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Lunisolar Cycle Multiples of Short Lunar Cycle

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	Re: Lunisolar Cycle Multiples of Short Lunar Cycle by Helios :: Rate this Message: Reply to Author \| View Threaded \| Show Only this Message I didn't think I was going to add to the list, but... I add 3 more. I was corresponding with someone and I had to find a value of a "rune" equal to 1/19 month. Then I found two Short Lunar Cycles divisable by 19. these are the 507 month cycle and the 1438 month cycle. Also the 1340-month cycle's mean month was corrected. 725 years of 183 lunar 49-month cycles with mean month of 29.530612 days and mean year of 365.24276 days 2414 years of 73 lunar 409-month cycles with mean month of 29.530562 days and mean year of 365.24192 days 3014 years of 57 lunar 654-month cycles with mean month of 29.530581 days and mean year of 365.24253 days 3473 years of 71 lunar 605-month cycles with mean month of 29.530579 days and mean year of 365.24215 days 3511 years of 45 lunar 965-month cycles with mean month of 29.530570 days and mean year of 365.24210 days 4437 years of 46 lunar 1193-month cycles with mean month of 29.530595 days and mean year of 365.24228 days 5124 years of 125 lunar 507-month cycles with mean month of 29.530572 days and mean year of 365.24200 days 5181 years of 80 lunar 801-month cycles with mean month of 29.530587 days and mean year of 365.24223 days 5515 years of 39 lunar 1749-month cycles with mean month of 29.530589 days and mean year of 365.24225 days 5697 years of 49 lunar 1438-month cycles with mean month of 29.530598 days and mean year of 365.24223 days 6251 years of 86 lunar 899-month cycles with mean month of 29.530590 days and mean year of 365.242204 days 6707 years of 118 lunar 703-month cycles with mean month of 29.530583 days and mean year of 365.24228 days 6745 years of 88 lunar 948-month cycles with mean month of 29.530591 days and mean year of 365.24240 days 7364 years of 253 lunar 360-month cycles with mean month of 29.530556 days and mean year of 365.24212 days 8119 years of 74 lunar 1357-month cycles with mean month of 29.530582 days and mean year of 365.24227 days 8464 years of 105 lunar 997-month cycles with mean month of 29.530592 days and mean year of 365.24220 days 8518 years of 137 lunar 769-month cycles with mean month of 29.530559 days and mean year of 365.24219 days 8559 years of 79 lunar 1340-month cycles with mean month of 29.530597 days and mean year of 365.24232 days
	Re: Lunisolar Cycle Multiples of Short Lunar Cycle by Karl Palmen :: Rate this Message: Reply to Author \| View Threaded \| Show Only this Message Dear Helios and Calendar People I sort them by mean month. This time I express the cycle by the yerm era pattern in [], preceded by the number of lunar cycles in the lunisolar cycle. See http://www.hermetic.ch/cal_stud/lunarcal/lunacycl.htm . 7364 years of 253 lunar 360-month cycles with mean month of 29.530556 days and mean year of 365.24212 days 253[22] 8518 years of 137 lunar 769-month cycles with mean month of 29.530559 days and mean year of 365.24219 days 137[22,25] 2414 years of 73 lunar 409-month cycles with mean month of 29.530562 days and mean year of 365.24192 days 73[25] 3511 years of 45 lunar 965-month cycles with mean month of 29.530570 days and mean year of 365.24210 days 45[28,31] 5124 years of 125 lunar 507-month cycles with mean month of 29.530572 days and mean year of 365.24200 days 125[31] 3473 years of 71 lunar 605-month cycles with mean month of 29.530579 days and mean year of 365.24215 days 71[37] 3014 years of 57 lunar 654-month cycles with mean month of 29.530581 days and mean year of 365.24253 days 57[40] 8119 years of 74 lunar 1357-month cycles with mean month of 29.530582 days and mean year of 365.24227 days 74[40,43] 6707 years of 118 lunar 703-month cycles with mean month of 29.530583 days and mean year of 365.24228 days 118[43] 5181 years of 80 lunar 801-month cycles with mean month of 29.530587 days and mean year of 365.24223 days 80[49] 5515 years of 39 lunar 1749-month cycles with mean month of 29.530589 days and mean year of 