1 year = 153 gongs
1 month = N/M gongs
1 year = N/M months
From the first two we also get
1 year = 153*M/N months
N/M = 153*M/N
153 = (N/M)^2
Since 153 is not a square, there are no such integers M and N, exactly.
Let's take the number of lunar months in a year 12.36827... and square it. We get 152.9741... which is close to 153.
Also I note that 153 is a divisor of the number of months (4131) in a 334-year cycle (4131 = 153*27)
If a year of the 334-yesar cycle were divided into 153 gongs, then each gong would have 4131/(334*153) = 27/334 months.
So 27 months = 334 gongs. So I reckon M=27 and N=334
I recall a rough lunisolar cycle of 334 months in 27 years. For the tropical year, this is less accurate than the 19-year cycle.
Actually, 27 years have 153*27 = 4131 gongs, while 334 months have 334*334/27 = 4131 19/27 gongs = 27 19/4131 years.
Also there is no reference to the day and so the mean year in days cannot be worked out from the information supplied.
If all 334-year cycles were to have the same number of days, the mean year would be 365 81/334 days = 365.24251497... days.
From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Helios
Sent: 07 June 2012 01:33
To: CALNDR-L@... Subject: Mystic 153 calendar
A Himalayan monastery reckoned time by a calendar with a year divided into
153 parts called gongs. Every gong, a monk would strike the temple gong.
The lama was asked about this method of time-keeping. He explained that
seeing M months transpire after N gongs would portend that N months would
transpire after M years. In effect, the gong-lunar cycle is analogous to the
luni-solar cycle. What is the mean year of this calendar?