Acano a lunar calendar method
Diffusion of ancient near East lunar and solar calendars to the Canary Islands likely have contained a http://docs.google.com/viewer?a=v&q=cache:PPTp1ozN60J:webpages.ull.es/users/jbarrios/pdf/Acano1996.pdf+Jose+Barrios+Garica&hl=en&gl=us&pid=bl&srcid=ADGEESjjIisIz44I64cov5HSo4gOnWkP1A0w5vEovKeJgNApuUMLm8oysGQSNuAG4RQyg0mMsOhESGv_FK6oRPcHMDeta5W8Fx_CJbTpgkn5D9GibwuVf9IzI8ujRc8Q6PAtS68gnEM&sig=AHIEtbQR9ZIgZTzAlaoQ5o1npe5A_VdjAw3 x 4 matrix calendar.
The raw data was parsed and formally reported by Jose Barrios Garcia. An older http://www.crystalinks.com/bailysbeads.htmlBabylonian, Egyptian
an/or Phoenician 135moon cycle may have combined with a lunar solar calendar marks the movement of solstices (SS) across 12moons, adding 11 days each year and alternatively subtracting 29 or 30 days every time. The acano count gives the location of the SS and locations of the other seasonal moons. Making the acano count as possibly reported in http://en.wikipedia.org/wiki/Babylonian_calendarBabylonian astronomy in an 135moon context, used until 499 BCE, and replaced by Metonic 235moon method, an equivalent^{} count is 29+30+29 days = 8*11 days. Thus, the SS stays 8 solar years in the first three moons, the first column. The SS then jumps to the second column. This give us the basic statement:
8 solar year = 8 lunar year + 3 moons = 99 moons, which forms the http://en.wikipedia.org
/wiki/OctaeterisOctaeteris, another lunisolar calendar from antiquity.
The basics of the Canary Island 9moon, 12moon and 270moon lunar eclipse calendars may have been used during the
period 900 BCE to 400 AD, and passed down in oral traditions after that time. It is unknown if these calendars were
based on an Babylonian Egyptian or Phoencian (Libyan) 135moon lunar calendar.
The Canary Island calendar is used today and is named
http://webpages.ull.es/users/jbarrios/pdf/Acano1996.pdfacano. The acano calendar used three colors and is parsed
by a 3 x 4 matrix revealing multiple mathematical topics.
Matrix math subjects may include aspects of a 260 day Mayan calendar, 520 eclipse calendar, 135moon, 270moon,
and Mayab 405mpon lunar eclipse calendar.
In addition^{} there is solstice number system that is easy to explain facetoface, with drawings, reports
Jose Barrios Garcia, Professor of Mathematics at the University of Laguna, Canary Islands (Spain). Without
drawings, and a lengthy discussion the specifics of the ancient acano calendar are difficult to grasp. An
attempt to explain details outside of its threecolors follows.
LUNAR CALENDARS Imagine a chessboard of 3 (horizontal) by 4 (vertical) files, equaling 12 squares alternatively painted in http://webpages.ull.es/users/jbarrios/pdf/Acano1996.pdfblack and red. Each square represented one synodic moon, let us say, from new moon to new moon. So the acano represents 12 consecutive moons, alternatively colored red and black. The moons are ordered vertical, let us say, from left to right.
1 4 7 10
2 5 8 11
3 6 9 12
From this point of view, the acano was an (eventually eternal) temporal framework measuring the pass of time from the endless repetition of this exact group of 12 synodic moons. There are no intercalary moons in this pattern. Time is measured by the eternal sequence of synodic moons packed in groups of exactly 12 moons. Red and black chessboards have been preserved in ancient caves on the Canary Islands.
Attending to a 19th century indirect source (La luna es la madre de los tiempos) the alternative coloring helps to track the duration of an actual moon. If we assume an average synodic month of 29.5 days, let red moons to be 29 days and black moons to be 30 days (or vice versa). On this way, two consecutive moons average 29.5 days. The acano accounts for a total of 6*29+6*30=354 days.
Let the Sun move across the acano, assume a solar year of 365 days, and suppose that we begin to count just from the coincidence of the New moon with the Summer Solstice in just the first day of the first month of the first acano.
First acano:
Since equinoxes and solstices are never less than three moon spaced, if Summer solstice (SS) occurs in the first day of the first moon of the first acano, the Autumn equinox (AE) occurs in the 4th moon, the Winter solstice (WS) in the 7th moon and the Spring Equinox (SE) in the 10th moon. So the equinoctial and solstice moons (from now on the seasonal moons) are aligned in the first file of the acano.
A Canarian priest working on this pattern would have readily located on the acano the very important (from astronomical, calendrical, social and agricultural perspective) the four seasonal moons. So they would prepare the social and economical activities for the year knowing exactly and anticipated in which moon everything occurs.
Second acano:
Now 12 moons have passed and we are in the first moon of the second acano. Since there is a 11 days difference^{} between the acano and the Solar year, SS would occur in the 11th day of the first moon, so the seasonal moons continue to be aligned in the first file of the acano.
