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Hand trick[edit]

If you're like me, you can't quickly remember how many days are in October or April. However, there is a simple trick to determining how many days are in each month, and it doesn't involve any complex calculations. In fact, the only things involved are carried with you 24 hours a day (except, of course, if for some reason, you no longer have your original hands); your knuckles.

The trick goes as such:

1) Make your hands into fists

2) Hold your fists together so that your thumbs and (curled) index fingers are touching.

3) Now, count both the knuckles and valleys between them as months (i.e. count the first knuckle as January, the adjoining valley as February, and so on). The orientation of the counting makes no difference, so those that prefer to think in a Hebrew mentality can count from right to left and still get the desired effect.

4) Now for the important part of the trick: Each month that was counted on a knuckle has 31 days, and each month that was counted in a valley has fewer than 31 days (well, 80% of them have 30. The remaining month has 28 (or 29) days. Figuring out which is the odd one out will be an exercise left to the reader.

NOTE: this is "stupid as hell" (in the opinion of some people, but widely taught and practiced by others). And it is "extremely retarded" in the opinion of those not abiding by any sense of political correctness.

I like this version of the hand trick better:
1) Hold out one fist.
2) Starting with the index finger knuckle, count knuckles and valleys.
3) When you run out of knuckles and valleys, start again from the other direction as in this illustration.
I like this better because February gets the lowest valley (for most people)
Victor Engel (talk) 20:33, 7 January 2008 (UTC)

Continued fractions and other approximations[edit]

Some history: at the time I wrote lemmata for the various astronomical months; they were later consolidated into this general "month" page. So my elaborations on approximations for days-per-month and months-per-year ended up here. My emphasis has been on continued fractions, because those are successive optimal approximations. They are a standard against whih accuracy of calendars can be assessed. I object to inserting other approximations into the current lists because the context (though admittedly not the title) is all about continued fractions. Instead, I endorse adding another list of approximations actually used. Other examples: Egyptians used 9125/309 days (equal to 25 "wandering years" of always 365 days); the fixed islamic calendar uses 10631/360 days. I am doubtful that the Coligny calendar has been reconstructed with sufficient confidence to fix a mean lunation length. Tom Peters 23:59, 3 October 2005 (UTC)

That particular section is in fact entitled Calendrical implications and the second half of it starts More importantly, in lunisolar calendars, an integral number of synodic months is fitted into some integral number of years. . The example I gave is indeed a lunisolar calendar and does indeed have an integral number of synodic months (62) in an integral number of years (5). The introduction of continued fractions in that context seems spurious; feel free to add examples to the continued fractions page. Meanwhile, since the article is actually about months, in calendars, I plan to remove the 'continued fractions' reference and talk about approximations that were actually used in calendars.
If you have some evidence for any published work that argues a case for a different number of months or years, please cite it. --Nantonos 11:52, 2 October 2005 (UTC)
I think information like that is better placed at the pages describing those calendars. For example, the article on the Egyptian calendar doesn't even mention the 9125/309 days cycle. squell 00:56, 4 October 2005 (UTC)
If you do remove the continued fractions, please move the year/month continued fraction approximation to lunisolar calendar and the month/day continued fraction approximation to lunar calendar. --Karl Palmen 4 Oct 2005
The Egyptian calendar now does mention the 9125/309 days cycle. ----Karl Palmen 4 Oct 2005
I agree that the individual calendars should have the apropriate mentions, but the re is also value in having comparisons somewhere central sothat calendars can be compared.
As for continued fractions, it seems n irrelevant distraction. The page talks about the number of months in some number of years, where both are integer; the correct term for that is a rational number. For a page about months to add things which happen to be continued fractions but which were not used to describe months; and to remove things which were used to descrinbe months because they do not happen to be continued fractions, seems very odd and not at all helpful.
Its unfortunate if a snippet on some subject ends up as an aside in some other topic, and is then edited out for clarity and relevance. I suggest that the examples of calendrical approximations which happen to be continued fractions be moved onto an examples section in the continued fractions page. --Nantonos 07:09, 4 October 2005 (UTC)
The mention of continued fractions somewhere is relevant, but I think information about it is indeed better put at solar calendar, lunisolar calendar and lunar calendar. squell 13:13, 4 October 2005 (UTC)
NO, banishing the continued fractions approximations to the maths page would hide relevant info in a place wehere no-one would find it; and as an example it would be rather odd out there too. The relevance here is not the technique of continued fractions, but the accuracy of approximations. Mind that the subject of that section is about the proper ratio of lunar months to tropical years. With all the astronomical content merged into this page, it has become rather heavy in discussing the astronomical and computational background of months as unit of time. In any case, different rational approximations are not equally accurate, and the current list gives the theoretical optimal approximations for successive longer cycles. Inserting other approximations like you did is very confusing. I agree that approximations in actual calendars do have a place, but do not put them at par with the theoretical ones.
In fact, I wouldn't mind splitting out the astronomical and computational details into one or more specialized pages like they used to be. The discussion of the lunisolar ratio could go to that lemma like Karl proposed. I think a discussion of approximations of the length of the synodic month (in days) should stay here, because it is the basis of many calendar months.
ceterum censeo that the assertion that the Coligny calendar approximated 5 tropical years to 62 lunations is an inaccurate representation of the facts and the proposed reconstructions. The approximation is so bad that it is unworkable. From what I read, there are indications from the Coligny fragments themselves and from Latin sources that the Gauls used longer periods (25, 30, 75 years may have been used) to keep track of Sun and Moon: the main characteristic is that the tropical solar year moved back and forth through the Moon-based calendar year in a controlled way. In the long term the calendar year may have approximated the tropical year, but AFAIK there is more speculation than fact on how the Gauls actually worked their calendar. So we can not put a reliable number on the ratio and accuracy they achieved. In any case it looks like that the 5 calendar years of Coligny were not intended to approximate 5 tropical years in just that one cycle. Tom Peters 15:15, 4 October 2005 (UTC)

