This website is an exposition of the Trigrammaton Qabalah, (TQ). The basis of the TQ can be found in Liber Trigrammaton sub figura XXVII, Being the Book of the Mutations of the Tao with the Yin and the Yang. This brief document, commonly known as Liber XXVII, was penned by Aleister Crowley in 1907, and was called by him “the foundation of the highest theoretical qabalah.”
The primary text of the TQ is The Book of Mutations; a 500 page e-book which is available for purchase directly from the author. Excerpts from this work are used in this website to demonstrate some of the main principles of the TQ. Much more detailed information can be found in the full-length book. All excerpts are copywritten, and may be used only with permission from the author.
The key to unlocking Liber XXVII is the realization that the 27 trigrams of this Holy Book comprise all the numbers from 0 to 26, written in Base 3 notation.
Most of us are familiar with Base 2, or binary, mathematics. Most computers are based on this principle of counting using only 0’s and 1’s.
In Base 3, there is a third possible digit, so that all numbers are written with 0s, 1s, and 2s. In Liber XXVII, these digits are represented as Tao, Yang, and Yin. By taking these three principles, or digits, three at a time, there are 27 possible “trigrams”, or figures of three lines.
The first principle of the TQ: Tao = 0, Yang = 1, and Yin = 2.
The second principle: Tao is Neutral, while Yang and Yin are opposites.
In line with these two axioms, there is a single trigram that is completely neutral: the Zero, which is composed of three Tao lines, or 000.
The other result of these axioms is that the remaining 26 trigrams form 13 pairs of “opposites”, which we will call antigrams.
Antigrams: A pair of trigrams where one is comprised of a set of lines that are the opposite of the other’s lines. For example, 11 and 19 are Antigrams:
The trigrams of the TQ are used as a classification scheme, to provide a framework for the symbolism of both the Eastern and Western esoteric traditions. Astrology and magic squares, the tarot and runes, divination and arithmology, the Tree of Life and sacred geometry, Taoism and the I Ching, are all absorbed into the TQ system, and explored by the use of the trigrams.
All of this activity derives from the abandonment of the old paradigm of decimal mathematics, in favor of the new paradigm of Base 3 mathematics. Simply put, Base 3 is the foundation for the mathematical mysticism, or qabalah, of the New Aeon.
In our normal decimal system, every digit of a number occupies a place value, which we refer to as the “ones place”, the “tens place”, the “hundreds place”, and so on. In actuality, every place-value in the decimal system is an exponential power of 10, starting with 10 to the Zero power, then 10 to the first power and so on.
Any number raised to the Zero power equals 1, and thus any number base, (whether it’s binary, ternary or hexadecimal), has the last digit representing how many “ones” there are in the number. Also, any number raised to the first power is that number itself, so the next place-value will be the same number as the base; thus in decimal this is the “tens place”, while in ternary it is the “threes place”.
The decoding of the trigrams is a simple process. In Base 3, there are only three digits: 0, 1, and 2. These numerals correspond to the symbols for Tao, Yang, and Yin. As with the hexagrams of the I Ching, the trigrams are analyzed starting from the bottom line and moving to the top line.
In the decoding process, the bottom line corresponds to the first digit of the ternary system. This digit represents the “ones” place, (since 3 to the zero power equals 1).
The middle line of each trigram corresponds to the second digit in ternary, which represents the “threes” place, (where 3 to the first power equals 3).
The top line of each trigram corresponds to the third digit in ternary, which represents the “nines” place, (because 3 to the second power equals 9).
Each line may be occupied by the number 0, 1, or 2, which designates how many ones, threes, and nines go to make up the number.
According to this system, a value can be generated for each trigram by considering which symbol is in which place, and converting those symbols into Base 3, (although almost all numbers in this essay should be considered in Base 3, they will all be converted into decimal for ease of explanation).
For example, the trigram containing three Yang lines has a value of one for the “ones” place, one for the “threes” place, and one for the “nines” place. The sum of 1 + 3 + 9 = 13, therefore that trigram is an expression of the decimal number 13 in the ternary number base.
The same method is used for all the trigrams, with the three symbols of Tao, Yang, and Yin determining how many ones, threes, and nines are involved in each number.
The following diagram should make this clear. It dissects all the digits of a six-digit number in Base 3, (otherwise known as a hexagram). On the left are the powers of 3 that make up the place values. On the right are the sums of those powers, based on whether a Tao, Yang, or Yin occupies that line. The lower trigram thus has a value of 19.
After being decoded, the 27 trigrams found in Liber XXVII are seen to represent all the numbers from 0 to 26. These 27 numbers are not in serial order, and this makes the sequence all the more fertile for creating a new qabalah.
The first trigram contains a zero value for every digit, and therefore equals zero. After the initial zero, the trigrams arrange themselves in three groups of 6, 12, and 8 members, based on the number of zeroes in their digits.
After the zero trigram, the next six trigrams all contain two zeroes, (or Tao-lines), and designate the numerical sequence 1, 2, 3, 6, 9, 18. The total of all six of these numbers is 39; this is the key number of Liber Trigrammaton.
The next twelve trigrams all contain only one zero, or Tao-line. This sequence is in the order 4, 5, 7, 8, 10, 11, 19, 20, 12, 15, 21, 24. The sum of these twelve numbers is 156.
The final set of eight trigrams are the eight Kwa of I Ching; these contain no Tao, and appear in the order 13, 14, 16, 22, 17, 23, 25, 26. The sum of these eight numbers is also 156.
The sum of all the trigrams, (or the numbers from 0 to 26), is 351. This total is split into three sections; the first section of seven trigrams equals 39, and this mediates between the following two sections, both of which equal 4 times 39.
Having decoded the numerical identity of each trigram, the next step in the creation of a new qabalah is to attribute various Elements, Zodiac signs, and Planets to these trigrams. Since the numbers 0, 1, and 2 are also the only digits of the ternary system, they are accorded a special status, and function as the axis of the system.
The initial trigram, valued at Zero, is attributed to the Element of Spirit. The next trigram, valued at 1, is called the Positive pole, followed by the 2 trigram, which is called the Negative pole. Essentially these three numbers are the Trinity; they are a pair of opposites with a neutral Zero between them.
The next four trigrams in the sequence are attributed to the four classical Elements: Fire is 3, Water is 6, Air is 9, and Earth is 18. This is the Elemental order that forms the basis for the tarot found in Crowley’s The Book of Thoth.
The next twelve trigrams symbolize the 12 signs of the Zodiac. These trigrams come in groups of 4, based on the location of the single Tao-line in them: at the top, middle or bottom of the trigram. This allows the groups to be aligned with the Triplicities of the Zodiac. Thus the first four trigrams are the Mutable signs, the next four are the Cardinal signs, and the last four are the Fixed signs. Also, trigrams with two Yang lines are Fire signs, while trigrams with two Yin lines are Water signs, thus reflecting the fundamental polarity found in the Elemental trigrams. The six trigrams with one of each type of line are the Air and Earth signs.
The final eight trigrams are attributed to the seven classic Planets, plus the Earth. These attributions are an unconventional scheme based on structural similarities between the Zodiac trigrams and the Planets that have either their rulership or exaltation in a particular sign. So, for example, the ‘Juppiter’ trigram and the ‘Sagittarius’ trigram both have two lower Yang lines, because Juppiter rules Sagittarius.