Talk:Lunisolar calendar

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Discussion

How dow you know when is the year has 12 months or 13 months

That depends on the actual intercalation rules of the respective calendar. As a rule of thumb: the 13th month is inserted when the date of the the beginning of spring (vernal equinox) is more then 30 days earlier then its last possible date. andy

The 19-year cycle (235 synodic months, including 7 embolismic months) is the classic Metonic cycle, which is used in most arithmetical lunisolar calendars. It is a combination of the 8- and 11-year period, and whenever the error of the 19-year approximation has built up to a full day, a cycle can be truncated to 8 or 11 years, after which 19-year cycles can start anew.

A full day? 61.131.122.70 (talk) 03:05, 19 February 2011 (UTC)

Truncating a 19-year cycle to only 11 years (skipping 8 years including 3 embolismic months) is the appropriate correction after the error has accumulated to ¹/₁₉ of a lunar cycle, provided that the target mean is any equinoctial or solstitial year or the mean tropical year, all of which have a shorter mean year than the mean year of the metonic cycle. Alternatively, one could truncate when the error has accumulated to ¹/₂ of ¹/₁₉ = ¹/₃₈ of a lunar cycle. Truncation to 11 years always shifts the calendar earlier by ¹/₁₉ of a lunar cycle, so in that alternative case the error would swing from ¹/₃₈ of a lunar cycle late to ¹/₃₈ of a lunar cycle early.

Truncating to only 8 years (skipping 11 years including 4 embolismic months) will make the drift worse for any calendar where the target mean year is shorter than that of the 19-year cycle, but would be valid if the target is longer than the mean year of the 19-year cycle, as would be the case for a sidereal calendar. What is the size of the step adjustment that truncation to only 8 years causes? Kalendis (talk) 03:52, 9 May 2011 (UTC)

Having now calculated to confirm, I answer my own question: truncation of a 19-year cycle to only 8 years shifts the calendar later by ¹/₁₉ of a lunar cycle. Kalendis (talk) 04:40, 9 May 2011 (UTC)

Merging "Calendrical implications" from Month

I updated this article (which looked rather dilapidated) by merging information that didn't fit nicely in Month. However I didn't know what to do with the following section, so I've put it here:

A representative sequence of common and leap years is ccLccLcLccLccLccLcL, which is the classic nineteen-year Metonic cycle. The Hebrew and Buddhist calendars restrict the leap month to a single month of the year, so the number of common months between leap months is usually 36 months but occasionally only 24 months elapse. The Chinese and Hindu lunisolar calendars allow the leap month to occur after or before (respectively) any month but use the true motion of the sun, so their leap months do not usually occur within a couple of months of perihelion, when the apparent speed of the sun along the ecliptic is fastest (now about 3 January). This increases the usual number of common months between leap months to roughly 34 months when a doublet of common years occurs while reducing the number to about 29 months when only a common singleton occurs.

This section is pretty technical, and I feel it doesn't "fit". I suggest including it in the articles of the mentioned calendars, or adding an external link to a site by a calendar expert. squell 00:20, 29 October 2005 (UTC)

The list of fractions are continued fractions. I've added 136/11; I've also added how these fractions relate to "real world" cycles; I have removed 4131/334; at that accuracy, this figure starts getting sensitive to the exact choice of tropical year (Besselian? vernal equinox? etc). squell 00:36, 29 October 2005 (UTC)

I don't see a good reason for excluding the deleted section, although I am partial to it because I wrote it. Being technical should not exclude anything from any Wikipedia article. It does 'fit' because it discusses leap months in lunisolar calendars. — Joe Kress 06:16, 29 October 2005 (UTC)

But so does the merged section from Month. Simply including both does the reader a disservice because it mentions the same topic twice, with possible contradictions. Perhaps I should have said "doesn't fit in the article as it is now." Regarding the technicality; being technical is not a criteria for exclusion from Wikipedia, but the quoted paragraph very quickly dives into complex territory (true motion of the sun) and adds article-jargon (compare doublet, singleton).