365.24225 days 39[52,55] 6251 years of 86 lunar 899-month cycles with mean month of 29.530590 days and mean year of 365.242204 days 86[55] 6745 years of 88 lunar 948-month cycles with mean month of 29.530591 days and mean year of 365.24240 days 88[58] 8464 years of 105 lunar 997-month cycles with mean month of 29.530592 days and mean year of 365.24220 days 105[61] 4437 years of 46 lunar 1193-month cycles with mean month of 29.530595 days and mean year of 365.24228 days 46[73] 8559 years of 79 lunar 1340-month cycles with mean month of 29.530597 days and mean year of 365.24232 days 79[82] 5697 years of 49 lunar 1438-month cycles with mean month of 29.530598 days and mean year of 365.24223 days 49[88] 725 years of 183 lunar 49-month cycles with mean month of 29.530612 days and mean year of 365.24276 days 183[] Helios said he found two cycles divisible by 19. By that I think he means divisible by 19 days (rather than 19 months). Such a cycle can be divided into 19 parts with an equal number of days, that each form a cycle for the 1/19 month rune. In yerm era notation these cycles are [31] and [88]. The difference between them is 19 49-month cycles ( 19[] ). The 3104-year lunisolar cycle ( 57[40] ) is also divisible by 19 days, because it is made up of 193 lunar cycles. The following lunar cycles are divisible by 7-days: 654 months [40], 997 months [61] and 1651 months [49,52]. The following lunar cycles are divisible by 12 months: 360 months [22], 948 months [58] and 2654 months 2[40]. Karl 10(13(13 -----Original Message----- From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Helios Sent: 02 October 2009 03:40 To: CALNDR-L@... Subject: Re: Lunisolar Cycle Multiples of Short Lunar Cycle I didn't think I was going to add to the list, but... I add 3 more. I was corresponding with someone and I had to find a value of a "rune" equal to 1/19 month. Then I found two Short Lunar Cycles divisable by 19. these are the 507 month cycle and the 1438 month cycle. Also the 1340-month cycle's mean month was corrected. 725 years of 183 lunar 49-month cycles with mean month of 29.530612 days and mean year of 365.24276 days 2414 years of 73 lunar 409-month cycles with mean month of 29.530562 days and mean year of 365.24192 days 3014 years of 57 lunar 654-month cycles with mean month of 29.530581 days and mean year of 365.24253 days 3473 years of 71 lunar 605-month cycles with mean month of 29.530579 days and mean year of 365.24215 days 3511 years of 45 lunar 965-month cycles with mean month of 29.530570 days and mean year of 365.24210 days 4437 years of 46 lunar 1193-month cycles with mean month of 29.530595 days and mean year of 365.24228 days 5124 years of 125 lunar 507-month cycles with mean month of 29.530572 days and mean year of 365.24200 days 5181 years of 80 lunar 801-month cycles with mean month of 29.530587 days and mean year of 365.24223 days 5515 years of 39 lunar 1749-month cycles with mean month of 29.530589 days and mean year of 365.24225 days 5697 years of 49 lunar 1438-month cycles with mean month of 29.530598 days and mean year of 365.24223 days 6251 years of 86 lunar 899-month cycles with mean month of 29.530590 days and mean year of 365.242204 days 6707 years of 118 lunar 703-month cycles with mean month of 29.530583 days and mean year of 365.24228 days 6745 years of 88 lunar 948-month cycles with mean month of 29.530591 days and mean year of 365.24240 days 7364 years of 253 lunar 360-month cycles with mean month of 29.530556 days and mean year of 365.24212 days 8119 years of 74 lunar 1357-month cycles with mean month of 29.530582 days and mean year of 365.24227 days 8464 years of 105 lunar 997-month cycles with mean month of 29.530592 days and mean year of 365.24220 days 8518 years of 137 lunar 769-month cycles with mean month of 29.530559 days and mean year of 365.24219 days 8559 years of 79 lunar 1340-month cycles with mean month of 29.530597 days and mean year of 365.24232 days -- View this message in context: http://www.nabble.com/Lunisolar-Cycle-Multiples-of-Short-Lunar-Cycle-tp2 3562589p25709806.html Sent from the Calndr-L mailing list archive at Nabble.com. -- Scanned by iCritical.
