From ancient time there were some phenomenal calendars. In the 7th century, Princess Wen-Cheng brought Tang's calendar to Tibet, and later Princess Jin-Cheng did the same thing. Apparently, they did not bring with them the theoretical Astronomy which the calendars were based on. Those Tibetan students who were sent to Tang to study Arithmetics did not learn the computations to make calendars. After the down fall of the Tibetan Dynasty, Tibet became chaotic, and the transmissions of the Han calendars stopped, Tibetan were left without a scientific calendar until 11th century.
Around 9th century, Islam extended to India, many Indian Buddhists escaped to Tibet with 'aru-yoga' of the Esoteric (Tantric) Buddhism. Its part of 'Kala (time) Wheel' was a part of the Indian Astronomy, and not up to the early Tang's achievement. Tibetan fused the Indian Astronomy, the Tibetan creativities and the Han calendars (rgya-rtsis) to form their own calendars, later they adopted more from the Han calendars to form the present Tibetan calendars.
The main purposes of the Tibetan calendars were (1) providing a working seasonal schedule for farmers, shepherds, etc. (2) dating the enlightening date of Buddha, for Buddha propheted that Buddhism would exist for 5,000 years (different schools might have different figures). If we knew the precise date of the enlightening of Buddha, then the end of the world of Buddhism would be open to us. The important clue was that there was a complete moon eclipse on the enlightening day of Buddha. (3) computing the moon and sun eclipses. The complete moon eclipse on the date of the enlightening of Buddha indicated the importance of moon or sun eclipses which should increase one's intelligence 1 million times. Therefore, it was important to predict the timing of them for a believer to meditate or study. The Tibetan and the Han calendar are Solar-Lunar calendars
Basically, there are three kinds of calendars in the world: (1) the Solar calendar, used by Ancient Egyptian, Gregorian, etc. (2) the Lunar calendar, used by Islamic, Judaic, etc. (3) the Solar-Lunar calendar, used by Han, Tibetan, etc.
Many people mistakenly classify the Solar-Lunar calendar as a Lunar calendar. In fact, in the Solar-Lunar calendar, the month is counted by the position of the moon, and the year is counted by the position of the sun. For 12 lunar months (a lunar year), there are 354 or 355 days, which is 11 days short of the solar year. To compensate the discrepancy, a `leap' month is added every few years. The proper way to add the leap month was intelligently arranged in Tang Dynasty in the Han calendars, the Tibetan calendars followed them (see below). Leap Month
The way is to take a solar year and divide it into 24 notes, the odd ones (the first, third,...) are called 'jie', the even ones (the second, fourth, ...) are called 'zhong-qi'. The distances between successive `zhong-qi's are always bigger than any lunar month. Tang astronomers simply used the 12 `zhong-qi' as the indicators of months. If there is no `zhong-qi' for a particular month, then there is no indicator for the month, hence the month become nameless, and therefore become a `leap month' (or rather, it takes over the next month's indicator, the next month becomes a `leap' month). Tibetan followed it. 【1】 【2】