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Trigrams are a special case of the n-gram, where n is 3. They are often used in natural language processing for performing statistical analysis of texts and in cryptography for control and use of ciphers and codes. See https://www3.nd.edu/~busiforc/handouts/cryptography/Letter%20Frequencies.html for results of analysis of "Letter Frequencies in the English Language".
Context is very important, varying analysis rankings and percentages are easily derived by drawing from different sample sizes, different authors; or different document types: poetry, science-fiction, technology documentation; and writing levels: stories for children versus adults, military orders, and recipes.
Typical cryptanalytic frequency analysis finds that the 16 most common character-level trigrams in English are: [1] [2]
| Rank [1] | Trigram | Frequency [3] (Different source) |
|---|---|---|
| 1 | the | 1.81% |
| 2 | and | 0.73% |
| 3 | tha | 0.33% |
| 4 | ent | 0.42% |
| 5 | ing | 0.72% |
| 6 | ion | 0.42% |
| 7 | tio | 0.31% |
| 8 | for | 0.34% |
| 9 | nde | |
| 10 | has | |
| 11 | nce | |
| 12 | edt | |
| 13 | tis | |
| 14 | oft | 0.22% |
| 15 | sth | 0.21% |
| 16 | men |
Because encrypted messages sent by telegraph often omit punctuation and spaces, cryptographic frequency analysis of such messages includes trigrams that straddle word boundaries. This causes trigrams such as "edt" to occur frequently, even though it may never occur in any one word of those messages. [4]
The sentence "the quick red fox jumps over the lazy brown dog" has the following word-level trigrams:
the quick red quick red fox red fox jumps fox jumps over jumps over the over the lazy the lazy brown lazy brown dog
And the word-level trigram "the quick red" has the following character-level trigrams (where an underscore "_" marks a space):
the he_ e_q _qu qui uic ick ck_ k_r _re red
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In cryptanalysis, frequency analysis is the study of the frequency of letters or groups of letters in a ciphertext. The method is used as an aid to breaking classical ciphers.
Letter case is the distinction between the letters that are in larger uppercase or capitals and smaller lowercase in the written representation of certain languages. The writing systems that distinguish between the upper- and lowercase have two parallel sets of letters: each in the majuscule set has a counterpart in the minuscule set. Some counterpart letters have the same shape, and differ only in size, but for others the shapes are different. The two case variants are alternative representations of the same letter: they have the same name and pronunciation and are typically treated identically when sorting in alphabetical order.
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Letter frequency is the number of times letters of the alphabet appear on average in written language. Letter frequency analysis dates back to the Arab mathematician Al-Kindi, who formally developed the method to break ciphers. Letter frequency analysis gained importance in Europe with the development of movable type in 1450 AD, where one must estimate the amount of type required for each letterform. Linguists use letter frequency analysis as a rudimentary technique for language identification, where it is particularly effective as an indication of whether an unknown writing system is alphabetic, syllabic, or ideographic.
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