Tenpō calendar

The Tenpō-reki system was the work of Shibukawa Kagesuke. This was the last traditional calendar system created by Japanese astronomers and mathematicians.[2]

The calendar is a lunisolar calendar which adopted Teiki-hō, where solar terms are equally divided by solar longitude, in place of Heiki-hō, in which they are equally divided by time. The lunar month starts on a day with a new moon. A leap month is added when there are three lunar months between a lunar month which includes a solstice/equinox and the following lunar month which includes a solstice/equinox. In that case the leap month is the lunar month which does not include any chūki 中気 (one of the twelve solar terms that are used to determine the months of the year). The months which include a solstice/equinox are fixed as the second, fifth, eighth and eleventh months respectively. The time of the day used in the calendar to determine the dates of solar terms and lunar phases is that observed at Kyoto. [3][4]

In previous calendars, hours were of uniform lengths. In the Tenpō calendar, the length of hours changed depending on the time of year.[5] This made it extremely challenging to make Japanese mechanical clocks.

The Tenpō calendar is no longer officially maintained.

The calendar did not define the months of the year when there is only one lunar month or when there are two months which do not include any chūki, between a lunar month which includes a solstice/equinox and the following lunar month which includes a solstice/equinox. These problems lead to what is called the Year 2033 Problem.

• Japanese calendar
• Sexagenary cycle
• Tenpō

• National Diet Library, "The Japanese Calendar"