	Re: Lunisolar Cycle Multiples of Short Lunar Cycle by Karl Palmen :: Rate this Message: Reply to Author \| View Threaded \| Show Only this Message Dear Helios and Calendar People The following of these cycles have a common divisor between the number of years and number of months, so form a multiple of a shorter year/month cycle such as the 353-year cycle. 3014 years of 57 lunar 654-month cycles with mean month of 29.530581 days and mean year of 365.24253 days 2(1507 years with 555 leap months) 5124 years of 125 lunar 507-month cycles with mean month of 29.530572 days and mean year of 365.24200 days 3(1708 years with 629 leap months) 5181 years of 80 lunar 801-month cycles with mean month of 29.530587 days and mean year of 365.24223 days 3(1727 years with 636 leap months) 6707 years of 118 lunar 703-month cycles with mean month of 29.530583 days and mean year of 365.24228 days 19(353 years with 130 leap months) 7364 years of 253 lunar 360-month cycles with mean month of 29.530556 days and mean year of 365.24212 days 4(1841 years with 678 leap months) 8119 years of 74 lunar 1357-month cycles with mean month of 29.530582 days and mean year of 365.24227 days 23(353 years with 130 leap months) Two examples are multiples (19 and 23) of the 353-year cycle. The following of these cycles have a common divisor between the number of years and number of days, so form a multiple of a shorter solar calendar cycle such as a 1899-year cycle with 460 leap days. 2414 years of 73 lunar 409-month cycles with mean month of 29.530562 days and mean year of 365.24192 days 2(1207 years with 292 leap days) 5124 years of 125 lunar 507-month cycles with mean month of 29.530572 days and mean year of 365.24200 days 4(1281 years with 310 leap days) 5697 years of 49 lunar 1438-month cycles with mean month of 29.530598 days and mean year of 365.24223 days 3(1899 years with 460 leap days) 6745 years of 88 lunar 948-month cycles with mean month of 29.530591 days and mean year of 365.24240 days 5(1349 years with 327 leap days) 8464 years of 105 lunar 997-month cycles with mean month of 29.530592 days and mean year of 365.24220 days 2*(4232 years with 1025 leap days) The largest multiplier is just 5. The 3104-year cycle is of interest, because it seems to be two Maya 1508-haab cycles reckoned at 1507 years each, but is actually one day longer than that, so giving a mean year of 365.24253 days rather than 365.24220 days and a mean month of 29.530581 days rather than 29.530554 days. Karl 10(13(19 -----Original Message----- From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Helios Sent: 02 October 2009 03:40 To: CALNDR-L@... Subject: Re: Lunisolar Cycle Multiples of Short Lunar Cycle I didn't think I was going to add to the list, but... I add 3 more. I was corresponding with someone and I had to find a value of a "rune" equal to 1/19 month. Then I found two Short Lunar Cycles divisible by 19. these are the 507 month cycle and the 1438 month cycle. Also the 1340-month cycle's mean month was corrected. 725 years of 183 lunar 49-month cycles with mean month of 29.530612 days and mean year of 365.24276 days 2414 years of 73 lunar 409-month cycles with mean month of 29.530562 days and mean year of 365.24192 days 3014 years of 57 lunar 654-month cycles with mean month of 29.530581 days and mean year of 365.24253 days 3473 years of 71 lunar 605-month cycles with mean month of 29.530579 days and mean year of 365.24215 days 3511 years of 45 lunar 965-month cycles with mean month of 29.530570 days and mean year of 365.24210 days 4437 years of 46 lunar 1193-month cycles with mean month of 29.530595 days and mean year of 365.24228 days 5124 years of 125 lunar 507-month cycles with mean month of 29.530572 days and mean year of 365.24200 days 5181 years of 80 lunar 801-month cycles with mean month of 29.530587 days and mean year of 365.24223 days 5515 years of 39 lunar 1749-month cycles with mean month of 29.530589 days and mean year of 365.24225 days 5697 years of 49 lunar 1438-month cycles with mean month of 29.530598 days and mean year of 365.24223 days 6251 years of 86 lunar 899-month cycles with mean month of 29.530590 days and mean year of 365.242204 days 6707 years of 118 lunar 703-month cycles with mean month of 29.530583 days and mean year of 365.24228 days 6745 years of 88 lunar 948-month cycles with mean month of 29.530591 days and mean year of 365.24240 days 7364 years of 253 lunar 360-month cycles with mean month of 29.530556 days and mean year of 365.24212 days 8119 years of 74 lunar 1357-month cycles with mean month of 29.530582 days and mean year of 365.24227 days 8464 years of 105 lunar 997-month cycles with mean month of 29.530592 days and mean year of 365.24220 days 8518 years of 137 lunar 769-month cycles with mean month of 29.530559 days and mean year of 365.24219 days 8559 years of 79 lunar 1340-month cycles with mean month of 29.530597 days and mean year of 365.24232 days -- View this message in context: http://www.nabble.com/Lunisolar-Cycle-Multiples-of-Short-Lunar-Cycle-tp2 3562589p25709806.html Sent from the Calndr-L mailing list archive at Nabble.com. -- Scanned by iCritical.