I get the impression your paragraph is more about the average interval between leap months (unrelated to a calendar being arithmetic or not) while the section I added (expanding on Tom Peters' work) is only about their overall frequency (with a inclination towards arithmetic calendars). I will probably attempt to merge the two sections later, keeping this in mind. squell 17:05, 29 October 2005 (UTC)

It is not appropriate to use the so-called "mean tropical year" (MTY) for any calendar, as it cannot be observationally verified -- no related equinox or solstice -- and because the MTY is in the wrong time units. Calendars must use mean solar days, but the MTY is comprised of days measured by atomic time. The mean year of the lunisolar Gregorian Easter computus is the same as the mean year of the Gregorian calendar, of course, but it was intended to match the mean spring equinox year for the northern hemisphere, which currently is 365 days 5 hours 49 minutes and a fraction of a second, or almost 12 seconds shorter than the Gregorian calendar mean year. By contrast, the mean year of the Hebrew calendar is more than 6 minutes and 25 seconds too long. I hesitate to apply an edit in this regard, because many changes would be necessary, and because it could also be valid for such a general discussion of lunisolar calendars to choose the mean summer solstice year for the northern hemisphere, which would endure for much longer relative to the actual astronomy. Kalendis (talk) 02:18, 6 May 2011 (UTC)

External Link section

I'm not sure why the external links section was deemed to have too many to the same site since the site is not straight-forward to navigate, but I have reverted this simple deletion and believe the section is now in compliance with Wikipedia:External_links#External_links_section Kind regards, --Greatwalk 00:41, 18 March 2007 (UTC)

It is a shame you have still not read the appropriate guidelines. Please see Important points to remember, point 3: "Try to avoid linking to multiple pages from the same website". --Pak21 08:23, 19 March 2007 (UTC)

Further Examples section

Is there anything at all notable about the content in the Further Examples section? It looks like self-aggrandizement to me. QVanillaQ 19:35, 22 June 2007 (UTC)

I've removed the section, since the external links point to the same information anyway. QVanillaQ 15:24, 23 June 2007 (UTC)

Solilunar vs. lunisolar

Solilunar is the correct term for calendars which are both lunar and solar but more successful in tracking the lunar cycle than the solar. Lunisolar means calendars which are both lunar and solar but more successful in tracking the solar cycle than the lunar. Lunisolar calendars actually aren't possible at all if it's better on tracking the solar cycle than the lunar, and most of the so-called 'lunisolar' calendars are actually solilunar. There's no such thing as lunisolar! —Preceding unsigned comment added by 172.216.110.42 (talk) 17:56, 23 November 2007 (UTC)

I've reverted your change for several reasons. It was within what appears to be a direct quote which must written as it appears without any changes. Although I understand your argument, solilunar is non-standard. Lunisolar is standard in all sources. Furthermore, the Shorter Oxford English Dictionary does not support your distinction. It says that both lunisolar and soli-lunar or solunar (or sol-lunar) mean of or pertaining to both the sun and moon (although probably a coincidence, "sun" is listed before "moon" in all three definitions). — Joe Kress (talk) 23:51, 23 November 2007 (UTC)

You're right, there's no such thing as solilunar. That was what Peter Meyer said.

Calculation of the exact mean year for a lunisolar calendar

This can be tricky, and is explained at http://www.sym454.org/leap/, use your web browser to find the places where the term "lunisolar" is mentioned. It seems to me worthwhile to add such a section to this Wikipedia page, but I hesitate to follow a similar verbose equation format. Kalendis (talk) 20:08, 16 May 2011 (UTC)

It would be helpful to state exactly where in http://www.sym454.org/leap/ this working out of the mean year for a lunisolar calendar is. Karl (talk) 12:08, 18 May 2011 (UTC)

It's spread in several places there, as the focus there is not limited to lunisolar calendars, that's why it is necessary to use the web browser to search for the term lunisolar, and it is also why I didn't think it was appropriate to add an external link, and suggest that the pertinent equations be gathered and posted here. What's there assumes that the mean month fixes also the mean year, but if there is a rule that regulates the insertion of a leap month relative to some kind of solar reckoning then the mean year equals the mean solar year. Kalendis (talk) 13:49, 19 May 2011 (UTC)

