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The Jewish Calendar was
changed
by Hillel II in 4119 Jewish Year or 359 AD,
from
a visually observed
such as by the testimony of two or more witnesses
who had observed the New Moon to proclaim a new month
to
a calculated or mathematical derived calendar which is
identical to the visually observed calendar

The Jewish Calendar is based on the
METONIC CYCLE of 19 repeatable Years,
of which
⠀12 are Common Years
+ 7 are Leap Years
= 19 METONIC CYCLE Years.

To determine a METONIC CYCLE number
you Divide the Jewish Year
such as 5793 ÷ by 19 = 304.894736842
then take the Mantissa .894 and
divide .894 by .052 = 17th Year
of the METONIC CYCLE number

The Jewish Calendar follows the Lunar Cycle
but is still aligned with the seasons.

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12 METONIC CYCLE Years
are Common Years
which are Years:
1,⠀⠀2,⠀⠀4,⠀⠀5,⠀
7,⠀⠀9,⠀10,⠀12,
13,⠀15,⠀16,⠀18

⠀12 Common Years
* 12 months in each of thoses years
= 144 total Common Year Months
and

---

7 METONIC CYCLE Years
are Leap Years
which are Years:
3,⠀⠀6,⠀⠀8,⠀11,
14,⠀17,⠀19
consisting of 13 Months:

⠀⠀7 Leap Years
* 13 months in each of those years
= 91 total Leap Year Months

---

⠀⠀144 total Common Year Months
⠀+⠀91 total Leap Year Months
⠀-------
⠀= 235 total METONIC CYCLE Synodic Months
(the period of orbit of the moon, reckoned from its successive conjuctions with the sun ( i.e. from new moon to new moon ) a lunar month.

A Synodic Month = 29.530588 Days
⠀⠀29.530588
* 235 Synodic Months
-----------------
= 6,939.68818 Days every 235 Synodic Months

A non leap year can have 353 days, 354 days, or 355 days.
A⠀⠀⠀leap year can have 383 days, 384 days, or 385 days.

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Months with 30 Days = 01, 03, 05, 07, 11, "12 (ADAR I)"
Months with 29 Days = 02, 04, 06, 10, "12 (ADAR) and 13 (ADAR II)"

---

AΩ⠀METONIC⠀CYCLE of AΩ⠀Calendar⠀Jewish ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀

