Lectures on the weekly Torah
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In the Mishnah (Rosh ha-Shanah 1.1) we read:
“The first of Shvat is the New Year for
Trees, according to the House of Shammai; the House of Hillel say the fifteenth.”
This difference of opinion is not “one
of the leniencies of the House of Shammai” (Mishnah Eduyot chs. 4, 5),
but neither it is a question of a lenient ruling by the House of Hillel. What
underlies their disagreement in this case?
Rashi commented on the text at hand:
“This is in regard to tithes,”
[2]
i.e. the New Year for Trees marks the beginning of a new year as far as tithes
(ma’asrot) were concerned, and on this day a new year also begins with
respect to computing the number of years for orlah (whether a tree is
too young for its fruit to be permissible to eat).
The Talmud (Rosh ha-Shanah
14a) comments on this mishnah:
“What is the reason? Rabbi
Eleazar quoted Rabbi Oshaiah as saying:…
‘Even though most of the season is without [or outside], nevertheless
most of the rains of that year have already fallen’.”
Rabbi Eleazar, quoting Rabbi Oshaiah, was trying to
establish the basis for setting the date for the New Year for Trees, but it is
unclear whether the reason he gives explains the approach of the House of
Shammai or the approach of the House of Hillel, or perhaps both.
[3]
In order to understand Rabbi Eleazar in
the name of Rabbi Oshaiah, we must understand what is meant by the expression
“most of the season is without.”
The Jewish
calendar is comprised of lunar months and solar years;
[4]
the length of the month is determined by the time it takes for the moon
to orbit around the earth, whereas the length of the year is determined by the
time it takes for the sun “to go around the earth”.
[5]
The average month is 29.5 days long,
[6]
and therefore some Jewish months are 29 days long (deficient months) and some
are 30 days long (full months).
The average year is 365 days long; regular years have 12 lunar months, leap
years have 13 lunar months. Simple
arithmetic shows that a regular year has about 354 days and a leap year around
383 days.
[7]
The solar year is
divided into four equal parts,
[8]
called seasons (Heb. tekufot
), each one beginning with yom ha-tekufah
, the designated day of the season:
the season of Tevet
begins at the peak of winter, when the day
is shortest and the night longest; the season of Nisan begins in the
spring, when day and night are of equal length; the season of Tammuz
begins at the peak of summer, when the day is longest and the night
shortest; and the season of Tishre
begins in the fall, when day and night are
of equal length.
[9]
By the end of the
period of the Sages, a fixed calendar had been established containing clear and
fixed principles regarding deficient and full months, regular and leap
years. Leap years were inserted into
a cycle of nineteen years, during which there were seven leap years and twelve
regular years.
[10]
We are also familiar with the general (Gregorian)
calendar in use in the world today, which is a fixed solar calendar.
In that system, the beginning of winter
(the period of Tevet
) always falls on December 21 or 22,
[11]
while the beginning of spring (the period of Nisan) falls on March 21
or 22.
Returning to the
meaning of R Oshaiah’s words: The Talmud notes that on the New Year for Trees
“most of the season is still without,” meaning that on this day the half-way
point of the winter season (Tevet
) has not yet been reached.
According to the solar calendar, the
middle of the season falls on February 4 or 5; thus the New Year for Trees must
come before February 4. Here a
difficulty arises: examining the
Jewish calendar we note that in the nineteen-year cycle of leap years there are
seven years in which Tu b-Shvat does not fall when “most of the season
is without.”
[12]
However, if one follows the system of
the school of Shammai, who said that the New Year for Trees is on the first of Shvat
, then the principle that “most of the season is without” is always
upheld.
[13]
One could argue that the explanation
that “most of the season is without” pertains only to the approach advocated by
the school of Shammai,
[14]
nevertheless we should try to understand R. Oshaiah’s reason also according to
the approach of the school of Hillel.
[15]
The problem we
have raised becomes more severe if we examine the calendar as it was managed in
the time of the Sages of the Mishnah.
In their day the calendar had not yet been fixed; the new month was
declared on the basis of witnesses who sighted the new moon, so that actually
the number of days in a regular year fluctuated between 352 and 356,
[16]
and in a leap year between 381 and 386.
[17]
The solar year, according to the Sages’
knowledge of astronomy,
[18]
was 365.25 days long,
[19]
and therefore each of the four seasons lasted exactly 91.3125 days.
[20]
Leap years were proclaimed at the
discretion of a special court established for the purpose.
Calculating when it would be a regular
year and when a leap year was a complex matter, referred to as “the secret of
proclaiming leap years,” and the Rabbis considered that knowledge to be “proof
of your wisdom and discernment to other peoples” (Deut. 4:6).