So the issue is how often to insert a leap month. This is the fractional part of the mean year expressed in mean months. For mean year between 365.2416 and 365.2428 days and mean month between 29.53057 and 29.53060 days, this ranges between 36.824% and 36.830%. Within this range are the fractions 109/296, 116/315, 123/334, 130/353, 137/372, 144/391 and 151/410. Karl (talk) 08:48, 20 May 2011 (UTC)

There already is the section "Calculating a leap month" for that discussion, although that could be expanded. I'm saying that regardless of the leap month insertion scheme, the arithmetic for exactly evaluating the calendar mean year would be useful to outline after that section. Kalendis (talk) 04:56, 24 May 2011 (UTC)

I don't understand exactly what Kalendis wants here. For example, one could work out the mean year for a given mean month and proportion of years that have leap months. Is this what is wanted? If not, what is it? Karl (talk) 10:48, 24 May 2011 (UTC)

Why this section should be removed

Determining leap months

A rough idea of the frequency of the intercalary or leap month in all lunisolar calendars can be obtained by the following calculation, using approximate lengths of months and years in days:

• Tropical year: 365.2422 (Y), Synodic month: 29.5306 (M)
• Y/M = 12.36826: 12 months per common year or 13 months per leap year
• Y - (M × 12) = 10.875 days per year (the epact)
• 1/0.36826 = M/10.875 = 2.7155 (L): 1 leap month per 3 or 2 years, ccL or cL (average interval (in years) between intercalations).
• 1L = 2.7155: 1(st) leap month in 3 years or in year 3 ccL
• 2L = 5.4309: 2 leap months in 6 years ccLccL
• 3L = 8.1464: 3 leap months in 9 years ccLccLccL
• 4L = 10.8618: 4 leap months in 11 years ccLccLccLcL
• 5L = 13.5772: 5 leap months in 14 years ccLccLccLcLccL
• 6L = 16.2927: 6 leap months in 17 years ccLccLccLcLccLccL
• 7L = 19.0082: 7 leap months in 19 years ccLccLccLcLccLccLcL
• 19-year cycle: ccLccLccLcLccLccLcL (3 + 3 + 3 + 2) + (3 + 3 + 2) = 11 + 8 = 19 = 8 + 11 = (3 + 3 + 2) + (3 + 3 + 3 + 2) ccLccLcLccLccLccLcL
• The year 2017 is a leap year in the traditional Chinese calendar: 2017 mod 19 = 3, ccLccLccLcLccLccLcL

Intercalation of leap months is frequently controlled by the "epact", which is the difference between the lunar and solar years (approximately 11 days). The Metonic cycle, used in the Hebrew calendar and the Julian and Gregorian ecclesiastical calendars, adds seven months every nineteen years. The classic Metonic cycle can be reproduced by assigning an initial epact value of 1 to the last year of the cycle and incrementing by 11 each year. Between the last year of one cycle and the first year of the next the increment is 12. This adjustment, the saltus lunae, causes the epacts to repeat every 19 years. When the epact goes above 29 an intercalary month is added and 30 is subtracted. The intercalary years are numbers 3, 6, 8, 11, 14, 17 and 19. Both the Hebrew calendar and the Julian calendar use this sequence. ... — Preceding unsigned comment added by 27.154.63.66 (talk) 04:42, 20 January 2017 (UTC)

Your argument, which is based on original research, does not make clear why 3, 8 or 19 years make useful luni-solar calendars, while other years don't, nor does the traditional Chinese calendar follow a strict Metonic rule. AstroLynx (talk) 11:06, 20 January 2017 (UTC)

The discussion in this proposed section is purely hypothetical and fails to discusss the intercalation cycles that were actually used in specific historical calendars. Furthermore, it fails to provide citations of sources to document those uses. As such it fails both WP:OR and WP:VERIFY.

