Halakhah sa Exodo 34:22: Sefer HaChinukh & The Sabbath Epistle

It is from the roots of this commandment [that it is] so that Israel shall make God’s holidays in their (proper) times, as God commanded that we make Pesach in the time that the produce is in [bloom], as it is written (Deuteronomy 16:1), “Observe the month of Spring, and you shall offer the Pesach sacrifice.” And the holiday of Sukkot is [to fall] at the time of the harvest, as is written, “And the holiday of the harvest at the turn of the year” (Exodus 34:22). And were it not for intercalation, the holidays would come not at these times, since Israel calculates their months and festivals according to the lunar year, which has three hundred and fifty-four days, eight hours, and eight hundred and seventy-six parts, which is less than the solar year by ten days, twenty-one hours and two hundred and four parts — its mnemonic is ten, twenty-one, two hundred and four. Due to the ripening of the produce and fruit from the power of the sun, it turns out that but for intercalation — by which we align the lunar and solar years — Pesach would not come in the Spring, nor Sukkot at the time of the harvest. And this matter is to be fixed by the greatest [sages] of the generation, since it is a matter requiring great wisdom. And since it is also said that from this [calculation, one comes to know] the agricultural happenings of the year, it is appropriate to give [this task] only to great and pious men.

Judah the Persian¹⁹ Mentioned by Ibn Ezra in his Commentary to the Pentateuch and elsewhere. Nothing is known of this scholar. (See Encyclopedia Judaica, second edition, vol. 11, p. 505.) said that the years used by Israel were solar years, because he found the festivals were on fixed dates: Passover when the barley ripens (Exodus 34:18), Pentacost at reaping time (ibid. 34:22), and Tabernacles at harvest time (Deuteronomy 16:13). However, what can be done since Moses did not specify the length of a year?²⁰ Since the Bible does not specify the exact length of a solar year, the Karites are left with the matter being undecided. This will also affect determination of the festivals. Also, how will he explain the use of the Hebrew term “hodesh” (new) for “month,” for what is renewed relative to the sun? The uncircumcised (Christians), because their years are solar years and they found that a full year contains twelve lunations, divided the days of the year into twelve parts, for this number is closest to the number of lunar months. The result is that some months are 30 days and some months are 31 days.²¹ Here Ibn Ezra accounts for the division of a year into twelve parts, even if one uses a solar calendar. However, the term “hodesh” would not be appropriate for such solar months.

Therefore, natural philosophers said that by right the year should begin with the point of intersection (equinoctial point) from which the sun begins to approach the inhabited portion of the earth (the northern hemisphere).⁷³ This is a “tropical year,” the period from one vernal equinox until the following vernal equinox. This is the cycle of Rav Adda.⁷⁴ Rav Adda’s year is a tropical year. Although his cycle is based on the average orbit, its correction is simple.⁷⁵ Rav Adda’s figure is for a mean solar year. Corrections need to be made to accommodate apparent variations in the solar orbit. This was also the beginning of the year for those who developed the Hebrew calendar. This was also the beginning of the year for the early Greeks.⁷⁶ See Evans, pp. 182–184 for a discussion of early Greek calendars. This is the vernal equinox. The Persians begin their year with the summer solstice, the Chaldeans with the autumnal equinox, and the Christians with the winter solstice. However the Christians are in error since their calculation of the solar year is not correct.⁷⁷ During the lifetime of Ibn Ezra, Christians followed the Julian calendar, with a year consisting of exactly 365¼ days. In the year 1582 the Church reformed its calendar and adopted the Gregorian version, improving upon the approximation of the Julian calendar.