark J. Reed
> Sent: 19 November 2009 14:08
> To: CALNDR-L@...
> Subject: Gregorian Easter question
>
> The epact of a year is the nominal age of the moon on January 1. Does
> an epact of 1 or 0 ("*") mean a nominal new moon on that date?
>
> --
> Mark J. Reed <markjreed@...>
>
>