The Bhutanese Calendar

This article was revised in June 2013 as new information had come to light in the writings of Abhayākaragupta.

The Bhutanese calendar is a variant form of the main Tibetan calendars. It is very much like the Phugpa system, but has different values for some of the main variables – for example, the mean longitude of the Sun at any time. The mean motions of the Sun, Moon and planets are exactly the same as those used in the Phugpa and Tsurphu systems.

However, the Bhutanese calendar has one very curious and unique feature – the weekdays are one ahead, not only of the main Tibetan calendars, but the western calendar as well. I am sitting writing this on 5th May 2008. It is a Monday, both in the standard Gregorian calendar and in the Phugpa and Tsurphu calendars (and all other Tibetan calendars that I know of). However, in Bhutan, it is a Tuesday.

If you look at the website of the Bhutan Government you will see a small calendar in both Tibetan and western scripts. Those who can read Tibetan will see that the Tibetan for Monday (zla ba) is written together with the western word "Sunday", the Tibetan for Tuesday (mig dmar) is written together with "Monday", and so forth. Clearly, the Bhutanese need to tread carefully to avoid misunderstandings with the rest of the world.

The reasons for this difference are not now clear. I have been told that it comes from interpretations of the Kālacakra Tantra and its calendar by the great Kālacakra expert Buton Rinchen Drup (bu ston rin chen grub), as passed through the Drukpa tradition by Pema Karpo (padma dkar po). However, the exact reasoning is not now known. It seems surprising that Buton is mentioned in this way, as many others, including the founders of the Phugpa tradition, relied heavily on his work. If he had held such radical views regarding the naming of weekdays, we would surely know this.

As the Bhutanese themselves now no longer understand the exact reason that their calendar is out of step in this way, one Bhutanese calendar expert recently asked me: "We need to have a really good reason why we are right, or a really good reason why we are wrong." So, what would constitute a "really good reason", one way or the other? This present article is an attempt to answer this.

A quick look at the calculations used to produce Tibetan style calendars will show that the weekday is calculated almost as if it were an astronomical quantity. This is simply a result of the style of calculation used, which is actually very practical. The first main calculations are all performed for the moment of new Moon at the beginning of a month: the time of new Moon, solar longitude, and so on. The time that matters is the time since the epoch from which the calculations are made, and is simply expressed in terms of a weekday (Sunday, Monday, etc.) plus fractions of a day. The total count of solar days since the epoch is easily and accurately calculated from that information.

There is no astronomical phenomenon that makes today a Monday or a Tuesday. The naming of the weekdays appears to come from an old system of naming the 24 hours of a day after the seven luminaries – the Sun, Moon and five visible planets – in order of decreasing period of revolution: Saturn, Jupiter, Mars, and so on. These simply cycle every seven hours, and the first hour of each day gives its name to the weekday. They are, together with the numbers used to represent them in the Tibetan and Kālacakra systems:

0 Saturday – Saturn
1 Sunday – Sun
2 Monday – Moon
3 Tuesday – Mars
4 Wednesday – Mercury
5 Thursday – Jupiter
6 Friday – Venus

There certainly are some astronomical associations here. One of the main theories for the existence of a seven-day week is that such a week is very close to the period of time between the four quarters of a lunar month – between new Moon and first quarter, for example. There may very well have been some astronomical reason for the original start of the whole cycle, but such knowledge is certainly lost. Apart from the order in which they occur, the weekdays are essentially arbitrary.

In the absence of any astronomical phenomenon that defines weekdays, what objective criterion would convince a Bhutanese calendar maker one way or the other? As the Bhutanese calendar is said to be derived from the interpretations of the Kālacakra Tantra and its calendar by Buton Rinchen Drup, I suspect that the best solution to the weekday dilemma lies in the Kālacakra Tantra calendar itself.

If it can be shown that the weekdays in the original Kālacakra calendar were out of step with the then Julian calendar, in the same way that the Bhutanese calendar is now, then the originators of the Bhutanese calendar would be vindicated, and their calendar could be considered to be "right", in so far as it is intended to be an interpretation of the original Kālacakra system.

On the other hand, if the Kālacakra weekdays were not out of step, but agreed with the Julian calendar, then the Bhutanese calendar is simply the victim of a mistaken interpretation a few hundred years ago. It should then be considered to be "wrong".

As with other later calendars, the Kālacakra system defines an epoch from which calculations are made. The year is clearly 806 C.E. It describes the mean positions of the Sun and planets for the moment of mean new Moon, at the beginning of the month of Caitra (nag pa).

After the time of mean new Moon has been calculated, it is adjusted for the ellipticity of the orbit of the Moon and of the apparent orbit of the Sun. These first calculations also include the longitude of the Sun (also adjusted) and of the Moon. The latter is trivial for new Moon, as it is the same as that of the Sun.

The Kālacakra Tantra gives the time of mean new Moon as 2;30,0. In this notation, the figure before the semi-colon represents a weekday – see the listing above. The first figure after the semi-colon represents a number of nāḍī, there being 60 nāḍī in a solar day, and the last figure represents a number of pala, there being 60 pala in one nāḍī.