	Re: Lunisolar Cycle Multiples of Short Lunar Cycle by Karl Palmen :: Rate this Message: Reply to Author \| View Threaded \| Show Only this Message Dear Helios and Calendar People Here I list those lunisolar cycles where the number of leap days in the equivalent solar calendar has a common divisor with the number of lunar cycles. One example already mentioned is the 2414-year cycle whose number of leap days is a multiple (8) of the number (73) of lunar cycles. 2414 years of 73 lunar 409-month cycles with mean month of 29.530562 days and mean year of 365.24192 days - 584 leap days: 8 in each lunar cycle 3511 years of 45 lunar 965-month cycles with mean month of 29.530570 days and mean year of 365.24210 days - 850 leap days: 170 in nine lunar cycles 5124 years of 125 lunar 507-month cycles with mean month of 29.530572 days and mean year of 365.24200 days - 1240 leap days: 248 in 25 lunar cycles 5181 years of 80 lunar 801-month cycles with mean month of 29.530587 days and mean year of 365.24223 days - 1255 leap days: 251 in 16 lunar cycles 8464 years of 105 lunar 997-month cycles with mean month of 29.530592 days and mean year of 365.24220 days - 2050 leap days: 410 in 21 lunar cycles In all cases, besides the one already mentioned, the common divisor is 5. Solar yerms for 1/10 year would repeat once every 1/5 of a lunisolar cycle in a whole number of lunar cycles. Is there a reason why the only common divisors are also divisors of 365? Karl 10(13(26 -----Original Message----- From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Helios Sent: 02 October 2009 03:40 To: CALNDR-L@... Subject: Re: Lunisolar Cycle Multiples of Short Lunar Cycle I didn't think I was going to add to the list, but... I add 3 more. I was corresponding with someone and I had to find a value of a "rune" equal to 1/19 month. Then I found two Short Lunar Cycles divisable by 19. these are the 507 month cycle and the 1438 month cycle. Also the 1340-month cycle's mean month was corrected. 725 years of 183 lunar 49-month cycles with mean month of 29.530612 days and mean year of 365.24276 days 2414 years of 73 lunar 409-month cycles with mean month of 29.530562 days and mean year of 365.24192 days 3014 years of 57 lunar 654-month cycles with mean month of 29.530581 days and mean year of 365.24253 days 3473 years of 71 lunar 605-month cycles with mean month of 29.530579 days and mean year of 365.24215 days 3511 years of 45 lunar 965-month cycles with mean month of 29.530570 days and mean year of 365.24210 days 4437 years of 46 lunar 1193-month cycles with mean month of 29.530595 days and mean year of 365.24228 days 5124 years of 125 lunar 507-month cycles with mean month of 29.530572 days and mean year of 365.24200 days 5181 years of 80 lunar 801-month cycles with mean month of 29.530587 days and mean year of 365.24223 days 5515 years of 39 lunar 1749-month cycles with mean month of 29.530589 days and mean year of 365.24225 days 5697 years of 49 lunar 1438-month cycles with mean month of 29.530598 days and mean year of 365.24223 days 6251 years of 86 lunar 899-month cycles with mean month of 29.530590 days and mean year of 365.242204 days 6707 years of 118 lunar 703-month cycles with mean month of 29.530583 days and mean year of 365.24228 days 6745 years of 88 lunar 948-month cycles with mean month of 29.530591 days and mean year of 365.24240 days 7364 years of 253 lunar 360-month cycles with mean month of 29.530556 days and mean year of 365.24212 days 8119 years of 74 lunar 1357-month cycles with mean month of 29.530582 days and mean year of 365.24227 days 8464 years of 105 lunar 997-month cycles with mean month of 29.530592 days and mean year of 365.24220 days 8518 years of 137 lunar 769-month cycles with mean month of 29.530559 days and mean year of 365.24219 days 8559 years of 79 lunar 1340-month cycles with mean month of 29.530597 days and mean year of 365.24232 days -- View this message in context: http://www.nabble.com/Lunisolar-Cycle-Multiples-of-Short-Lunar-Cycle-tp2 3562589p25709806.html Sent from the Calndr-L mailing list archive at Nabble.com. -- Scanned by iCritical.