There is an extensive literature in the history of calendars and the history of astronomy to document the various luni-solar calendars. I recommend that editors do proper research in the scholarly literature before restoring this section. --SteveMcCluskey (talk) 14:47, 20 January 2017 (UTC)

Routine calculations do not count as original research, provided there is consensus among editors that the result of the calculation is obvious, correct, and a meaningful reflection of the sources.Here the calculations are based on mean lengths of tropical year and synodic month and the Metonic cycle. where is the original research? the results of the calculations are not obvious or correct? Q5968661 61.131.75.3 (talk) 15:16, 20 January 2017 (UTC)

It isn't enough that calculations be routine and correct; they must be important enough to bother including in the article. A sequence that can't be proved through reliable sources to have been actually used in some important calendar isn't worth mentioning. Jc3s5h (talk) 15:24, 20 January 2017 (UTC)

The sequence just is the Metonic cycle. you don't agree the cycle? Whithout the section, how could you tell readers why the cycle has 19 years and 7 leap months in years 3, 6, 9, 11, 14, 17, and 19 or 3, 6, 8, 11, 14, 17 and 19 and which years are leap ones? Q5968661 61.131.75.3 (talk) 15:46, 20 January 2017 (UTC)

According to Urban & Seidelmann in the Glossary to Explanatory Supplement to the Astronomical Almanac:

Metonic cycle: a 69400 6940-day cycle closely approximating 19 tropical years or 235 synodic months. [Italics indicate terms that are in the glossary.]

So there is no particular sequence of leap months associated with the Metonic cycle; it could be implemented with many different sequences. Jc3s5h (talk) 17:23, 20 January 2017 (UTC) Typo corrected 15:39, 21 January 2015 UTC

References

"Metonic cycle: a 69400-day cycle"? 69400≠6940. Where is the source for "So there is no particular sequence of leap months associated with the Metonic cycle; it could be implemented with many different sequences." ? The table you removed can tell you all about it. More calculations for you:

• 235M-19Y=6939.691-6939.6018=0.0892 day, 1/0.0892=11.2108 cycles, 11.2108×19=213.0045 years, that is a full day difference between them.

Don't tell me you need the sources for these calculations again. Now a question for you, what does it mean by 123L=334.0013?

• 19-year cycle in Chinese calendar Q5968661 27.154.63.66 (talk) 04:06, 21 January 2017 (UTC)

Your point on 6940 days is correct. Other than that, you are putting the obligation to provide sources backwards. Opponents of an addition are not obliged to provide sources to rebut it; advocates of an addition are obliged to support it. In particular, advocates of proposing this particular sequence of intercalary and ordinary years as an implementation of the Metonic cycle are obliged

• to show that this particular sequence of intercalary and ordinary years follows from their calculations,
• to show where this particular sequence was used, and
• to discuss whether and if so, when and where, other sequences have been used.

To do this, as I stated above, requires further research in the historical literature.--SteveMcCluskey (talk) 14:14, 21 January 2017 (UTC)

"A rough idea of the frequency of the intercalary or leap month in all lunisolar calendars can be obtained by the following calculation, using approximate lengths of months and years in days", someone said. That is, all lunisolar calendars must have it or they are not a lunisolar calendar. It does not require any research at all because it is very simple and can be verified by arithmetic calculations.

• ccLcLccLccLcLccLccLccLcLccLccLcLccLccLccLcLccLccLcLccLccL, there are 57 years or 3 cycles in the sequence which can start from any years. Q5968661 61.131.75.3 (talk) 15:42, 21 January 2017 (UTC)

This discussion implies that all luni-solar calendars must adhere to contemporary concepts of mathematical precision. This is not the case. Different cultures have different criteria which can lead to subtly different patterns of common and intercalary years.

Furthermore, this presentation seems to imply there is something special about three Metonic cycles. That is not apparent from your analysis nor have I ever seen this claimed in the literature; the only multiple of the Metonic cycle of which I'm aware is the 76 year Callippic cycle, which consists of four Metonic cycles, integrating the leap year cycle (every 4 years) with the Metonic cycle.

The closer I look at this presentation, the more I see it as pushing the limits of original research.--SteveMcCluskey (talk) 04:11, 22 January 2017 (UTC)

You simply misunderstood it. The more discussing, the more it appears that you had no knowledge of lunisolar calendars. Q5968661 59.57.223.8 (talk) 08:59, 22 January 2017 (UTC)

It is not helpful to indulge in ad hominiem comments like the above that I "have no knowledge of lunisolar calendars". For general historical background on lunar calendars you might want to consider:

• Ben-Dov, Jonathan; Horowitz, Wayne; Steele, John M., eds. (2012), Living the Lunar Calendar, Oxford and Oakville, CT: Oxbow Books, ISBN 978-1-84217-481-4, which I reviewed in the Journal for the History of Astronomy, 44 (2013): 485-487.

