The Shemitah calculation for today’s calendar:
The cycle first began when the Jews entered Eretz Yisrael and settled the lands. This occurred 14 years after the entrance into Eretz Yisrael, as it took 7 years to conquest the land and another 7 to settle it. They then counted Shemitahs and Yovlos for over 16 Jubilee cycles plus another 36 years [836 total years] until the destruction of the Temple. Thus there were a total of 117 Shemitahs and 16 Yovlos counted from the settling into Eretz Yisrael until the destruction of the first Temple. The year of destruction was the first year of the 118th Shemitah cycle. When some of the tribes of the Jewish people were exiled in the times of Sancheirev [many years prior to the destruction] the Yovel year was abolished as it is contingent on the inhabitance of Eretz Yisrael by all Jews. Nevertheless they continued counting the Yovel year every 50th year in order not to confuse the Shemitah cycle which is only to begin after the Yovel year. However during the time of the 70 year exile between the destruction of the first Temple and rebuilding of the 2nd Temple it is disputed as to whether the Jews counted the Yovlos during that time. The Rambam 10/3 holds that they continued to count the Yovlos just like prior to the destruction, while the Geonim have a tradition that they did not count the Yovlos during these 70 years. This same dispute applies also for after the destruction of the second Temple. According to the Geonim, ever since the destruction of the second Temple we no longer count the Yovel year at all and hence the 50th year is the first year of the next Shemitah cycle. According to this opinion the year 5775 is the seventh year of the 278th Shemitah cycle since the destruction in 3829. However according to the Rambam ibid it is a totally different calculation as every 50th year we push off the start of the new Shemitah cycle one year. Hence according to the Rambam, in the 1,946 years between the destruction in 3829 and our current year of 5775 we have 38 Jubilee years that were not counted in the cycle and hence in his calculation 5755 is the 4th year of the 272nd year of the Shemitah cycle and the year 5775 is not Shemitah! Practically even the Rambam concludes that we rely on the Geonim as tradition is a great pillar in Jewish law and is to be relied upon. This is the final ruling today as brought in the calculated years of: Admur 36; Rama, Choshen Mishpat 67/1 [year 5320]; Michaber Yoreh Deah 331/19 [year 5313]
Final ruling of Shemitah Year calculation:
The year of Shemitah [in the time of the writing of these laws by the Alter Rebbe] was 5544/1784. Thirty three cycles of Shemitah have passed since that time. This year 5775 is the next Shemitah year which began the 34th Shemitah cycle from the Shemitah year written in Admur.
 The Yovel years in between do not count as part of the seven year cycle and hence one must decrease 16 Yovel years from the 836 year calculation. See Rambam 10/7; Nedarim 61 following the opinion of Rabanan as opposed to Rebbe Yehuda
 See Rambam 10/4 and 8
 Erechin 32b; Rambam 10/8
 Erechin 32b; Rambam 10/3
 Admur Hilchos Halvah 36; Geonim; Custom of Eretz Yisrael brought in Rambam Shemitah 10/6; Rama Choshen Mishpat 67/1 [year 5320]; Michaber Yoreh Deah 331/19 [year 5313]
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