Letter frequencies

The frequency of letters in text has been studied for use in cryptanalysis, and frequency analysis in particular, dating back to the Iraqi mathematician Al-Kindi (c. 801–873 CE), who formally developed the method (the ciphers breakable by this technique go back at least to the Caesar cipher invented by Julius Caesar, so this method could have been explored in classical times).

Letter frequency analysis gained additional importance in Europe with the development of movable type in 1450 CE, where one must estimate the amount of type required for each letterform, as evidenced by the variations in letter compartment size in typographer's type cases.

Linguists use letter frequency analysis as a rudimentary technique for language identification, where it's particularly effective as an indication of whether an unknown writing system is alphabetic, syllablic, or ideographic. For example, the Japanese Hiragana syllabary contains 46 distinct characters, which is more than most phonetic alphabets, e.g. the Hawaiian alphabet which has a mere 13 letters, or English which has 26.

No exact letter frequency distribution underlies a given language, since all writers write slightly differently. However, most languages have a characteristic distribution which is strongly apparent in longer texts. Even language change as extreme as from old English to modern English (regarded as mutually unintelligible) show strong trends in related letter frequencies: over a small sample of Biblical passages, from most frequent to least frequent, enaid sorhm tgþlwu (æ)cfy ðbpxz of old English compares to eotha sinrd luymw fgcbp kvjqxz of modern English, with the most extreme differences concerning letterforms not shared.

Linotype machines (which seem to have been primarily or exclusively marketed for English-language typesetting) assumed the letter order, from most to least common, to be etaoin shrdlu cmfwyp vbgkjq xz based on the experience and custom of manual compositors.

Modern International Morse code (generally believed to have been developed by Alfred Vail based on English-language letter frequencies of the 1830s) encodes the most frequent letters with the shortest symbols; arranging the Morse alphabet into groups of letters that require equal amounts of time to transmit, and then sorting these groups in increasing order, yields e it san hurdm wgvlfbk opxcz jyq. Similar ideas are used in modern data-compression techniques such as Huffman coding.

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