Normally I wouldn't mention my own work, but given your comments, let me also recommend these works on luni-solar calendars:

• McCluskey, Stephen C. (1977), "The Astronomy of the Hopi Indians", Journal for the History of Astronomy, 8: 174–195, which deals primarily with their observational luni-solar calendar.
• McCluskey, Stephen C. (1998), Astronomies and Cultures in Early Medieval Europe, Cambridge: Cambridge University Press, ISBN 0-521-77852-2. Chapter five deals with the Easter computus and the luni-solar calendar.

--SteveMcCluskey (talk) 22:29, 22 January 2017 (UTC)

I am sorry for that and thanks for your recommendation. In this case, all we need is the mean lengths of tropical years and synodic months because lunisolar calendars or the Metonic cycle depend on them. Most of sources only tell what it is but not why it is. Let me recommend these calculations again:

• Tropical year: 365.2422 (Y), Synodic month: 29.5306 (M)
• Y/M = 12.36826
• 1/0.36826 = 2.7155 (L)
• 7×L = 19.0082

Please think about them twice and twice, thanks! If you are clear about them, you will clearly understand the law for lunisolar calendars. Q5968661 27.154.63.66 (talk) 03:53, 23 January 2017 (UTC)

OMG, you are the author of the books! Why didn't you accept the results of the calculations in the section? Maybe it is that you didn't believe it is so simple for all of them. Maybe it is all my fault because of my poor English and if so, sorry again! Q5968661 27.154.63.66 (talk) 05:56, 23 January 2017 (UTC)

I noticed from your user page and talk page that there have been recurring comments about your additions of calculated results, without any further support by reliable sources, or even by reasoned discussion, to a range of articles concerning the calendar.

It seems that you believe that a mathematical calculation provides a self-evident demonstration of truth. This is not so. The development and presentation of ideas may use mathematics as a tool to support a presentation, but the mathematics must be supported by clear discussions and (in Wikipedia) by the citation of other sources that use similar mathematical analyses.

I hope this helps.--SteveMcCluskey (talk) 14:13, 23 January 2017 (UTC)

Thanks, I have decided to remove the edits I made in WP. Q5968661 (talk) 14:33, 23 January 2017 (UTC)

This article in its current state can be deleted too because there is nothing important in it. It has been destroyed by people like AstroLynx and Jc3s5h who seem to protect it. Q5986661 27.154.63.66 (talk) 02:43, 24 January 2017 (UTC)

Second opinion requested at 'Epact'

Would someone look at talk:Epact#Leap day or leap month?, please, to confirm or deny my belief that there is a serious error in need of correction. --John Maynard Friedman (talk) 10:43, 7 October 2021 (UTC)

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Participate in the deletion discussion at the nomination page. —Community Tech bot (talk) 17:23, 8 February 2022 (UTC)

Determining leap months

At present, the section Determining leap months in the article begins A tropical year is longer than 12 lunar months and shorter than 13 of them. and continues with The arithmetical equation 12 × 12 + 7 × 13 = 235 allows it to be seen that a combination of 12 'short' years (12 months) and 7 'long' years (13 months) will be equal to 19 solar years. which has a {{clarify}} tag that says Because 253 lunar months is as long as 19 solar years? If so, that needs to be shown. The arithemetic is not difficult, the only question is how to express it succinctly – and it is critical that the words "year" and "month" be disambiguated.

(FWIW, I suggest that opening paragraph of the section needs to be rewritten in English because at present it is self-indulgent waffle. But one issue at a time.)

So how about:

• A combination of 12 'short' lunar years (12 lunar months) and 7 'long' lunar years (13 lunar months) (or 12 × 12 + 7 × 13 = 235 ) will be almost equal to 19 solar years. This is because an average lunar month#synodic month lasts about 29.53059 days and so 235 × 29.53059 = 6,939.68865 days. An average solar year is 365.2422 days thus 19 × 365.2422 = 6,939.6018 days. So this simple algorithm is accurate to 0.08 days a year or a little less than one day a century.

Any advance on that? 𝕁𝕄𝔽 (talk) 11:28, 11 February 2024 (UTC)