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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 with the development of movable type in Asia in 1040 CE and in Europe 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 language 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. Likewise, 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 opjxcz yq. Similar ideas are used in modern data-compression techniques such as Huffman coding. Letter frequency was also used by other telegraph systems, such as the Murray Code. ==Introduction== Letter frequencies, like word frequencies, tend to vary, both by writer and by subject. One cannot write an essay about x-rays without using frequent Xs, and the essay will have an idiosyncratic letter frequency if the essay is about the frequent use of x-rays to treat zebras in Qatar. Different authors have habits which can be reflected in their use of letters. Hemingway's writing style, for example, is visibly different from Faulkner's. Letter, bigram, trigram, word frequencies, word length, and sentence length can be calculated for specific authors, and used to prove or disprove authorship of texts, even for authors whose styles are not so divergent. Accurate average letter frequencies can only be gleaned by analyzing a large amount of representative text. With the availability of modern computing and collections of large text corpora, such calculations are easily made. Examples can be drawn from a variety of sources (press reporting, religious texts, scientific texts and general fiction) and there are differences especially for general fiction with the position of 'h' and 'i', with H becoming more common. Herbert S. Zim, in his classic introductory cryptography text "Codes and Secret Writing", gives the English letter frequency sequence as "ETAON RISHD LFCMU GYPWB VKJXQ Z", the most common letter pairs as "TH HE AN RE ER IN ON AT ND ST ES EN OF TE ED OR TI HI AS TO", and the most common doubled letters as "LL EE SS OO TT FF RR NN PP CC". The "top twelve" letters comprise about 80% of the total usage. The "top eight" letters comprise about 65% of the total usage. Letter frequency as a function of rank can be fitted well by several rank functions, with the two-parameter Cocho/Beta rank function being the best. Another rank function with no adjustable free parameter also fits the letter frequency distribution reasonably well (the same function has been used to fit the amino acid frequency in protein sequences.) A spy using the VIC cipher or some other cipher based on a straddling checkerboard typically uses a mnemonic such as "a sin to err" (dropping the second "r")〔 Friedrich L. Bauer. ("Decrypted Secrets: Methods and Maxims of Cryptology" ). 2006. p. 57. 〕〔 Greg Goebel. ("The Rise Of Field Ciphers: straddling checkerboard ciphers" ) 2009. 〕 or "at one sir"〔 Dirk Rijmenants. ("One-time Pad" ) 〕 to remember the top eight characters. The use of letter frequencies and frequency analysis plays a fundamental role in cryptograms and several word puzzle games, including Hangman, Scrabble and the television game show ''Wheel of Fortune''. One of the earliest description in classical literature of applying the knowledge of English letter frequency to solving a cryptogram is found in E.A. Poe's famous story ''The Gold-Bug'', where the method is successfully applied to decipher a message instructing on the whereabouts of a treasure hidden by Captain Kidd.〔(【引用サイトリンク】title=The works of Edgar Allan Poe in five volumes )〕 Letter frequencies had a strong effect on the design of some keyboard layouts. The most-frequent letters are on the bottom row of the Blickensderfer typewriter, and the home row of the Dvorak Simplified Keyboard. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Letter frequency」の詳細全文を読む スポンサード リンク
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