The longer period of 30 years is certainly likely, and dropping one intercalary month each 30 years gives a much better approximation. This does not however follow directly from the Coligny calendar, which is why, being conservative, I did not include it. As it stands, the Coligny Calender does indeed have 62 lunations and 5 years - that is the undisputed fact of the actual bronze tablet. The 30 year period is from Pliny the Elder, and would make the use of the Coligny Calendar more accurate: (62*6 - 1)/ 5*6 = 12.367

Its a pity that your dedication to a particular mathematical theorem drives you to exclude historical calendars that don't follow it. I reiterate that the topic of the page is months. All months are, therefore, on topic and mathematicalcuriosities are only of value where they happen to illustrate the primary topic. That way, and far less confusingly, all the approximations listed would relate to actual calendars;currently, ther eis a list of approximations that relates to a pet theory, some of which were not used by any calendar , and attempts to add actual calendrical approximations are deleted. The accuracy of approximations can be more conveniently given in parts per million, or in days drift per millenium, or whatever units. --Nantonos 16:14, 23 October 2005 (UTC)

As has been suggested before, information about continued fractions can be moved to the appropriate calendar page. It is too technical for inclusion here, and lunar calendar, solar calendar and lunisolar calendar could really use some 'meat', too! squell 16:59, 23 October 2005 (UTC)
This discussion circles around what the scope of this page is supposed to be. In its current state is is mostly about the various astronomical periods called month, and then some added material about months in various calendars. Obviously calendar months need have no relation to astronomical months. In the case at hand, I think it would be confusing and unfair to put actual mean calendar months in the same list with the successive approximations: some calendar months might not even try to approximate the synodic months (like in the Roman-derived calendars). Finding equations of so many lunations in so many days, or so many lunations in so many years, has been a major challenge in constructing calendars. The list I gave does exactly this and has been intended as a reference for those calendars that do try to do such approximations. For this reason I think it is better placed on this central location than distributed or repeated on each individual calendar page.
This is what I propose: the first part of the page is all about the astronomical months. The part on "Calendrical implications" obviously should be re-written (and re-titled); but the purpose may remain to link the astronomy to calendrics. Then we may write a section comparing months in various lunar and luni-solar calenders (rather than discuss them individually like now). Finally a section on calendar months that are no (longer) related to a lunation. Tom Peters 19:51, 24 October 2005 (UTC)
I understand what the list is about. However, as you say, those approximations are devices that are/were used in constructing calendars, not properties of the months themselves, so I think they would fit much better in the lunar calendar article. As a reader, I'd expect to find that information there. Having them tucked away in this article causes confusion. Better to simply replace "Calendrical implications" with a lead section, like this:
For more details on this topic, see lunar calendar and lunisolar calendar.
squell 13:26, 25 October 2005 (UTC)

Ok, I've done the first part of this. Check out lunisolar calendar. I have removed some of the wording which seemed to indicate all lunisolar calendars are arithmetical — which is clearly not the case. To Tom Peters: please see Talk:Lunisolar calendar wrt the changes I have made to the fraction list. squell 00:30, 29 October 2005 (UTC)

"Months in Various Calenders" should be deleted[edit]

that section is pointless, considering the fact that there is already a section for many specific calenders. Instead of it, a link should be added to the specific calenders section.

