Tenpō calendar

The Tenpō calendar (天保暦), officially known as the Tenpō sexagenary unitary calendar (天保壬寅元暦 Tenpō jin'in genreki), was a Japanese lunisolar calendar. It was published in the Tenpō era (1830–1844) it remained in use throughout the late Edo period, from 1844 to 1872.

History
The Tenpō-reki system was developed by. Marking the final traditional calendar system devised by Japanese astronomers and mathematicians.

Overview
The Tenpō calendar is a lunisolar system which adopted Teiki-hō method, dividing solar terms by solar longitude instead of time, unlike the previous Heiki-hō method. It begins each lunar month on the day of the new moon and adds A leap month when necessary- specifically when three lunar months occurs between those including a solstice/equinox. the leap month lacks any chūki 中気 (one of the twelve solar terms that are used to determine the months of the year), and is inserted accordingly. Solstice and equinox consistently fall within the second, fifth, eighth and eleventh months. Observations from Kyoto dictates the time used for determining solar terms and lunar phases.

Unlike previous calendars with uniform hours lengths, the Tenpō calendars hour vary seasonally, posing the length of hours changed depending on the time of year. This made it extremely challenging to make Japanese mechanical clocks.

The Tenpō calendar is no longer officially maintained.

Known problems
The Tenpō calendar's assume of fixed month either two or three full lunar months will always occur between such months, containing Solstice and equinoxes. When there are three, that there will be one month without a chūki to be designated as the leap month. It does not clearly define how to treat the case where there is only one full interceding lunar month, nor when such a period contains more than one month not containing any chūki. In 2033, for the first time in the calendar's history, there will be only one complete lunar month between the autumnal equinox and winter solstice, and two chūki-less months between the winter solstice and 2034 spring equinox. This situation leads to what is called the.