Hinduism has a variety of lunisolar calendars that it uses for marking festivals. The precise details of each calendar may vary -- for example, some of them mark months based on full moons, others use new moons, but the scheme is roughly the same:
- Each new (or full) moon is a named month
- Every few years an extra month (Adhik Maas) is inserted to keep the calendar in sync with the seasonal cycle
- Rarely, a month is deleted.
From what I can find, the leap month calculation is done by the following rules:
- If a month occurs within which there is no zodiac transit (i.e., there is no Sankranti, no change of the Raśi), it is a leap month, and the "real" (Shudh) month occurs after it
- If a month occurs within which there are two zodiac transits, the next month is deleted.
By this scheme, every Shudh month corresponds to a Raśi.
The Indian zodiac is a sidereal zodiac (unlike, say, the zodiac typically used in Western sun signs, which is tropical). What this means is that instead of the zodiac being tied to a specific part of the seasonal cycle; the zodiac is tied to the relative position of the sun against the constellations -- when we say the sun is "in capricorn", it means that if you draw a line through the earth and sun it will overlap with the "house" of capricorn in the celestial sphere.
The tropical and sidereal zodiacs as used in Western and Hindu astrology overlapped roughly 2000 years ago, but have since diverged by around 20 days, due to the precession of the equinoxes. Ayanāṃśa corrections can be used to figure out the difference.
This error is also why, for example, Makar Sankranti (transition into Capricorn), which was originally a solstice celebration, now occurs a couple weeks after the solstice.
Put all together, assuming that the leap month calculations are done based on sidereal Raśi, it means that over the course of time, the months will lose their connection to the seasons.
Except, there are strong seasonal connotations of many of the months -- for example, Śrāvaṇa is strongly associated with the monsoon, and there seem to be records of that association, including in texts by Kalidasa (4th century CE). It's unclear exactly how old these connotations are, however these two statements cannot be simultaneously true:
- The Hindu months have permanent connections with the seasons
- The Hindu lunar calendar inserts Adhik Maas based on a tropical zodiac as opposed to a sidereal zodiac.
I'd like to confirm the latter: What, precisely, is the mechanism for calculating Adhik Maas?