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Harvest Moon Festival in East Asian Calendar.
The calendar in East Asian countries (China, Japan, Korea, Vietnam) is a Luni-Solar calendar. The months of this calendar begins with each New Moon. A month is named based on the position of the Sun in the Celestial sphere during that month.
1. Naming of months in a Luni-Solar year.
In summary, the months are named according to the following rules:
11th month must encompass the Winter solstice day 21st of December,
12th month always follows 11 month,
1st month of next New Year always follows 12th month.
2nd month must encompass the Spring Equinox day of 21st of Mar,
3rd month must encompass the day when the Sun has Right Ascention of 30°
4th month must encompass the day when the Sun has Right Ascention of 60°
5th month must encompass the Summer solstice day 21st of June,
6th month must encompass the day when the Sun has Right Ascention of 120°
7th month must encompass the day when the Sun has Right Ascention of 150°
8th month must encompass the Autumn Equinox day of 23rd of September,
9th month must encompass the day when the Sun has Right Ascention of 210°
10th month must encompass the day when the Sun has Right Ascention of 240°
When a year has 13 months it will be called a leap year, the extra month will be called a leap month and that leap month will NOT satisfy any of the above conditions for naming. It will then bear the same name as the preceding month defined by the above rules. Due to the naming convention, there will be no leap month between month 11 and the 1st month of the following New Year.
2. Harvest Moon Festival.
The full Moon day of the 8th month is the day of Harvest Moon Festival.
Therefore, East Asian Havest Moon Festival is always the Full Moon nearest to September 23rd Equinox day.
3. Seasons in East Asian luni-solar calendar.
Seasons return after the stars in the sky have come back to their previous positions, that is after 365.25 days. Simple calculations  shows that each lunar month is 29.530 days. Two lunar months has a length of 59.06 days.
The luni-solar calendar used in China since ancient time has had Winter solstice falling on the 11th month of the year since more than 2000 years ago, since 113BC (Han Dynasty II p.38 ) .
4. Midnight stars can identify luni-solar months.
Country people often use stars to identify their luni-solar months. The following examples show how a bright star can be used to identify a month:
4th month must encompass the day when the Sun has Right Ascention of 60°, its midnight stars should be of 240 degree R.A., and Delta Scorpii (240.22° R.A., –22.60° decl.) is almost its midnight star.
6th month must encompass the day when the Sun has Right Ascention of 120°, its midnight stars should be of 300 degree R.A., and Altair of Aql (297.7° R.A., 8.85° decl.) is almost its midnight star.
1st month of next New Year always follows 12th month, Regulus of Leo (152.05° R.A., 12° decl.) is almost the midnight star for one night of that month.
. tonytran2015, simple-determination-of-east-asia-lunisolar-new-year, survivaltricks.wordpress.com,
. tonytran2015, Finding North direction and time accurately from the horn line of the Moon, survivaltricks.wordpress.com, https://survivaltricks.wordpress.com/2015/08/12/finding-north-direction-and-time-accurately-from-the-horn-line-of-the-moon/
. Sima Qian, Records of History by the grand historian (translated by Burton Watson), Qin Dynasty, Han Dynasty I (Rev. Ed.) and Han Dynasty II (Rev. Ed.), the Res. Cent. for Transl. The Chinese Univ. of Hon Kong and Colubia Univ. Press, Hong Kong and New York, 1961.Han Dynasty II p.38 showed that in 113BC, month 11 has the solstice.
. Helmer Aslaksen, The Mathematics of the Chinese Calendar, http://www.math.nus.edu.sg/aslaksen/calendar/chinese.shtml, accessed 19 Jan 2017.
. Ho Ngoc Duc, Thuat toan am lich (in Vietnamese), https://www.informatik.uni-leipzig.de/~duc/amlich/calrules.html, accessed 19 Jan 2017.
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