⠀METONIC⠀ ⠀CYCLE #

⠀

⠀Leap⠀ ⠀Year

⠀

⠀Common⠀ ⠀Year

⠀

⠀Jewish⠀ ⠀Year ⠀5776

⠀

⠀÷⠀19⠀=⠀

⠀

⠀304.0⠀

⠀

⠀MC⠀Days⠀

⠀

⠀Gregorian⠀Days⠀

⠀

⠀1

⠀

⠀

⠀

⠀1

⠀

⠀5777

⠀

⠀÷⠀19⠀=⠀

⠀

⠀304.052⠀

⠀

⠀353

⠀

⠀366

⠀

⠀2

⠀

⠀

⠀

⠀2

⠀

⠀5778

⠀

⠀÷⠀19⠀=⠀

⠀

⠀304.105⠀

⠀

⠀354

⠀

⠀365

⠀Leap⠀

⠀3

⠀

⠀1

⠀

⠀

⠀

⠀5779

⠀

⠀÷⠀19⠀=⠀

⠀

⠀304.157⠀

⠀

⠀385

⠀

⠀365

⠀

⠀4

⠀

⠀

⠀

⠀3⠀

⠀

⠀5780

⠀

⠀÷⠀19⠀=⠀

⠀

⠀304.210⠀

⠀

⠀355

⠀

⠀365

⠀

⠀5

⠀

⠀

⠀

⠀4⠀

⠀

⠀5781

⠀

⠀÷⠀19⠀=⠀

⠀

⠀304.263⠀

⠀

⠀353

⠀

⠀366

⠀Leap⠀

⠀6

⠀

⠀2

⠀

⠀

⠀

⠀5782

⠀

⠀÷⠀19⠀=⠀

⠀

⠀304.315⠀

⠀

⠀384

⠀

⠀365

⠀

⠀7

⠀

⠀

⠀

⠀5⠀

⠀

⠀5783

⠀

⠀÷⠀19⠀=⠀

⠀

⠀304.368⠀

⠀

⠀355

⠀

⠀365

⠀Leap

⠀8

⠀

⠀3

⠀

⠀

⠀

⠀5784

⠀

⠀÷⠀19⠀=⠀

⠀

⠀304.421⠀

⠀

⠀383

⠀

⠀365

⠀

⠀9

⠀

⠀

⠀

⠀6⠀

⠀

⠀5785

⠀

⠀÷⠀19⠀=⠀

⠀

⠀304.473⠀

⠀

⠀355

⠀

⠀366

⠀

⠀10

⠀

⠀

⠀

⠀7⠀

⠀

⠀5786

⠀

⠀÷⠀19⠀=⠀

⠀

⠀304.526⠀

⠀

⠀354

⠀

⠀365

⠀Leap⠀

⠀11

⠀

⠀4

⠀

⠀

⠀

⠀5787

⠀

⠀÷⠀19⠀=⠀

⠀

⠀304.578⠀

⠀

⠀385

⠀

⠀365

⠀

⠀12

⠀

⠀

⠀

⠀8⠀

⠀

⠀5788

⠀

⠀÷⠀19⠀=⠀

⠀

⠀304.631⠀

⠀

⠀355

⠀

⠀365

⠀

⠀13

⠀

⠀

⠀

⠀9⠀

⠀

⠀5789

⠀

⠀÷⠀19⠀=⠀

⠀

⠀304.684⠀

⠀

⠀354

⠀

⠀366

⠀Leap⠀

⠀14

⠀

⠀5

⠀

⠀

⠀

⠀5790

⠀

⠀÷⠀19⠀=⠀

⠀

⠀304.736⠀

⠀

⠀383

⠀

⠀365

⠀

⠀15

⠀

⠀

⠀

⠀10⠀

⠀

⠀5791

⠀

⠀÷⠀19⠀=⠀

⠀

⠀304.789⠀

⠀

⠀355

⠀

⠀365

⠀

⠀16

⠀

⠀

⠀

⠀11⠀

⠀

⠀5792

⠀

⠀÷⠀19⠀=⠀

⠀

⠀304.842⠀

⠀

⠀354

⠀

⠀365

⠀Leap

⠀17

⠀

⠀6

⠀

⠀

⠀

⠀5793

⠀

⠀÷⠀19⠀=⠀

⠀

⠀304.894⠀

⠀

⠀383

⠀

⠀366

⠀

⠀18

⠀

⠀

⠀

⠀12⠀

⠀

⠀5794

⠀

⠀÷⠀19⠀=⠀

⠀

⠀304.947⠀

⠀

⠀355

⠀

⠀365

⠀Leap⠀

⠀19

⠀

⠀7

⠀

⠀

⠀

⠀5795

⠀

⠀÷⠀19⠀=⠀

⠀

⠀305.0⠀

⠀

⠀385

⠀

⠀365

⠀

⠀Repeat

⠀

⠀

⠀

⠀

⠀

⠀

⠀

⠀

⠀

⠀⠀

⠀

⠀6940

⠀

⠀6941

⠀

⠀1

⠀

⠀

⠀

⠀1

⠀

⠀5796

⠀

⠀÷⠀19⠀=⠀

⠀

⠀305.052⠀

⠀

⠀354

⠀

⠀365

⠀

⠀2

⠀

⠀

⠀

⠀2

⠀

⠀5797

⠀

⠀÷⠀19⠀=⠀

⠀

⠀305.105⠀

⠀

⠀353

⠀

⠀366

⠀Leap⠀

⠀3

⠀

⠀1

⠀

⠀

⠀

⠀5798

⠀

⠀÷⠀19⠀=⠀

⠀

⠀305.157⠀

⠀

⠀385

⠀

⠀365

⠀

⠀4

⠀

⠀

⠀

⠀3⠀

⠀

⠀5799

⠀

⠀÷⠀19⠀=⠀

⠀

⠀305.210⠀

⠀

⠀354

⠀

⠀365

⠀

⠀5

⠀

⠀

⠀

⠀4⠀

⠀

⠀5800

⠀

⠀÷⠀19⠀=⠀

⠀

⠀305.263⠀

⠀

⠀355

⠀

⠀365

⠀Leap⠀

⠀6

⠀

⠀2

⠀

⠀

⠀

⠀5801

⠀

⠀÷⠀19⠀=⠀

⠀

⠀305.315⠀

⠀

⠀383

⠀

⠀366

⠀

⠀7

⠀

⠀

⠀

⠀5⠀

⠀

⠀5802

⠀

⠀÷⠀19⠀=⠀

⠀

⠀305.368⠀

