The first and second of the five inclusive features (*lnga-bsdus*) of a Tibetan calendar are the lunar weekday (*gza’*) and the date of the lunar month (*tshe*). These are involved in the mechanism through which the lunar and solar calendars are brought into harmony. To understand lunar weekdays, it is necessary to understand lunar date days (*tshe-zhag*) and their difference from solar days (*nyin-zhag*).

## Lunar Date Days and Solar Days

Lunar date days are the period of time it takes for the moon to travel one-fifteenth the distance between new moon and full moon, or full moon and new moon positions in each successive sign in the zodiac. They divide into 15 units the waxing and waning phases of the moon. Solar days are the period of time from dawn to dawn.

Western days are divided into 24 hours. In the Tibetan system, most types of days are divided into 60 astro hours. Just as each solar day is divided into 60 solar astro hours, each lunar date day is divided into 60 lunar astro hours. Solar and lunar astro hours are not equal to each other in length, just as these two types of days differ in length.

Western days are solar and last from midnight to midnight. They are all equal in length. Tibetan solar days are from dawn to dawn. Since the time of dawn changes each day, and on the same day is different the further away one is from the equator, Tibetan solar days vary in length. For calendar purposes, however, dawn is taken standardly to be at 5 A.M. Consequently, Tibetan solar days used in the calendar have a standard length.

There are approximately 29.5 solar days between new moons, whereas there are 30 lunar date days during the same period. A lunar month, then, has either 29 or 30 solar days, while it always has 30 lunar date days. Because of the discrepancy between the number of solar and lunar date days in a lunar month, the exact new moon does not occur at precisely the same time of solar day in each month. In other words, each month the beginning of the first lunar date day will occur at a different time on the first solar day of that month.

Furthermore, although solar days all have a standardized, equal length, lunar date days are not similarly standardized.

The moon's motion is linked to that of the sun. Imagine a child running round the inside of a giant tire tube, while throwing a ball ahead of him. Each time he pitches the ball, he sends it circling round the inside of the tube. The ball reaches him from behind, whereupon he catches it and hurls it again. The motion of the sun around the zodiac is like that of the child, while the motion of the moon in its cycle of phases is like that of the ball. The new moon is like when the child catches the ball and then throws it. The full moon is like when the ball is at exactly the opposite point in the tire from the child so that it starts to come back to him rather than going further away.

Imagine that the child runs at different speeds in different parts of the tire tube. In addition, regardless of where the child is inside the tube, imagine that the ball travels at different speeds depending on how far away it is from the child. Thus, the amount of time it takes for the ball to travel one-fifteenth the distance away from or back to the child depends on how fast the child is running as well as how fast the ball is moving simply from its being thrown. Likewise, the amount of time it takes the moon to travel one lunar date day, in other words one-fifteenth the distance from new to full, or full to new moon, depends on where the sun is in the zodiac and where the moon is in its waxing or waning cycle of phases.

Therefore, since the beginning of the first lunar date day of a lunar half-month does not necessarily correspond to the start of the first solar day of that half-month, and since the lengths of each of the 15 lunar date days during the half-month are different, consequently the lunar date days of the half-month do not coincide with the solar days. During the 60 solar hours between the dawns of two consecutive solar days, from 54 to 64 lunar hours can pass. Either one, two or no lunar date days can begin during that solar day.

In summary, lunar date days can be slightly longer or shorter, or equal in length to solar days. Any hour of a lunar date day can occur at dawn, the start of the solar day. A varying amount of a lunar date day can pass between the dawns of two successive solar days.

## Lunar Weekdays and Solar Weekdays

To correlate the lunar and solar calendars, the lunar date days must be assigned to solar days. The Kalachakra system makes this assignment by working with lunar and solar weekdays, and dates of the lunar month. The calendar is arranged in solar days, each with a date and a day of the week. The lunar date days are converted into lunar weekdays and are mapped on top of it.

Although the number of lunar phase and solar days in a lunar month can be different, the number of lunar and solar weekdays is always the same. But lunar weekdays are not the same as solar weekdays.

- Solar weekdays are a way of counting solar days in cycles of 7 and are totally equivalent to solar days. Both solar days and solar weekdays begin at the same time and last 60 solar hours.
- Lunar date days generate lunar weekdays. Sometimes these two types of lunar days are equivalent, sometimes they are not. A lunar weekday may cover either one, two or no lunar date days. Thus, although a lunar date day has 60 lunar astro hours, a lunar weekday may span a varied number of lunar astro hours.

Solar weekdays begin at a fixed point each solar day, namely its start. Lunar weekdays do not necessarily begin at the same time time as lunar date days, and neither begin at the same time each solar day. For this reason, the lunar weekdays that count the lunar date days do not coincide with the solar weekdays that count the solar days. Both solar and lunar days of the week, however, are assigned numbers, from 0 to 6, with zero being Saturday. Lunar date days are also numbered in cycles of seven, from 0 to 6.

## Dates of the Lunar Month

The second inclusive calendar feature is dates of the lunar month. These are numbered one to 30 and last from dawn to dawn in the manner of solar days. The dates of the lunar month number the solar days, and thus number the solar weekdays.

Imagine 30 solar days, numbered one to 30, theoretically available for use in a lunar month. Each must be assigned a solar day of the week. There are always 30 lunar date days and thus 30 lunar weekdays in a lunar month: a phase of the moon cannot be skipped. The lunar weekday occurring at the dawn of each solar day determines the solar weekday assigned to that day. If the lunar weekdays were all of equal length, the assignment would be straightforward, one for one. For instance, if the lunar Sunday were occurring at the dawn of the first solar day, that day would be a solar Sunday and the first of the month. If the lunar Monday began sometime during that first solar day and was still occurring at the dawn of the second, the second solar day would be a solar Monday and date number two. This process would continue in a symmetrical fashion for the entire month.

The lunar weekdays, however, vary in length. Suppose lunar Monday began five minutes before the dawn of the second solar day and lunar Tuesday began five minutes after the dawn of the third solar day. Lunar Monday is occurring at the dawns of both the second and third theoretical solar days, and so both the second and the third would be solar Mondays. This is not allowed. The rule is that solar weekdays must be consecutive, with no days of the weeks occurring twice in a row and none omitted. If two consecutive theoretical solar days would each be assigned the same solar day of the week, the second of the two is omitted. Therefore, in the above example, the theoretical solar day numbered three is omitted. Note that this adjustment does not eliminate either a lunar or solar weekday. It merely eliminates a date. Solar Monday is date two and solar Tuesday is date four.

Suppose lunar Monday began five minutes after the dawn of the second theoretical solar day and lunar Tuesday began five minutes before the dawn of the third. Lunar Sunday is thus occurring at the dawn of the second and lunar Tuesday at the dawn of the third theoretical solar day. This would make the second a solar Sunday and the third a solar Tuesday. This is also not allowed. There must be a solar day Monday in between the two. Theoretical solar days are not actual solar days, and so an extra theoretical one can be added. This added one will be a solar Monday, named after the lunar Monday. Whenever an extra solar weekday is added, it is given the same date as the day after it. Therefore, there are two theoretical solar days numbered date three. The first of these two is solar Monday and the second of the two solar Tuesday. Note that this adjustment does not add a doubled lunar or solar weekday. It merely doubles a date.