I would have done this myself, except that I am very clumsy with the site (seeing as I've edited for the first time today) and before deletion, people who know more than me about all of the topics presented in the section should check whether information that appears there is missing in the entries for the specific topics. I've already noticed that the alternate endings of the mnemonic for the memorisation of the length of months did not appear in the entry about the gregorian calender, so I added them to the appropriate section there. I probably missed some things, however.

  • I was thinking the same thing about "Months in Various Calendars". 02:32, 2 August 2006 (UTC)

Months of the Year[edit]

I've tried searching for a similar article to "Days of the Week" for the "Months of the year." Would someone be able to create that page? Read this article to find out what I mean:

Unlike Days of the Week, Months of the Year depend upon the calendar system in use. Consequently the information would be found on the pages about the particular calendar system, such as Gregorian calendar, Hebrew Calendar, Islamic Calendar , Coptic Calendar, French Republican Calendar and others in Category:Specific calendars.

Karl 8 September 2006 08:00 UT

What was synodic month length in 3009BCE? Can it be calculated mathematicaly?

6 x 6 = 66[edit]

Invocation 6x6=66 is derived from satanic origin, because this invocation is derived from fictitious assumption that is 6*6=66, or two sixes side by side: 6*6, that is rougly similar to 666. This is placed in Polish satanic book called "Agent Dołu" or in English "Pit's Agent":[1] Thus much better solution would be using septenary or at least decimal units for measuring time. For example 343 day year (nearly the same as draconic year) would be divided into 7 seasons and each season into 7 weeks. More about full septimalization of all units here: [2]

Comprehensive proof of evilness of these unholy numbers such as 6,60,90,180,270,360,666,3600,6666, which refuses to be completed up to multiples of holy seven is placed here: [3] 09:52, 15 March 2007 (UTC)

Thanks for the laugh.  :-) Strange that the ancient Israelites also used a 12- or 13-month calendar ... Nik42 00:00, 3 July 2007 (UTC)
For all that doesn't know Polish I explain that following Polish text of "Pit's Agent" [4]:
"Na pytanie, ile jest 6x6 można czasem usłyszeć: 66."
means in English:
"Onto question, how many is six times six, there may be sometimes heard following answer: sixty six." Wikinger 19:41, 1 November 2007 (UTC)

Month symbolism[edit]

althought heavily tied to the northern hemisphere there's a lot deal of symbolic meaning tied to each month... Anyone with precise knowledge on this matter could enhance the article please?Undead Herle King 02:59, 1 June 2007 (UTC)

See each month's article for its derivation and symbolism. This article is not the proper place for that information. — Joe Kress 05:26, 1 June 2007 (UTC)

Ok I am like thus too much Jujharsingh 029 (talk) 06:15, 26 June 2015 (UTC)

Ok good luck Jujharsingh 029 (talk) 06:15, 26 June 2015 (UTC)

Icelandic Calendar[edit]

How did the Icelandic calendar work? I get the impression that they agreed with the rest of the Western world on the days of teh week, that is, a Sunday in Iceland was always a Sunday in Europe. So, how did they maintain the correspondance of dates and days of teh week? Was there a "leap week" or some sort added on a regular basis? I'd once created a fictional calendar that worked that same way, so I'm quite interested to see that a real calendar apparently did the same Nik42 00:00, 3 July 2007 (UTC)


Note: Years are 365.2425 days, not 365.25

Will Entriken (talk) 04:21, 16 January 2008 (UTC)

The mean Gregorian year in 365.2425 days, whereas the mean Julian year in 365.25 days. Both are correct. — Joe Kress (talk) 01:35, 17 January 2008 (UTC)

JASON in months[edit]

Has anyone ever noticed if you write down the first letters in the list of months you see JASON? JFMAMJ(JASON)D. Is that something or just a coincidence? (talk) 20:57, 20 August 2008 (UTC)

Hmm, funny. Anyone else have an opinion? (talk) 03:13, 27 November 2008 (UTC)