In the normal Tibetan interpretation of this value, this represent a Monday, at 30 nāḍī and 0 pala. In the Bhutanese interpretation, the weekday number indicates that the Monday has passed, and the value is therefore a Tuesday, at 30 nāḍī and 0 pala. It has to be said that this interpretation would be at odds with other data used in Tibetan astronomy. For example, a value of 3;47 of longitude means 47 nāḍī within the third lunar mansion, not in the fourth, after the third has completed.

Once the mean time for new Moon has been adjusted for the solar and lunar eccentricities, the time of true new Moon is determined as: 3;4,45,4,8 – the 4 and 8 are further subdivisions of time. This represents a Tuesday (Bhutan: Wednesday) at 4 nāḍī, 45 pala...

The mean new Moon has a time that is exactly halfway through the solar day: this is 5.00pm Local Mean Solar Time. The true new Moon the following day has a time of just after daybreak, at 6.54am. We shall come back to these figures.

I wrote earlier that the year of the epoch was 806 C.E. This is easily calculated from Tibetan texts, but has been disputed by some. In order to be sure, it is necessary to look at the planetary positions given in the Tantra. With the exception of an obvious error in the position of Venus, everything matches up reasonably well with real astronomy only on one particular day – the new Moon just after the Sun entered Aries, in the year 806 C.E. No other day within a very long period either side of that date comes even close. The data in the Kālacakra Tantra give a reasonably approximate picture of the positions of the Sun, Moon and planets (apart from Venus) only for that one day.

Modern scientific calculation systems are able to calculate the positions of the planets in historic times with very high accuracy, and also the timing of events such as new Moon. Taking the meridian through Ujjain at longitude 75.78° as the basis of calculation, and converting the time into units of nāḍī and pala (and breaths, the third sub-division, six in one pala) from mean daybreak, the mean new Moon in question occured on:

23rd March 806 at 26,27,5

The true new Moon was on:

24th March 806 at 1,26,5.

These figures are sufficiently close to the values given in the Kālacakra Tantra that we can consider them to be proof that we have the correct pair of days. If we were to take a meridian a little further to the east of Ujjain, the results would come even closer to the Tantra values.

It is now trivial to check the weekdays: in the Julian calendar, 23rd March 806 was a Monday and the 24th March a Tuesday. The first of these is indicated by the 2 in 2;30,0. The Bhutanese would interpret this as a Tuesday (the Monday having passed), but for the rest of the world it was a Monday. Now, it seems very unlikley that the Kālacakra system would have followed an interpretation that was so out-of-step with everybody else without clearly stating so in the literature. In fact, the main commentary to the Kālacakra Tantra, the Vimalaprabhā, when describing the first year of the sixty-year cycle, Prabhava, states that "this year is well known to other karaṇas, just as the Sunday (is the first) of the weekdays." Such a statement could not have been made if the original Kālacakra writers followed the current Bhutanese interpretation of the weekdays. It can only the case that the figure 2;30 means halfway through that Monday, back in 806 CE.

However, we can be more certain by looking at the Kālacakrāvatāra of Abhayākaragupta, one of medieval India's greatest experts on Kālacakra. When I first wrote this article, the only version of that text that I had looked at was the Derge edition. Having recently obtained a readable Sanksrit edition and compared with other Tibetan editions, I realise that a key sentence in the Derge editon is ambiguous, presumably due to an editing error; at least, it is not as clear as one would wish. The Narthang edition, however, is unambiguous and agrees with the Sanksrit edition:

Narthang Tibetan:
de nas gza'i gnas su gcig la sogs pas nyi ma la sogs pa'i gza' rtogs par bya'o // tshes su ni dbyu gu la sogs pa rnams nyi ma shar ba nas brtsams nas longs spyod par bya ba yin no //
tato vārasthāne ekādikamādityādivāraṃ pratipādayati / tithau daṇḍādikaṃ sūryodayāt prabhṛiti bhoktavyam /
These sentences tell us that the weekday is identified by the number in the weekday place: Sunday and so forth associated with 1 and so forth. Also that the (end of the) lunar day is indicated by the following values for the nāḍī and so forth, and that these give the time from daybreak when the lunar day ends. This is how these values are interpreted by most Tibetan calendar makers and is much clearer than the Kālacakra Tantra and the Vimalaprabhā; this was of course Abhayākaragupta's intention, to explain the calculation of a Kālacakra calendar in easier to understand terms. This settles the Bhutanese question: a day that calculates to 1, for example, is certainly a Sunday and not a Monday.

The Kālacakra Tantra weekdays were clearly in step with the rest of the world, and that in so far as it is expected to adhere to the Kālacakra system, the Bhutanese calendar is therefore in error.

Maybe the original reasoning for this out-of-step weekday will turn up in some text that is currently not available. It is tempting to speculate what the reason might be; but this is a temptation I shall resist...

E Henning.
Last updated 2 September 2013.
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