Jewish & Civil Time, Lunar+leap years=luni-solar, Jewish time units (Parts), Moladot
The JMT clock is an educational tool to help people understand and become more familiar with the principles that are explained in this document (with more detail provided in other documents linked to below). First time users may find the JMT clock a little confusing, largely because of its strange hour numbering. That is explained in the first section below. But I also recommend that first-timers start by trying out the simpler Night/Day clock, which shows only civil time, while the JMT clock shows both civil time and Jewish Time.
The Night/Day clock has two different skins and the same two sets of numbers on each one. The daytime numbers are given greater prominence on the day skin and the night-time numbers are given greater prominence on the night skin. This makes it a 24-hour clock, but with a conventional 12-hour dial. It will help you get used to 24-hour time notation. All of those features are also features of the JMT clock.
The numbers on the JMT clock are shifted six hours forward of their conventional positions. This is because the JMT clock tells time in two different time systems, corresponding to two different calendars, the Jewish and the civil calendar, whose days start at different times. The clock shows the time in both sytems simultaneously.
Most people can tell time on an analog clock - even if, like this one, it has no numbers - just from the positions of the hands. If you ignore the numbers on the JMT clock and observe only the hand positions, the clock tells time as counted in the civil calendar that we are all familar with. (That is the Gregorian calendar, which is used as the civil calendar almost universally.) In our civil calendar, a new calendar day begins at midnight, which, therefore, is zero hours of the day (00:00) in that calendar, and 06:00 hours, 12:00 hours and 18:00 hours are the mean times of sunrise, solar noon, and sunset at the central meridian of your time zone.
On the other hand, if you observe the numbers on the JMT clock, the clock indicates Jewish Mean Time (JMT), in which the hours of the day are numbered from when a new day of the Jewish calendar begins.
A noctdiem (24-hour day) of the Jewish calendar consists of a whole night plus the daytime period following it. In other words, the entire night belongs to the same calendar date as the following daytime period. So in the Jewish calendar, a new calendar day begins, not at midnight, but six hours earlier, at mean sunset. (See footnote 2 for the reason for this.)
Therefore, in Jewish Mean Time, zero hours is the time of mean sunset and the mean times of midnight, sunrise, and solar noon are 06:00 hours, 12:00 hours and 18:00 hours. More generally, JMT = civil time plus 6 hours, e.g. Friday, 18:00 civil time = Saturday, 00:00 hours JMT. This applies everywhere, in all time zones, all locations and in all seasons.
So, as you can now see, there really is such a thing as Jewish Mean Time, and the term is not just the exclusive property of comedians joking about how Jewish functions never start on time.
The "mean" in "Jewish Mean Time" signifies that all hours are standard hours, which are exactly 60 minutes long. (Sixty minutes is one 24th of the mean interval between two real, i.e. solar, noons.) This is in contrast to Jewish Seasonal Time (JST), which is a different Jewish system for specifying times. JST is similar to local solar time (AKA sundial time). In JST, a new day begins at real (not mean) sunset, and times of the day and night are relative to local sunrise and sunset. JST uses seasonal hours, which are of variable length. A seasonal hour of the day is one twelfth of the daytime, so it is proportional to the length of daytime, and a seasonal hour of the night is one twelfth of the night-time, so it is proportional to the length of the night. So in JST, a daytime hour usually differs in length from an hour of the night and both vary in length depending on the season and your latitude. Only around the time of the two equinoxes, or all year round at the equator, are those hours exactly 60 minutes.
Seasonal hours are used for specifying the times of religious observances that apply to specific days, or to daytime only or night-time only, or to particular portions of the day or night. Examples would be Shabbat observance and prayer times.
In Jewish calendric calculations, all times are in JMT, not JST, and they are specified in 24-hour notation, where the hours are numbered zero to 23.
In both lunar and luni-solar calendars, the months are lunar, meaning they are synchronised with the cycle of the Moon's phases. That cycle notionally begins at New Moon, so that is when a month begins in those calendars - either at astronomical New-Moon or at the first appearance in the sky, after astronomical New Moon, of the Moon's waxing (i.e. growing) crescent. The latter is often called a "New Moon," colloquially, by non-astronomers. (A more accurate colloquialism would be the new crescent moon.) (In those calendars, the middle of the month coincides with Full Moon, which occurs half way between one New Moon and the next.)
Examples of calendars whose months are lunar are the Chinese, Jewish and the ancient Greek and Babylonian calendars, all of which are luni-solar, and the Moslem calendar, which is purely lunar.
The Gregorian calendar (which is used almost universally as the world's civil calendar) is a purely solar calendar. Its dates line up almost exactly with the seasons. The summer and winter solstices and the spring and autumnnal equinoxes, which are the four turning points of the solar year, regularly occur on the same dates, but that was achieved at the expense of losing the synchronicity between the days of the month and the phases of the Moon. A luni-solar calendar attempts to achieve both, but its main emphasis is on the latter, with the former being maintained only approximately.