Y in days or years?[edit]

In the table of lengths of lunar months, the correction factor variable Y is described as days since the epoch. In the text Y is described as years. Which is it?--agr (talk) 16:35, 18 May 2011 (UTC)

It is both. For example, 29.530588853 + 0.000000002162 × Y days means take the value of Y (in years) to compute the sum. The result is a value whose units are days. Victor Engel (talk) 16:49, 18 May 2011 (UTC)
Perhaps illustrating by example would help. Today's date is about 11.38 years after the 2000 epoch. So we use 11.38 in the equation to produce the sum 29.530588853 + 0.000000002162 * 11.38 = 29.5305888776 (which sum is a period of days). Victor Engel (talk) 16:55, 18 May 2011 (UTC)
OK I understand what is intended, but the article wording is very confusing. I would suggest taking the word "days" out of each row in the table and changing the first sentence of the section to "Here is a list of the average length, in days, of the various astronomical lunar months." --agr (talk) 03:13, 19 May 2011 (UTC)
I modified the table by adding a column header, etc. Victor Engel (talk) 19:50, 19 May 2011 (UTC)
Thanks, that's much better. I made a few minor edits. --agr (talk) 00:05, 20 May 2011 (UTC)

Arabic calendar[edit]

Who uses the "Arabic calendar" (recently added)? Most of the month names resemble the Hebrew; are they used by Israeli Arabs perhaps? (If so, the sections ought to be merged.) —Tamfang (talk) 08:55, 19 June 2011 (UTC)

Arabs use the "Arabic Calendar". Most daily use calendars used in Arab countries include the Gregorian, Islamic as well as the Arabic Calendars. The names resemble the Hebrew months because Arabic and Hebrew belong to the same sub-family (Semitic) of the Afro-Asiatic language family, and hence, they are quite similar to each other. More information is available at Arabic names of calendar months. --Wahj-asSaif (talk) 20:35, 30 April 2013 (UTC)

Another Mnemonic[edit]

I still remember the mnemonic my high school Latin teacher taught us for remembering which months have the ides on the 15th and the calends on the 7th: MOM & July. HankW512 (talk) 23:10, 29 April 2013 (UTC)

P.S.: Is anyone aware of a mnemonic device for remembering that the leap years in the Hebrew calendar are the 3rd, 6th, 8th, 11th, 14th, 17th and 19th years of each Metonic cycle?


The draconic month is stated here 27.212220817. There should be said, that it is an average value, where actual time distances between ascending node passages (relative to dynamic ecliptic plane) are currently (this year) in range 27.05644 - 27.3645 days (the difference is over 7 hours), varying on a sinusoide with 173.3 day period, as detected from NASA/JPL ephemerides DE422. Similar variability (173 day sinusoide) shows the angle between angular momentum vector (orbit axis) of Moon orbit relative to Earth and of angular momentum vector of EMB orbit relative to Sun (on range 5.0328° - 5.30428°). The angular frequency of rotation of a vector from EMB to Moon Ascending Node ranges from 1.6e-5° to 3.21° per 27 days (the low bound could be probably an artifact of discrete position of ascending node calculation? But probably it is not...). I found no mention of the variability of Moon precession here...?! There should be at least the word average draconic month... P.A.Semi (talk) 22:35, 18 October 2013 (UTC)

Khmer & Malayalam Calendars[edit]

It is clear that the names in both of these calendars are cognates. The Khmer section has little information apart from the list of months, but perhaps some linkage between the two sections, either overtly in a list format or simply by putting them back to back, would shed light on their relevant cultural and linguistic connections. (talk) 17:32, 14 January 2014 (UTC)Tom in Florida

Knuckles and musical keyboard is nonsense, just a coincidence[edit]

The keyboard wasn't invented according to month lengths. F doesn't correlate to January. The key has no special position in music. Using knuckles is a stupid method to remember the months. I never understood this. The length alternates between long and short, with an exception between July and August. Who needs to put their knuckles together to count? After some years of use, children automatically know how many days each month has. We use the calendar everyday, it should be clear to everyone. Besides, you have more knuckles and between the knuckles than months. Children might get confused more than just remembering by heart. February may be a short month, but you can't see from the knuckles that it has only 28 instead of 30 days. Another confusion arises when you put both hands together: Children could count the space between the two index fingers as August, making it a short month. -- (talk) 13:02, 13 August 2015 (UTC)