[21]
The most important
factor in determining whether to proclaim a leap year is the commandment,
“observe the month of Abib,” which was a practical matter:
the Sages who proclaimed leap years had
to make sure that the (solar) season of Nisan, the Spring, always
fell before the 16th day of the (lunar) month of Nisan.
[22]
In the course of the month of Adar
, at the very latest, the Sages who proclaimed the leap years had to
calculate when the season of Nisan
would begin, and if they foresaw that it
would fall on the 16th of Nisan
or later, they had to declare that the next
month would be Adar II
.
Precise calculation shows that the season of Nisan can begin between
the 19th of Adar
and the 15th of Nisan in a regular year,
or between the 16th of Adar II
and the 29th of Adar II in a leap year.
For the fifteenth
of Shvat
to fall before the halfway-point of the
season of Tevet
, to fulfill R. Oshaiah’s reason that “most
of the season is without,” the season of Nisan must always begin
after the second of Nisan
,
[23]
and this, of course is an impossible requirement.
On the other hand, for the first of Shvat
to fall before the middle of the season of Tevet, following the
approach of the school of Shammai, the season of Nisan must begin after the
eighteenth of Adar
. As we have said, the nineteenth of Adar
is precisely the earliest possible date for the new season, according
to the rules of determining leap years as well.
If so, it appears simply that the talmudic remark, “most of
the season is without,” pertains exclusively to the the school of Shammai.
The name Shvat
, however, may refer to something else.
Generally it means the fifth lunar month (counting from Tishre
), but we find that it is also used as the name for the thirty days
that fall in the middle of the season.
For example (Rosh Ha-Shanah
15a):
“Rabbi Yohanan asked Rabbi Yannai:
When is the New Year for citron trees?
He said, Shvat
.
Shvat
of the months or Shvat
of the season? He said,
of the months.”
[24]
Rashi comments:
“‘Shvat of the season’
means in the solar calendar; after thirty days of the season of Tevet
comes the beginning of the solar Shvat.”
In other words,
the term Shvat
can refer to Shvat of the [lunar]
months or to Shvat
of the season.
The first thirty days of the season of Tevet
(Winter) are called Tevet
and the next thirty days are called Shvat
. Tu b-Shvat (or the fifteenth of Shvat) of the season is
the forty-fifth day of the season of Tevet
, after which come the remaining forty-six
days of the season. If we
interpret according to the school of Hillel, that the New Year for Trees is on
the fifteenth of “Shvat
of the season,” then according to their
approach as well “most of the (winter) season is without.”
[25]
Thus one might say
that the essence of the dispute between the school of Hillel and the school of
Shammai was, ‘Which calendar should be used to determine the New Year for Trees?’
The school of Shammai was of the
opinion that one should use the generally accepted lunar calendar, whereas the
school of Hillel advocated the solar calendar.
[26]
According to the lunar calendar,
following the school of Shammai, the New Year for Trees was the first of Shvat
, so that “most of the season is without.”
In contrast, according to the solar calendar, following the
school of Hillel, the New Year for Trees was the fifteenth of Shvat
. In actuality, halakhic
practice followed both schools: Tu
B-Shvat is celebrated on the fifteenth of Shvat like the school of
Hillel, but reckoned by the lunar calendar according to the system of the
school of Shammai.
Dr. Yoel Shiloh
Ashkelon
College
[1] The following articles which have appeared in the Bar- Ilan Weekly Parasha Page deal with the Hebrew calendar in general and with calculating the seasons in particular: Y. Loewinger, “This month is the month of Abib”; S. Feigelstock, “The Seasons of the Year”; Y. Loewinger, “Can the founding of the Hebrew calendar be dated by astronomical clarification?”; R. Sar-Shalom, “Establishment of the Calendar by Hillel and its Finalization in the Period of the Geonim”; A. Mirsky, “The Structure of the Hebrew Calendar”; Y. Adler, “On Setting the Years and their Cyclic Nature” (Studies 167, 209, 248, 274, 322, 431).
[2]
Thus Rashi wrote in Rosh Hashana 14a:
“One should not give terumah from fruits of trees that began
forming their fruits before that date, on behalf of the fruit of trees that
began forming after that date.
[3]
Tosefot (s.v. le-tekufot) is of the opinion that the question
pertains to both views. The remainder
of our paper deals with this issue.
[4]
Maimonides, Kiddush Ha-Hodesh 1.1.
[5]
Of course it is now known that the earth orbits around the sun, but we used the
expression that was generally accepted at that time.
