Gematria - Methods

Methods

There are several methods used to calculate the numerical value for the individual words, phrases or whole sentences. More advanced methods are usually used for the most significant Biblical verses, prayers, names of God and angels etc.

• Mispar Hechrachi (absolute value) that uses full numerical value of the twenty-two letters. Sometimes its also called Mispar ha-Panim (face number), as opposed to the more complicated Mispar ha-Akhor (back number).
• Mispar Gadol counts the final forms (sofit) of the Hebrew letters as a continuation of the numerical sequence for the alphabet, with the final letters assigned values from 500 to 900.
• The same name, Mispar ha-Gadol, is also used for another method, which spells the name of each letter and adds the standard values of the resulting string.
• Mispar Katan calculates the value of each letter, but truncates all of the zeros. It is also sometimes called Mispar Me'ugal.
• Mispar Siduri (ordinal value) with each of the 22 letters given a value from one to twenty-two.
• Mispar Bone'eh (building value) uses the sum of each letter added to the next letter within the word to total the value of the word. Therefore, the value of the word "Achad" (one) is 1 + (1 + 8) + (1 + 8 + 4) = 23.
• Mispar Kidmi (triangular value) uses each letter as the sum of the all the standard gematria letter values preceding it. Therefore, the value of Aleph is 1, the value of Bet is 1 + 2 = 3, the value of Gimmel is 1+2+3=6, etc. It's also known as Mispar Meshulash (triangular or tripled number).
• Mispar P'rati calculates the value of each letter as the square of its standard gematria value. Therefore, the value of Aleph is 1 × 1 = 1, the value of Bet is 2 × 2 = 4, the value of gimmel is 3 × 3 = 9, etc. It's also known as Mispar ha-Merubah ha-Prati'.
• Mispar ha-Merubah ha-Klali is the square of the standard absolute value of each word.
• Mispar Meshulash calculates the value of each letter as the cube of their standard value. The same term is more often used for Mispar Kidmi.
• Mispar ha-Akhor The value of each letter is its standard value multiplied by the position of the letter in a word or a phrase in either ascending or descending order. This method is particularly interesting, because the result is sensitive to the order of letters. It's also sometimes called Mispar Meshulash (triangular number).
• Mispar Mispari spells out the standard values of each letter by their Hebrew names ("Achad" (one) is 1+8+4=13 etc.), and then adds up the standard values of the resulting string.
• Mispar Shemi (also Millui letter "filling"), uses the value of each letter as equal to the value of its name. For example, the value of the letter Aleph is (1 + 30 + 80) = 111, Bet is (2 + 10 + 400) = 412, etc. Sometimes the same operation is applied two or more times recursively.
• Mispar Ne'elam (hidden number) spells out the name of each letter without the letter itself (e.g. "Leph" for "Aleph") and adds up the value of the resulting string.
• Mispar Katan Mispari (integral reduced value) is used where the total numerical value of a word is reduced to a single digit. If the sum of the value exceeds 9, the integer values of the total are repeatedly added to produce a single-digit number. The same value will be arrived at regardless of whether it is the absolute values, the ordinal values, or the reduced values that are being counted by methods above.
• Mispar Misafi adds the number of the letters in the word or phrase to their gematria.
• Kolel is the number of words, which is often added to the gematria. In case of one word, the standard value is incremented by one.

Within the wider topic of Gematria are included the various alphabet transformations where one letter is substituted by another based on a logical scheme:

• Atbash uses exchanges each letter in a word or a phrase by opposite letters. Opposite letters are determined by substituting the first letter of the Hebrew alphabet (Aleph) with the last letter (Tav), the second letter (Bet) with the next to last (Shin), etc. The result can be interpreted as a secret message or calculated by the standard gematria methods. A few instances of Atbash are found already in the Hebrew Bible. For example, see Jeremiah 25:26, and 51:41, with Targum and Rashi.
• Albam the alphabet is divided in half, eleven letters in each section. The first letter of the first series is exchanged for the first letter of the second series, the second letter of the first series for the second letter of the second series and so forth.
• Achbi divides the alphabet into two equal groups of eleven letters. Within each group, the first letter is replaced by the last, the second by the tenth, etc.
• Ayak Bakar replaces each letter by another one that has a 10-times-greater value. The final letters usually signify the numbers from 500 to 900. Thousands is reduced to ones (1000 becomes 1, 2000 becomes 2 etc.)
• Ofanim replaces each letter by the last letter of its name (e.g. "Fe" for "Aleph").
• Akhas Beta divides the alphabet into three groups of 7, 7 and 8 letters. Each letter is replaced cyclically by the corresponding letter of the next group. The letter Tav remains the same.
• Avgad replaces each letter by the next one. Tav becomes Aleph. The opposite operation is also used.

Most of the above mentioned methods and ciphers are listed by Rabbi Moshe Cordevero.

Some authors provide lists of as many as 231 various replacement ciphers, related to the 231 mystical Gates of the Sefer Yetzirah.

Dozens of other far more advanced methods are used in Kabbalistic literature, without any particular names. In Ms. Oxford 1,822, one article lists 75 different forms of gematria. Some known methods are recursive in nature and are reminiscent of the graph theory or use heavily combinatorics. Rabbi Elazar Rokeach often used multiplication, instead of addition, for the above-mentioned methods. For example, spelling out the letters of a word and then multiplying the squares of each letter value in the resulting string produces very large numbers, in orders of trillions. The spelling process can be applied recursively, until a certain pattern (e.g. all the letters of the word "Talmud") is found; the gematria of the resulting string is then calculated. The same author also used sums of all possible unique letter combinations, which add up to the value of a given letter. For example, the letter Hei, which has the standard value of 5, can be produced by combining 1 + 1 + 1 + 1 + 1, 2 + 1 + 1 + 1, 3 + 1 + 1, 4 + 1, 2 + 2 + 1 or 2 + 3, which adds up to 30. Sometimes combinations of repeating letters are not allowed (e.g. 2 + 3 is valid, but 3 + 1 + 1 is not). The original letter itself can also be viewed as a valid combination.

Variant spellings of some letters can be used to produce sets of different numbers, which can be added up or analyzed separately. Many various complex formal systems and recursive algorithms, based on graph-like structural analysis of the letter names and their relations to each other, modular arithmetic, pattern search and other highly advanced techniques, are found in the "Sefer ha-Malchuth" by Rabbi David ha-Levi of Draa Valley, a Spanish-Moroccan Kabbalist of the 15–16th century. Rabbi David ha-Levi's methods take into consideration the numerical values and other properties of the vowels as well.

Kabbalistic astrology uses some specific methods to determine the astrological influences on a particular person. According to one method, the gematria of the person's name is added to the gematria of his of her mother's name; the result is then divided by 7 and 12. The remainders signify a particular planet and Zodiac sign.