The Mathematics of Yogas, part 2: Parivartana

Parivartana Yoga

Parivartana Yoga is formed when two planets simultaneously occupy a sign ruled by the other, eg, with Saturn in Cancer and the Moon in Capricorn, or Mars in Leo with the Sun in Scorpio, and so on. The two houses thus occupied and ruled become the focus of a symbiotic relationship rich for interpretation. In western astrology, this pattern is called mutual reception, or planetary exchange.

Mutual reception is not an equal-opportunity game. The true planets (Mars, Mercury, Jupiter, Venus and Saturn) have the greatest opportunity for exchange because they each own two signs. The Sun and Moon have the least opportunity because they own only one sign apiece.

In theory, mutual reception allows for the exchange of 12 house lords in 66 combinations. In practice, however, only 57 are possible for any given ascendant. Of the nine excluded, examination of any chart will reveal five by virtue of dual rulership, and four due to astronomical limitation:

• Mars, Mercury, Jupiter, Venus and Saturn each own two houses in every chart. By definition, none can exchange places with itself. For an Aries ascendant, there’s no exchange between the 1st and 8th houses because Mars rules both. Likewise, the 3rd/6th are both ruled by Mercury, the 9th/12th by Jupiter, the 2nd/7th by Venus, and the 10th/11th by Saturn. Similar logic governs every other ascendant. Five combinations of mutual reception are thus excluded – one for each dual house lord.
• Mercury and Venus are called “inferior” planets because their orbits lie within that of the Earth’s. From a geocentric point of view, the angular separation between the Sun and either of them is restricted. Mercury is never more than 28 degrees from the Sun, while Venus can’t exceed 48 degrees. Therefore, there’s no exchange between the lords of Leo and Gemini, since this would require the Sun and Mercury to be 30+ degrees apart, which is impossible. Likewise, no exchange between Leo and Taurus, which would require the Sun and Venus to be 60+ degrees apart, also impossible. Thus, two combinations are excluded.
• For similar reasons, there can be no mutual reception between Gemini and Libra, or between Taurus and Virgo. For Mercury and Venus to exchange across two air signs, or two earth signs, they would have to be separated by the span of three intervening signs, or 90+ degrees apart. Yet at maximum angular separation from each other, Mercury is 28 degrees on one side of the Sun, Venus 48 degrees on the other side, for a total separation of only 76 degrees. So their exchange between same-element signs is impossible. Thus, another two combinations are excluded.

The odds of any planet forming Parivartana Yoga

Although I don’t have the means to perform a scientific analysis of the astronomical potential for mutual reception between any pair of planets, logic alone will get us pretty close to whatever the reality is. Take for example, mutual receptions with the Sun.

If the Sun is in Leo, there is no mutual reception.

The odds of the Sun being in Cancer are one in 12, or 8.33%. The odds of the Moon being in Leo are also one in 12, or 8.33%. The odds of finding (at the same time) the Sun in Cancer and the Moon in Leo are therefore one in 144, or 0.69%.

If the Sun is in Aries, the same logic as above says the odds for mutual reception with Mars in Leo are also 0.69%. But since Mars owns two signs, equal odds apply for an exchange between the Sun in Scorpio and Mars in Leo. Therefore, for a Sun/Mars exchange, the chances that they will form a mutual reception are actually 1.39%. (Two chances at 0.69% each = 1.39% for both, with values rounded to two decimal places.)

If the Sun is in Sagittarius or Pisces, the same logic says the chances for an exchange with Jupiter are also 1.39%. Ditto for the Sun in Capricorn or Aquarius, in exchange with Saturn.

With the inferior planets, it’s a little more complicated, but no less logical. If the Sun’s in Gemini, we won’t find Mercury in Leo, because it can’t be more than 28 degrees from the Sun. So the odds for that exchange are zero. If the Sun’s in Taurus, we won’t find Venus in Leo, because it can’t be more than 48 degrees from the Sun. So the odds for that exchange are also zero.

But if the Sun’s in Virgo, chances are good to find Mercury in Leo because it’s the adjacent sign. In fact, Mercury could only be in Leo, Virgo or Libra, so its odds of being in position to exchange are one in three. Multiply that by the odds of Sun being in Virgo (one in 12) and you get the probability of Sun and Mercury in exchange across Virgo and Leo being 2.78%.

Similarly, if the Sun’s in Libra, chances are fair to find Venus in Leo. Recall that Venus can be up to 48 degrees away from the Sun. Depending on the Sun’s position within Libra, this allows Venus to range anywhere between mid-Leo to mid-Sagittarius. So the chances are (at best) one in five that Venus would be in Leo. Multiply that by the odds of the Sun in Libra and you get the probability of Sun and Venus in exchange across Libra and Leo being 1.67%.

Following the same logic as described in the above three paragraphs, we can also calculate the potential for mutual receptions between Mercury and Venus. For the outer planets (Mars, Jupiter, Saturn), their unfettered freedom of movement allows a much simpler exercise in logic. The following table summarizes the odds for any given exchange.

After taking care to eliminate any instances of double-counting, this analysis renders a probability that approximately 43% of all charts, natal or otherwise, will exhibit at least one mutual reception.

In fact, this very figure is borne out by research I’ve conducted using over 15,000 birth charts with accurate data (Rodden “AA” or “A” rating).

Since there are seven planets available to exchange across 12 signs, some charts will have two Parivartana Yogas, involving four different planets in exchange. This, however, happens in only 3% of charts.

The most Parivartana Yogas to be found in any chart, natal or otherwise, are three. This is quite rare, and happens in only 0.03% of charts, or three out of 10,000. One such example is the chart of Indira Gandhi, shown at the outset of this article.

Those interested in learning more about planetary exchange, including how to interpret it in a natal chart, are encouraged to acquire my book Parivartana Yoga, available in both digital and paper formats through online retailers. To study the same phenomenon through the lens of western astrology, see my expanded companion volume, Mutual Reception.

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Alan Annand is a graduate of the American College of Vedic Astrology and a former tutor for the British Faculty of Astrological Studies. 

His New Age Noir crime novels (Scorpio Rising, Felonious Monk, Soma County) feature astrologer and palmist Axel Crowe, whom one reviewer has dubbed “Sherlock Holmes with a horoscope.”

He’s also the author of several non-fiction books. Stellar Astrology offers a compilation of techniques, in-depth celebrity profiles, and analysis of world events. Parivartana Yoga is a reference text for one of the most common yet powerful planetary combinations in jyotish. Mutual Reception is an expanded companion volume for western practitioners, covering the same subject of planetary exchange through the lens of traditional astrology.

Websites: www.navamsa.com, www.sextile.com

You can find his books on Amazon, Apple, Barnes&Noble, Kobo and Smashwords.