	5181-year cycle for terms of 8/11 month RE: Lunisolar Cycle ... by Karl Palmen :: Rate this Message: Reply to Author \| View Threaded \| Show Only this Message Dear Helios and Calendar People Several of these cycles given by Helios have a multiple of 8 months and so can be used with a calendar with 11 terms to 8 months and 17 terms to a year plus a leap term about once every 157 years. For a cycle of Y years and L months, M-T = 11L - 136Y and so the number of leap terms is 1/8 of this, which is (11/8)L - 17Y, of course. 5181 years of 80 lunar 801-month cycles with mean month of 29.530587 days and mean year of 365.24223 days This has 110801 - 175181 = 33 leap terms. One per 157 years exactly! 6745 years of 88 lunar 948-month cycles with mean month of 29.530591 days and mean year of 365.24240 days This has 121948 - 176745 = 43 leap terms as already mentioned. 7364 years of 253 lunar 360-month cycles with mean month of 29.530556 days and mean year of 365.24212 days This has 253495 - 177364 = 47 leap terms (32 after 157 years & 15 after 156 years). So I think the 5181-year cycle is a better choice for this than the 6745-year cycle. I again suggest that for each period of eight months, have the first ten terms alternate between 21 and 22 years and the remaining (11th) term have the remaining 21 or 22 days of the eighth month. I think Helios may have selected the 6745-year cycle because the number of months is divisible by 11 (also applies to 7364-year cycle). However, it's the number of years being divisible by 11 that is useful. This is the case for the 5181-year cycle (5181=315711). All three cycles are a whole number of lunar 12-month years: 5181 years 5340 lunar years 159 drift cycles 6745 years 6952 lunar years 207 drift cycles 7364 years 7590 lunar years 226 drift cycles There are 33 terms to two lunar years. Karl 10(15(02 -----Original Message----- From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Helios Sent: 02 October 2009 03:40 To: CALNDR-L@... Subject: Re: Lunisolar Cycle Multiples of Short Lunar Cycle I didn't think I was going to add to the list, but... I add 3 more. I was corresponding with someone and I had to find a value of a "rune" equal to 1/19 month. Then I found two Short Lunar Cycles divisable by 19. these are the 507 month cycle and the 1438 month cycle. Also the 1340-month cycle's mean month was corrected. 725 years of 183 lunar 49-month cycles with mean month of 29.530612 days and mean year of 365.24276 days 2414 years of 73 lunar 409-month cycles with mean month of 29.530562 days and mean year of 365.24192 days 3014 years of 57 lunar 654-month cycles with mean month of 29.530581 days and mean year of 365.24253 days 3473 years of 71 lunar 605-month cycles with mean month of 29.530579 days and mean year of 365.24215 days 3511 years of 45 lunar 965-month cycles with mean month of 29.530570 days and mean year of 365.24210 days 4437 years of 46 lunar 1193-month cycles with mean month of 29.530595 days and mean year of 365.24228 days 5124 years of 125 lunar 507-month cycles with mean month of 29.530572 days and mean year of 365.24200 days 5181 years of 80 lunar 801-month cycles with mean month of 29.530587 days and mean year of 365.24223 days 5515 years of 39 lunar 1749-month cycles with mean month of 29.530589 days and mean year of 365.24225 days 5697 years of 49 lunar 1438-month cycles with mean month of 29.530598 days and mean year of 365.24223 days 6251 years of 86 lunar 899-month cycles with mean month of 29.530590 days and mean year of 365.242204 days 6707 years of 118 lunar 703-month cycles with mean month of 29.530583 days and mean year of 365.24228 days 6745 years of 88 lunar 948-month cycles with mean month of 29.530591 days and mean year of 365.24240 days 7364 years of 253 lunar 360-month cycles with mean month of 29.530556 days and mean year of 365.24212 days 8119 years of 74 lunar 1357-month cycles with mean month of 29.530582 days and mean year of 365.24227 days 8464 years of 105 lunar 997-month cycles with mean month of 29.530592 days and mean year of 365.24220 days 8518 years of 137 lunar 769-month cycles with mean month of 29.530559 days and mean year of 365.24219 days 8559 years of 79 lunar 1340-month cycles with mean month of 29.530597 days and mean year of 365.24232 days -- View this message in context: http://www.nabble.com/Lunisolar-Cycle-Multiples-of-Short-Lunar-Cycle-tp2 3562589p25709806.html Sent from the Calndr-L mailing list archive at Nabble.com. -- Scanned by iCritical.

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