Dear Calendar People,
The Sawtooth Square Diagram is the partitioning of 1377 months into 41 parts, hexaseasonal yerms or odd leap month periods. The average row has 153 months. The average short row has 135 months. Short rows combined in unlike pairs make a Double Tritos; 2*I  2*S. The longer of the short rows has 136 months equal to 11 years. There are 4 noncenter long rows or Common Long rows that combined in like pairs equal 27 years. This is a barely possible eclipse; 32*S  19*I.

Dear Calendar People,
I am trying an html correction

Dear Helios and Calendar People I don’t see any point of such an arrangement. A more useful arrangement would be rows of a whole number of years. This can be done by noting that ‘33’ is 2 & 2/3 year and ‘35’ is 2 & 5/6 years. One can count the number of hexaseasons, each falls short of 3 years, then ‘35’
counts as 1 and ‘33’ counts as 2. Then a whole number of years occurs, whenever this total of 1s and 2s is divisible by 6. I do this with 33
35 33 33 33
35 33 33
35 33 33
35 33 33 33 35 33 33
35 33 33 33 35 33 33
35 33 33 33 35 33 33
35 33 33
35 33 33 33 35 33 3 times to form a 334year cycle. 33
35 33 33 33
35 33 (12) 33
35 33 33
35 33 33 (12) 33
35 33 33 35 33 33 (12) 33
35 33 33 35 33 33 (12) 33
35 33 33
35 33 33 (12) 35 33 33 33
35 33 33
(12) 35 33 33 33
35 33 33 (12)
35 33
33
35 (6) 33 33 33 (6) 35 33 33
35 (6) 33 33 33 (6) 35 33 33
35 (6) 33 33 33 (6) 35 33
33
35 (6) 33
33
35 33 33 33 35 (12) 33 33
35 33 33 33
35 (12) 33
33
35 33 33
35 33
(12) 33 33
35 33 33 35 33 (12) 33 33
35 33 33 35 33 (12) 33 33
35 33 33
35 33 (12) 33 35
33 33 33 35 33
(12) The 33 33 33 in the middle of each Metonic cycle forms an Octaeteris of 8 years. The Metonic cycle can split into two parts of a whole number of years if and
only if this Octaeteris begin on a new year. This occurs near the middle of the 334year cycle. There it splits into an octaeteris of (33 33 33) and an 11year cycle of
35 33 33 35. Every whole year period must have an even number of
35s and the difference between the number of 33s and 35s must be divisible by three. A similar arrangement would occur with the GrattanGuinness cycle as suggested in previous note. Karl 15(01(27 From: East Carolina University Calendar discussion List [mailto:[hidden email]]
On Behalf Of Helios Dear Calendar People,
View this message in context:
Re: Sawtooth Square Diagram 
Dear Karl and Calendar People,
Instead of inserting odd leap month periods, I've tried 33m and 34m into the arrangement. Now the important eclipses DO reveal themselves by rows. rows 4th and 6th = Tritos middle 7 rows = Triad ( triple inex ) 34 33 34 33 34 34 33 34 33 34 33 34 34 33 34 33 34 34 33 34 33 34 33 34 34 33 34 33 34 34 33 34 33 34 33 34 34 33 34 33 34 = 1377 months 41 is a centered square number or sawtooth square. Each row averages to 153 months. 
Dear Helios and Calendar People
Thank you Helios for your reply. With 33 & 34, I prefer 34 33 34 33 34 34 33 34 33 34 33 34 34 33 34 33 34 34 33 34 33 34 33 34 34 33 34 33 34 34 33 34 33 34 33 34 34 33 34 33 34 = 1377 months = 334/3 years Each row is a yermlike period. The rows are arranged into a yermlike period. Each long row is a Metonic cycle. The middle 5 rows = Triad ( triple inex ) The last 3 of any row and the first 1 of next row = Tritos Also, the last 1 of any row and the first 3 of next row = Tritos. I look into wholeyear rows. All 7 in the Metonic cycle begin on different months: 01 10 06 03 11 08 04 and so the Metonic cycle can never be split into shorter periods of a whole number of years no matter what month it begins, unlike the cycle of 33 35 33 33 33 35 33, which can be split 33 33 33  35 33 33 35. This ensures every wholeyear row has at least 19 years. Some are longer than 19 years because the first 7 have 5 34s instead of the usual 4 34s. If a row has 3*M 33s and 4*N 34s, then it has 8*M + 11*N years. Finally. I mention that the shorter cycle of 34 33 34 33 34 34 33 34 33 34 33 34 = 403 months = 391/12 years is one 1/12 of a GrattanGuinness cycle. Any five rows beginning (and ending) with a long row = Triad (triple Inex). As before; The last 3 of any row and the first 1 of next row = Tritos Also, the last 1 of any row and the first 3 of the next row = Tritos. Karl 15(01(28  Original Message From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Helios Sent: 14 July 2015 04:40 To: [hidden email] Subject: Re: Sawtooth Square Diagram Dear Karl and Calendar People, Instead of inserting odd leap month periods, I've tried 33m and 34m into the arrangement. Now the important eclipses DO reveal themselves by rows. rows 4th and 6th = Tritos middle 7 rows = Triad ( triple inex ) 34 33 34 33 34 34 33 34 33 34 33 34 34 33 34 33 34 34 33 34 33 34 33 34 34 33 34 33 34 34 33 34 33 34 33 34 34 33 34 33 34 = 1377 months 41 is a centered square number or sawtooth square. Each row averages to 153 months.  View this message in context: http://calndrl.10958.n7.nabble.com/SawtoothSquareDiagramtp16006p16014.html Sent from the CalndrL mailing list archive at Nabble.com. 
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