Third acano:
Another 12 moons have passed so the SS would occur in the 22th day of the first month and the seasonal moons continue to be aligned in the first file of the acano.
Fourth acano:
Another 12 moons have passed so the SS would occur in the 33th day of the acano, that is to say, in the 4th day of the second moon. Since the SS has jumped to the second file of the acano, the other three seasonal moons also jump, so they remain aligned!, now in the second file.
And so on for the next followings years. A report from the Canary Islands considers 520 days as one and onehalf eclipse cycle, as discussed by Barrios. The Canary Island 520 day cycle was a minor cycle within the dominate 270moon calendar. The 270moon calendar calculated 135moon and 405moon calendars within the 260, 520, … 11960 day cycles.
Acano Number System
Quoting Barrios, ”As a matter of fact, to record a date on the acano you only need to write a number from 1 to 30 on one of its squares. The selected square fixes the moon while the number fixes the day of the moon counted, let us say, from new to new. Accordingly, it is possible to record unambiguously on a single acano the 33 successive dates fixing a whole round of the summer solstice through the lunar year. What is of the utmost importance is that this can be accomplished either through the years by actual observation, either at any desired moment by performing an easy arithmetical exercise on the acano.
Indeed, once recorded on the acano the date of a particular summer solstice, we obtain the dates of the next summer solstices simply adding 11 days by year to the previous number. Each time the accumulated shift is greater than 29 or 30 days, we jump to the next square, reduce the shift by 29 or 30 days, write the new date on the square and continue the count. Actually, this exercise can be done even mentally for a number of years.”
DISCUSSIONS
Aaboe argues for several classes of lunar eclipse calendars in ancient cultures. One was the acano. Several scholars argue the Egyptian and Babylonian 135moon case, including red to denote life, and black to denote death, following an acanolike cycle. Jose Barrios Garcia argues for Canarian 520 day eclipse and 270moon calendars in alternating red and black day colors. F. Lounsbury and http://www.le.ac.uk/archaeology/rug/aa/progs/pohualli.htmlA. Lebeuf argue the Mayan 260 day calendar, a Canarian 520 day calendar and a 405moon calendar, that include red to denote east (good), and black to denote west(almost bad), followed acano cycles. Aztecs and Mesoamericans used black to denote north, and death. Acano lunisolar eclipse calendars were well known to ancient cultures, such as 9moon (260 day) and 99moon calendars, cycles that may relate to ancients predicting eclipses.
Two recent acanotype uses aligned civil and scientific calendars connected to eclipses tables, and validated longitudes in land (map making) and http://phoenicia.org/proutes.htmlocean navigation. The far ranging Phoenicians circumnavigated http://www.livius.org/hehg/herodotus/hist01.htmAfrica in 600 BCE, made http://en.wikipedia.org/wiki/Hanno_the_Navigatorlater trips, as did Columbus in 1492 assisted by lunar eclipse tables and the http://mathforum.org/kb/message.jspa?messageID=1180034&tstart=0”Armed Guards of Polaris”, calibrated daily by ’ 1/2 hour glasses’ for http://www.navworld.com/navcerebrations/columbus.htmlongitude, and Polaris for latitude.
Acanotype lunar eclipse prediction tables, referenced to Spain port city longitudes, were carried by Columbus on four New World trips. Columbus, like the http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B75864D2MWSD2&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=f6f4727667f3a345724b8b46b505410dPhoenicians/Libyans had used the 135moon Egyptian eclipse tables. http://www.burlingtonnews.net/redhairedmummiescanaryislands.htmlPhoenicians/Libyans reached the Canary Islands in 900 BCE as deposed Egyptian pharaohs (denoted by http://books.google.com/books?id=njALAAAAIAAJ&pg=PA67&lpg=PA67&dq=canary+islands,+mummies&source=web&ots=pmiExR214p&sig=IgJRJOoej7rjJpwqaB0TPBeP6s&hl=en&sa=X&oi=book_result&resnum=10&ct=resultmummification and calendars), and stayed there until 400 AD, as a stop over on long voyages. Columbus debarked from the Canary Islands and observed http://starryskies.com/The_sky/events/lunar2003/columbus.eclipse.htmltwo eclipses on his voyages, determining http://sunsite.utk.edu/math_archives/.http/hypermail/historia/aug99/0131.htmllongitudes more accurate than historians have credited him (by only reading Bishop de Landa’s edited data). Columbus had based his longitude calculations on Ptolemy’s Almagest definition of the earth’s circumference^{}. Bishop de Landa edited Columbus’ ’armed guards of Polaris’ data as political protection from the http://www.zum.de/whkmla/period/disc/tordesillas.htmltreaty of 1494 sanctions  in which Spain may have lost New World lands had Columbus’ longitude hand written data been given to the http://en.wikipedia.org/wiki/Portugal_in_the_Age_of_DiscoveryPope or to Portugal.