The mean length (L) of a cycle of lunar phases is about 29.5 days, so lunar months have two lengths, 29 days and 30 days, usually occurring in alternation. This makes the mean length of a month equal to L. 12L = 354 days, which is eleven days shorter than a year of a solar calendar. So in a purely lunar calendar, the months do not stay aligned with the seasons. In a luni-solar calendar, the months do recur in the same seasons. This is achieved using a system of leap years. The difference (D) between a solar year and 12L is seven nineteenths of L (D = 7L/19). So seven out of every nineteen years are leap years in which an extra month is inserted. This lengthens the calendar's mean year-length to that of the solar year.
The first use of this 19-year cycle for the distribution of leap years in a luni-solar calendar was by the Athenian astronomer Meton in 432 BCE, when he reformed the ancient Greek calendar. It has been known ever since as the Metonic cycle. About 600 years later, the Jewish Talmudic sage Rav Adda bar Ahava recommended its adoption by the Jewish calendar. It eventually did so about 100 years after that, around the mid fourth century CE.
There is one other point of difference between Jewish Mean Time and Civil Time. The Jewish calendar is a fixed-arithmetic calendar, regulated by arithmetic rules. In those rules and in all time calculations relating to the Jewish calendar, time values are expressed, not in units of hours, minutes and seconds, but in hours and parts, where 1 part is a unit of time equal to 3 and 1/3 seconds. 1 hour = 1080 parts, and 1 minute = 18 parts. This time unit was borrowed from ancient Babylonian astronomy and its continued use is partly for mathematical convenience. So in the context of calendric discussions, a time of day in JMT would be specified as hh:pppp, where hh = 00 to 23 hours and pppp = 0000 to 1079 parts. In some modern texts, it is specified as hh:mm:pp, where hh = 00 to 23 hours, mm = 00 to 59 minutes, and pp = 00 to 17 parts.
Since parts figure so heavily in the "language" of Jewish Mean Time, this clock is marked with red dots on its (inner) rim so that the seconds hand can mark time not just in seconds but also in parts. This provides a visual aid to help people understand and become familiar with this unit of time.
Those units of time called parts, defined above, feature most prominently in the specification of the times of moladot (calendric approximations of mean New Moons) and the fixed interval between them. They also figure heavily in the specification of some of the calendar's fundamental rules, because their applicability is governed by the times of certain key moladot. The calculation of those molad times is crucial to determining the year-type of a year and hence the calendar for that year.
All moladot are expressed as a time of week, i.e. weekday W at time T, in Jewish Mean Time, and time T is expressed in 24-hour-clock notation, with the hours being numbered zero to 23. Weekday W is never ambiguous because the molad of a month always occurs on the first of the month or within the previous three days. This convention for specifying moladot was adopted for mathematical convenience; it greatly simplifies the arithmetic for calculating a molad time by allowing all whole weeks to be eliminated from the quantities used. (This does not affect the calculation because a time of week plus or minus one whole week is the same time of week.)
FOOTNOTE 1 [Back]
"Noctdiem" is a term coined by me in the document headed "The Jewish Calendar's Molad System," linked to above. It pairs the latin roots noct (night) and diem (day). I have defined it as a particular type of nycthemeron, meaning a 24-hour day. A noctdiem consists of an entire night plus the whole of the adjacent daytime period - either the one preceding the night or the one following it. The latter type of noctdiem is a Jewish calendar day.
FOOTNOTE 2 [Back]
Some readers may be interested to know why a Jewish calendar day begins at mean sunset. This is an essential feature of all calendars whose months are lunar and whose month begins at either astronomical New-Moon, or at the first appearance in the sky, after astronomical New-Moon, of the waxing lunar crescent, which always appears just after sunset. (It appears low in the western sky and it sets very soon after that.) The night of that first appearance belongs to the first of the new month. Consequently, a calendar day in such calendars begins at mean sunset and consists of a whole night plus the following daytime period.
This may be contrasted with a lunar calendar that, at one time, was used in ancient Egypt for religious purposes concurrently with a solar, civil calendar. In that lunar calendar, a new month began with the last appearance of the waning crescent moon, which rises in the eastern sky at dawn and is drowned out shortly afterwards at sunrise by the much stronger light of the Sun. Since the sunrise on that day of the old moon's last appearance marked the beginning of a new month, a new calendar-day in that calendar began at sunrise and a noctdiem (24-hour day) consisted of the daytime period plus the whole of the following night, the exact opposite of a Jewish noctdiem, because of the difference between those two calendars in when a new month began.