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An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent pitches is separated by the same interval. In other words, the pitches of an equal temperament can be produced by repeating a generating interval. Equal intervals also means equal ratios between the frequencies of any adjacent pair, and, since pitch is perceived roughly as the logarithm of frequency, equal perceived "distance" from every note to its nearest neighbor. In equal temperament tunings, the generating interval is often found by dividing some larger desired interval, often the octave (ratio 2:1), into a number of smaller equal steps (equal frequency ratios between successive notes). For classical music and Western music in general, the most common tuning system for the past few hundred years has been and remains twelve-tone equal temperament (also known as 12 equal temperament, 12-TET, or 12-ET), which divides the octave into 12 parts, all of which are equal on a logarithmic scale. That resulting smallest interval, the width of an octave, is called a semitone or half step. In modern times, 12TET is usually tuned relative to a standard pitch of 440 Hz, called A440, meaning one pitch is tuned to A440, and all other pitches are some multiple of semitones away from that in either direction, although the standard pitch has not always been 440 and has fluctuated and generally risen over the past few hundred years.〔The History of Musical Pitch in Europe p493-511 Herman Helmholtz, Alexander J. Ellis ''On The Sensations of Tone'', Dover Publications, Inc., New York〕 Other equal temperaments exist. They divide the octave differently. For example, some music has been written in 19-TET and 31-TET. Arabic music uses 24-TET. In Western countries, when people use the term ''equal temperament'' without qualification, they usually mean 12-TET. To avoid ambiguity between equal temperaments which divide the octave and ones which divide some other interval (or that use an arbitrary generator without first dividing a larger interval), the term equal division of the octave, or EDO is preferred for the former. According to this naming system, ''12-TET'' is called ''12-EDO'', ''31-TET'' is called ''31-EDO'', and so on. An example of an equal temperament that finds its smallest interval by dividing an interval other than the octave into equal parts is the equal-tempered version of the Bohlen–Pierce scale, which divides the just interval of an octave and a fifth (ratio 3:1), called a "tritave" or a "pseudo-octave" in that system, into 13 equal parts. String ensembles and vocal groups, who have no mechanical tuning limitations, often use a tuning much closer to just intonation, as it is naturally more consonant. Other instruments, such as some wind, keyboard, and fretted instruments, often only approximate equal temperament, where technical limitations prevent exact tunings. Some wind instruments that can easily and spontaneously bend their tone, most notably trombones, use tuning similar to string ensembles and vocal groups. ==History== The two figures frequently credited with the achievement of exact calculation of equal temperament are Zhu Zaiyu (also romanized as Chu-Tsaiyu. Chinese: ) in 1584 and Simon Stevin in 1585. According to Fritz A. Kuttner, a critic of the theory,〔 it is known that "Chu-Tsaiyu presented a highly precise, simple and ingenious method for arithmetic calculation of equal temperament mono-chords in 1584" and that "Simon Stevin offered a mathematical definition of equal temperament plus a somewhat less precise computation of the corresponding numerical values in 1585 or later." The developments occurred independently.〔Fritz A. Kuttner. "Prince Chu Tsai-Yü's Life and Work: A Re-Evaluation of His Contribution to Equal Temperament Theory", p.200, ''Ethnomusicology'', Vol. 19, No. 2 (May, 1975), pp. 163–206.〕 Kenneth Robinson attributes the invention of equal temperament to Zhu Zaiyu〔Kenneth Robinson: ''A critical study of Chu Tsai-yü's contribution to the theory of equal temperament in Chinese music''. (Sinologica Coloniensia, Bd. 9.) x, 136 pp. Wiesbaden: Franz Steiner Verlag GmbH, 1980. DM 36. p.vii "Chu-Tsaiyu the first formulator of the mathematics of "equal temperament" anywhere in the world〕 and provides textual quotations as evidence.〔Robinson, Kenneth G., and Joseph Needham. 1962. "Physics and Physical Technology". In Science and Civilisation in China, vol. 4: "Physics and Physical Technology", Part 1: "Physics", edited by Joseph Needham. Cambridge: University Press. p. 221.〕 Zhu Zaiyu is quoted as saying that, in a text dating from 1584, "I have founded a new system. I establish one foot as the number from which the others are to be extracted, and using proportions I extract them. Altogether one has to find the exact figures for the pitch-pipers in twelve operations."〔 Kuttner disagrees and remarks that his claim "cannot be considered correct without major qualifications."〔Fritz A. Kuttner. p. 163.〕 Kuttner proposes that neither Zhu Zaiyu or Simon Stevin achieved equal temperament, and that neither of the two should be treated as inventors.〔Fritz A. Kuttner. p. 200.〕 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「equal temperament」の詳細全文を読む スポンサード リンク
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