[6] Rosh Ha-Shanah 25a: “Rabban Gamaliel said to them: Thus I have received it from my father’s house: The moon is not renewed in less than twenty-nine and a half days and two thirds of an hour and seventy-three parts of an hour.” The Sages had a mnemonic device for the length of the month – kaf-tet yod-bet taf-shin-tzadeh-gimel, in other words twenty-nine days, another twelve hours, and another seven-hundred ninety-three parts of an hour. A “part of an hour” [heleq, halaqim] refers to the ancient practice of dividing the hour into 1080 equal parts of time, where one “part” equals approximately 3 seconds. It follows that according to the scheme of the Sages, the length of the average month is 29 days, 12 hours, forty-four minutes and three seconds. See Maimonides, Kiddush Ha-Hodesh 6.3. Maimonides, loc. sit. 6.2, explains that the hour was divided into 1080 parts because this number is divisible with no remainder by all the numbers up to ten (excluding 7). See E. Raviv, “Ta’am le-Zayin-Tet Taf-Resh-Mem-Bet,” Sinai 128 (2002), p. 91.
[7]
Arakhin 9b: “Between one
Shavuot and the next and between one New Year and the next there are
only four days, and if it is a leap year, five.”
In other words, if one divides the days of the year into
seven (into full weeks), then the remainder is four in a regular year or five
in a leap year.
[8] All the explanations below follow the scheme of Shemuel Yarhinaah, who attested (Berakhot 58b): “The paths of the Heavens are as clear to me as the paths of Nehardea.” At a later period the more complex scheme of Rabbi Adda Bar Ahavah was adopted, but the schools of Hillel and Shammai surely did not know of this scheme, nor is it likely that Rabbi Oshaiah knew of it.
[9]
Astronomists call these days the winter solstice, vernal equinox, summer
solstice and autumnal equinox, respectively.
[10]
For example, last year (5764) was the fifth year of
the 304th cycle.
On the history of setting the calendar, see Z. H. Yafe, Korot
Heshbon ha-Ibbur, 1931; H. Y. Bornstein, “Divrei Yemei ha-Ibbur
ha-Aharonim,” Ha-Tekufah vol. 14-15, p. 339.
[11]
In the past, the Julian calendar was used, in which the season of Tevet
began on December 7 or 8.
[12]
These are the years following a leap year:
1st, 4th, 7th, 9th,
12th, 15th, 18th.
[13]
The ninth year in the cycle is the latest one, and the first of Shvat on
such years comes out on January 30 or 31.
[14]
See S. Goren, “Keviat Tu-b’Shvat ke-Rosh ha-Shanah la-Ilan,” Torat
ha-Moadim, Jerusalem 1996, p. 234.
[15]
This is the view of Tosefot in note 3 above.
[16]
Mishnah Arakhin 2.2: “There
can be no fewer than four full months in a year nor more than eight.”
[17]
Arakhin 9b: “Once Rabbi
proclaimed nine deficient months … it was in a leap year.”
For an elegant explanation of these
calculations see R. Sar-Shalom, “Mispar ha-Yamim be-Luah ha-Shanah,” Shema’tin
147(1999), p. 54.
[18]
See note 8.
[19]
Three hundred and sixty-five days and six hours.
Modern astronomical measurements have established that the
solar year is 365.2422 days long.
[20]
Maimonides, Kiddush Ha-Hodesh 9.2.
[21]
Shabbat 75a.
[22] Rosh Ha-Shanah 21a: “Rav Huna bar Avin sent to Rabba: Seeing that the period of Tevet has continued until the twelfth of Nisan, make it a leap year and have no worry. For it is written (Deut. 16): “Observe the month of Abib,” make sure that the season of Spring be in the month of Nisan.” [I.e. that the month of Nisan fall in the springtime.]
[23]
If both Shvat and Adar are full months.
[24] See Tosefot (s.v. o shvat de-tekufah), who view the question as pertaining not only to citron trees, but to the New Year for Trees in general. According to their approach, however, the question returns, because the Talmudic discussion concludes that it is Shvat of the months; i.e., that the school of Hillel in the Mishnah should not be interpreted as we suggest. The matter requires further study.
[25]
A similar interpretation is given by Ritba on this text.
[26]
The Sages used the solar calendar for other needs, as well, such as:
blessing the sun (Berakhot 59b);
praying for rain in the Diaspora (Ta’anit 10a; see Resp. Iggerot
Moshe, Orah Hayyim 5.7, which uses the secular date); age with
respect to a sacrifice (Rosh Ha-Shanah 6b); the laws of the Nazirite (Nazir
8a); mixing the sacred incense (Keritut 6a), and others.