Mayan black and red numbers cite seasonal almanacs in the Dresden Codex (pages 6169) and Madrid Codex almanacs. A
405moon lunar calendar maybe implied one day by ring number 7.2.14.9 (51419 days) or other information in the seasonal
almanac. The http://articles.adsabs.harvard.edu/cgibin/nphiarticle_query?1988JHAS...19....1B&defaultprint=YES&filetype=.pdfBrickers in
1988.
Pages 6568 of the Dresden Code report eclipse, solstice and equinoxes almanac about 800 years (per 15 reference dates mentioned on pages 6164) and shorter seasonal 1910, 1924 and 1911 day cycles on pages 6568 analyzed by Bruce Friedman in 2012. Bruce Friedman argues for matrix table within three lines of raw data across pages 6568:
11 1 13 1 11 12 1 13 8 8 6 13 4 5 2 7 13 7 6 13 6 6 8 1
11 11 13 11 11 9 1 10 8 5 6 11 4 2 2 4 13 4 6 10 6 3 8 11
9 9 5 1 1 2 10 12 6 5 2 7 11 5 7 12 3 2 12 1 8 9 4 13
By following the Brickers’ paired ”framed” instructions within crosswise sums:
274 432 355 163 432 177 167 178 432 163 355 432 274
Note that the symmetry^{} is not perfect because 178 ”appears” where 177 is ”expected.” This is due to the part of line
two that referred to previously as an anomaly (namely line 2 on p.65 where 13,11 appears to break a consistent pattern
of 10 day mod 13 additions to alternate entries in all of lines one and two. 13,10 is ”expected” by the pattern and
would have made the 178 ”appears” as 177. The Bricker’s considered this anomaly as a scribal error (it MAY NOT).
All these numbers above are processed from the first two lines only but yield 163 (twice) and 167 (once at middle).
163 and 167 are still obscure but these are an anchor (of some kind) to the third line where the same values ”appear”
as a delta from the first and last entries on line 3 p.65 (167 as the delta between 9,9 and 1,2) and the first and last
entries of line 3 p.67 (163 as the delta between 11,5 and 3,2). Shelving analysis of these two quantities [163 and 167]
in favor of the more peculiar fourtime appearance of 432 seems important. To date 4 x 432 is 1728 and trivially is
1000 + (2 x 364), data that would be in error if the Brickers are correct (a strong possibility as their 2011 book
is digested).
However: Line three’s 13 quantities total 1911 which is 21 x 91 and if 1728 id deducted 183 as a result. Also look at
432 less one cycle of 260 and find result 172. 172+183 is 355. 355 ”appears” above (as may have been intended) to be
the 177+178 spacing of lunar eclipses. The 432 day number appears four times in a manner that needs to be precisely
understood. The other matrix numbers are associated with wellknown lunar eclipse cycles.
Mayans added red and black numbers as other keys, possibly in the acano manner, another issue that calls out to be
studied with the summer solstice acting as a possible beginning point.
Mayan astronomers worked from the midyear season, outwards, denoted by feet icons going forward and back,
and year bearers, aspects ofthe Brickers’ 2011 book. The matrix seasonal almanac data double checked itself by several
techniques. Transliteration errors will likely be eliminated by double checking the almanac’s matrix structure^{} within
a study being conducted by Bruce Friedman (with minor assistance by myself).
SUMMARY
The best known http://webpages.ull.es/users/jbarrios/pdf/Acano1996.pdfacano cycle is marked by 33 solar years and 34 lunar years. The
acano cycle uses 270 = 2 x 135 moons in which 46 lunar eclipses, and a complete^{} number system on the Canary Islands.
Lounsbury reports Mayan eclipse data, beginning with a 260 day calendar in the Dresden Codex as 405 moons = 3x 135
moons, as possibly extended to a 405month cycle. Related lunisolar calendars have been discovered around the world.
Several ancient 135moon, 270moon and 405moon lunar calendars show common features. One regional lunar calendar
used a red and black acano 3 x 4 matrix placed in http://www.mummytombs.com/mummylocator/group/guanche.htmCanary Island caves next to
mummies. The red and black 3 x 4 type matrix/abacus
innovation may pop up elsewhere in paintings, suggesting an academic connection. As individual cultural achievements
lunar eclipse tables were prepared by Egyptians, Libyans, Phoenicians, Mesoamericans, and other advanced cultures.
Several ancient lunar eclipse, solstice and equinox tables (almanacs) assisted in aligning civil and religious
calendars, map making, and ocean navigation are under investigation.
References
 1 Asger Aaboe, ”Remarks on the theoretical treatment of eclipses in antiquity”,Journal for the History of Astronomy (Cambridge), 1972.

2
Jose Barrios Garica, TARA: A Study on the Canarian Astronomical Pictures, Part II: The acano chessboard, Universidad de Laguna (Spain), 1996.
Title Acano a lunar calendar method Canonical name AcanoALunarCalendarMethod Date of creation 20160325 7:14:12 Last modified on 20160325 7:14:12 Owner milogardner (13112) Last modified by milogardner (13112) Numerical id 127 Author milogardner (13112) Entry type Definition Classification msc 01A15 Classification msc 01A13 Defines lunar calendar