Frequency Analysis of Letters in The Squares and Spells

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Editor’s appendix to the book: “Kingdoms of Flame: A Grimoire of Evocation and Sorcery” By E.A. Koetting

Frequency analysis shows that the text of the Squares is highly logical and competing in frequency with natural languages (European languages included). Furthermore, the frequency of the letters in the Squares is close to that in the Spells in the unknown language, though not the same (see tables below; the top-ten letters most frequent in both sources are highlighted red). This might mean that the Squares are anagrams in the same language as the Spells are written in (however, not the anagrams of the Spells themselves), which might also be the reason for their mathematical, gematrical and astrological randomness. Evidently, the Squares have only 21 letters of the Roman alphabet in them (J, Q, V, W и Y are missing). The set of letters in the Spells is virtually identical (missing are B=3 and X=1, which are rare in the Squares, although V, missing in the Squares, appears 5 times); altogether this makes 22 letters as in Hebrew or Enochian. The author also points at some similarity between the system of the grimoire and Enochian magic; however, the language of the Spells is not Enochian and the frequency of the letters in the Squares also differs from that in the Enochian language (see the table based on the Enochian Keys for comparisson).

Frequency of the Letters in the Squares Frequency of the Letters in the Spells Overall Frequency of the Letters Frequency of the Letters in the Keys
1 A 79 20.57% 1 A 85 21.25%   1 A 164 20.92%   1 A 827 15.70%
2 T 43 11.20% 2 T 64 16.00%   2 T 107 13.65% 2 O 654 12.42%
3 L 34 8.85% 3 E 41 10.25%   3 L 75 9.57% 3 I 506 9.61%
4 O 33 8.59% 4 L 41 10.25%   4 E 63 8.04% 4 D 312 5.92%
5 R 31 8.07% 5 U 31 7.75% 5 R 49 6.25%   5 L 308 5.85%
6 S 25 6.51% 6 S 23 5.75% 6 S 48 6.12% 6 R 299 5.68%
7 E 22 5.73% 7 K 20 5.00% 7 U 38 4.85% 7 S 281 5.34%
8 N 20 5.21% 8 M 18 4.50% 8 K 37 4.72% 8 C 247 4.69%
9 K 17 4.43% 9 R 18 4.50% 9 O 34 4.34% 9 N 245 4.65%
10 M 13 3.39% 10 Z 16 4.00% 10 M 31 3.95% 10 M 216 4.10%
11 I 12 3.13% 11 P 8 2.00% 11 N 27 3.44% 11 H 169 3.21%
12 H 11 2.86% 12 N 7 1.75% 12 Z 18 2.30% 12 B 166 3.15%
13 P 9 2.34% 13 F 6 1.50% 13 P 17 2.17% 13 G 162 3.08%
14 D 9 2.34% 14 V 5 1.25% 14 I 16 2.04% 14 T 161 3.06%
15 U 7 1.82% 15 H 5 1.25% 15 H 16 2.04% 15 P 160 3.04%
16 G 6 1.56% 16 C 5 1.25% 16 F 10 1.28% 16 Z 144 2.73%
17 F 4 1.04% 14 I 4 1.00% 17 D 10 1.28% 17 E 133 2.53%
18 C 3 0.78% 17 O 1 0.25% 18 C 8 1.02% 18 U 81 1.54%
19 B 3 0.78% 18 G 1 0.25% 19 G 7 0.89% 19 V 53 1.01%
20 Z 2 0.52% 20 D 1 0.25% 20 V 5 0.64% 20 F 49 0.93%
21 X 1 0.26%   21 B 3 0.38% 21 Q 38 0.72%
    22 X 1 0.13% 22 X 33 0.63%
      23 Y 22 0.42%

For comparison, there is a table of the frequency of letters in some European languages given below. . The top-ten letters of each language, which are also in the top-ten in the tables above, are marked with a red frame, those which are in the top-ten in the Squares only are marked blue, and those which are in the top-ten in the Spells only are marked green.

(Languages, left to right: Russian, English, French, German, Spanish, Italian, Polish, Swedish)

The fact that the last two Squared are missing one grid each also implies that they are anagrams of a coherent text. It seems like the anagrammed text has 2 letters less than can be expressed through the sum of the Squares of natural numbers form 2 to 9. Furthermore, it gives a certain clue to deciphering of the text: probably the eighth Square contains the last letter, the seventh Square contains the penultimate one, etc. The formula for deciphering has not been found, yet the following is obvious:

  1. The Squares are not a mere set of letters but a coherent text.
  2. It is likely to be in the same language as the Spells are.
  3. It is ciphered via letter replacement (like an anagram).
  4. The alphabet of the language almost certainly has 22 letters in it (certainly not less, and if more, than those extra letters are extremely rare).
  5. The text passes through tha Squares several times and not consecutively (first all the letters og one Square, then the letters of the next one, etc.).
  6. The sequence of the Squares is significant.
  7. The correctness of the decipher will be quite obvious because of the text’s readability, some endings characteristic of the language of the Spells and, perhaps, the riming of the text.

The clues to the Squares might be hidden in the text itself.

Fr. Nyarlathotep Otis