⠀

⠀354

⠀

⠀365

⠀Leap

⠀8

⠀

⠀3

⠀

⠀

⠀

⠀5803

⠀

⠀÷⠀19⠀=⠀

⠀

⠀305.421⠀

⠀

⠀385

⠀

⠀365

⠀

⠀9

⠀

⠀

⠀

⠀6⠀

⠀

⠀5804

⠀

⠀÷⠀19⠀=⠀

⠀

⠀305.473⠀

⠀

⠀353

⠀

⠀365

⠀

⠀10

⠀

⠀

⠀

⠀7⠀

⠀

⠀5805

⠀

⠀÷⠀19⠀=⠀

⠀

⠀305.526⠀

⠀

⠀355

⠀

⠀366

⠀Leap⠀

⠀11

⠀

⠀4

⠀

⠀

⠀

⠀5806

⠀

⠀÷⠀19⠀=⠀

⠀

⠀305.578⠀

⠀

⠀384

⠀

⠀365

⠀

⠀12

⠀

⠀

⠀

⠀8⠀

⠀

⠀5807

⠀

⠀÷⠀19⠀=⠀

⠀

⠀305.631⠀

⠀

⠀355

⠀

⠀365

⠀

⠀13

⠀

⠀

⠀

⠀9⠀

⠀

⠀5808

⠀

⠀÷⠀19⠀=⠀

⠀

⠀305.684⠀

⠀

⠀353

⠀

⠀365

⠀Leap⠀

⠀14

⠀

⠀5

⠀

⠀

⠀

⠀5809

⠀

⠀÷⠀19⠀=⠀

⠀

⠀305.736⠀

⠀

⠀384

⠀

⠀364

⠀

⠀15

⠀

⠀

⠀

⠀10⠀

⠀

⠀5810

⠀

⠀÷⠀19⠀=⠀

⠀

⠀305.789⠀

⠀

⠀355

⠀

⠀365

⠀

⠀16

⠀

⠀

⠀

⠀11⠀

⠀

⠀5811

⠀

⠀÷⠀19⠀=⠀

⠀

⠀305.842⠀

⠀

⠀355

⠀

⠀365

⠀Leap

⠀17

⠀

⠀6

⠀

⠀

⠀

⠀5812

⠀

⠀÷⠀19⠀=⠀

⠀

⠀305.894⠀

⠀

⠀383

⠀

⠀365

⠀

⠀18

⠀

⠀

⠀

⠀12⠀

⠀

⠀5813

⠀

⠀÷⠀19⠀=⠀

⠀

⠀305.947⠀

⠀

⠀354

⠀

⠀366

⠀Leap⠀

⠀19

⠀

⠀7

⠀

⠀

⠀

⠀5814

⠀

⠀÷⠀19⠀=⠀

⠀

⠀306.0⠀

⠀

⠀385

⠀

⠀365

⠀

⠀Repeat

⠀

⠀

⠀

⠀

⠀

⠀

⠀

⠀⠀

⠀

⠀⠀

⠀

⠀6939

⠀

⠀6940

So it takes
⠀◯⠀-->["29.530588 days"]
from any Moon Phase to
the same Moon Phase i.e.,
[ Full Moon to Full Moon ]
[ New Moon to New Moon ]

29.5305882 days ÷ 2 =
⠀◯⠀-->["14.7602941 days"]
from
[ New Moon to Full Moon ] or
[ Full Moon to New Moon ] and

14.7602941 days ÷ 2 =
⠀◯⠀-->["7.38014705 days"]
from
[ Half Moon to Full Moon ]

⠀New⠀Moon⠀⠀14⠀Days⠀to⠀Full⠀Moon⠀ ⠀⠀New⠀Moon⠀⠀7⠀Days⠀to⠀Half⠀Moon⠀Bright⠀Right⠀Half⠀	⠀	⠀
⠀Waxing⠀Cresent⠀Bright⠀Right⠀Side⠀⠀10⠀Days⠀to⠀Full⠀Moon⠀ ⠀Waxing⠀Cresent⠀Bright⠀Right⠀Side⠀⠀3⠀Days⠀to⠀Half⠀Moon⠀ ⠀⠀⠀Bright⠀Right⠀Half⠀	⠀	⠀
⠀First⠀Quarter⠀Half⠀Moon⠀Bright⠀Right⠀Half⠀ ⠀⠀7⠀Days⠀to⠀Full⠀Moon⠀	⠀	⠀
⠀Full⠀Moon⠀⠀7⠀Days⠀to⠀⠀Last⠀Quarter⠀ ⠀⠀Half⠀Moon⠀Bright⠀Left⠀Half⠀	⠀	⠀
⠀Last⠀Quarter⠀Half⠀Moon⠀Bright⠀Left⠀Half⠀	⠀	⠀
⠀Waning⠀Cresent⠀Bright⠀Left⠀Side⠀	⠀	⠀
⠀New⠀Moon⠀	⠀	⠀

A Full Moon falls
in the middle of
the Jewish Month
around the 14th day
although it can fall on the
13th, 14th, 15th and rarely the 16th.

The 14th of the Jewish Month falls on:
⠀Day 2 (Monday),⠀⠀⠀(roughly 30%).
⠀Day 4 (Wednesday),⠀(roughly 29%).
⠀Day 6 (Friday),⠀⠀⠀⠀(roughly 27%).
⠀Day 7 (Saturday).⠀⠀(roughly 12%).

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