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The Twelve-tone Equal Temperament
一種音樂定律方法，將一個(gè)八度音分成十二個(gè)音程相等的半音，任意相鄰的兩個(gè)半音的音程值均為2的12次方根。由明代音樂家朱載堉（1536—1611）最早提出。朱載堉是世界上最先確定十二平均律的學(xué)者，他不僅推動(dòng)中國律學(xué)進(jìn)入新的歷史階段，也在人類樂律史上樹立了里程碑。早在周朝，古人就發(fā)現(xiàn)了十二律，但是歷代學(xué)者用等差關(guān)系計(jì)算的十二律無法旋宮轉(zhuǎn)調(diào)。而朱載堉認(rèn)識到半音的音高關(guān)系其實(shí)是等比關(guān)系，經(jīng)過巧妙計(jì)算，他創(chuàng)制了“新法密率”，與今天的十二平均律完全一致，其優(yōu)點(diǎn)是可以實(shí)現(xiàn)旋宮轉(zhuǎn)調(diào)。朱載堉還將十二平均律的原理應(yīng)用到樂器中，設(shè)計(jì)制造了一些新樂器。在世界范圍內(nèi)，鍵盤類樂器均廣泛使用十二平均律，鋼琴就是據(jù)此原理發(fā)明并進(jìn)行定音的樂器。
The twelve-tone equal temperament is a standard scale tuning in which an octave is divided into 12 equal semitones, with the interval value of any two adjacent semitones being the 12th root of 2. It was first proposed by Zhu Zaiyu (1536-1611), a musician of the Ming Dynasty. Zhu was the first scholar in the world to determine the twelve-tone equal temperament, and he not only created a new historical stage of Chinese temperament, but also set a milestone in the music history of the world. As early as the Zhou Dynasty, the ancient Chinese had discovered the twelve-tone temperament, but the temperament calculated by scholars over the ages in terms of equivalence could not enable modulation, concerning both key and mode changes. However, Zhu realized that the relationship between the pitches of the semitones was in fact an equiproportional relationship, and after clever calculations, he created a new method of dividing the temperament equally with geometric progression, which is exactly the same as the twelve-tone equal temperament of today, and has the advantage that it enables key and mode changes. Zhu also applied the principles of the twelve-tone equal temperament to musical instruments and designed and built some new instruments. The twelve-tone equal temperament is widely used in keyboard instruments all over the world and the piano is an instrument invented and tuned according to this principle.
引例 Citations：
◎昔黃帝令伶?zhèn)愖鳛槁?。伶?zhèn)愖源笙闹鳎酥铌湥ɡ觯┲?，取竹于嶰谿（xièxī）之谷，以生空竅厚鈞者，斷兩節(jié)間，其長三寸九分，而吹之，以為黃鐘之宮，吹曰“舍少”。次制十二筒，以之阮隃（昆侖）之下，聽鳳皇之鳴，以別十二律。其雄鳴為六，雌鳴亦六，以比黃鐘之宮，適合。（《呂氏春秋·古樂》）
以前黃帝命令一個(gè)叫倫的樂官創(chuàng)制樂律。倫從大夏山的西邊，前往昆侖山的北邊，從昆侖山山谷中取來竹子，選取中空而內(nèi)壁厚度均勻的竹子，截取兩個(gè)竹節(jié)的中間部分，長三寸九分，將吹此竹管發(fā)出的聲音定為黃鐘宮，命名為“舍少”。然后倫依次制作了十二根竹管，帶往昆侖山下，聆聽鳳凰的鳴叫，用來區(qū)別十二律。雄鳳的鳴叫有六律，雌鳳的鳴叫也有六律，用它們來與黃鐘宮的聲音進(jìn)行比較，都適度諧和。
In olden days, the Yellow Emperor commanded the court musician Lun to create a tuning system for music. Lun traveled westward beyond the Daxia mountains and onward to the north side of Mount Kunlun, where he took bamboo from the valley, selected a hollow bamboo with even thickness of the wall, cut a length from the middle part between two bamboo joints measuring three cun (寸) and nine fen (分), and designated the sound produced while blowing this bamboo pipe as Huangzhong Gong (黃鐘宮), and named it Sheshao (舍少). After this, Lun made twelve bamboo pipes in turn which he took to the foot of Mount Kunlun to listen to the sound of the phoenixes, and used these to determine the temperament. The male phoenix's song was divided into six tones, likewise that of the female phoenix. He then compared these with the sound of Huangzhong Gong, and found them both moderate and harmonious. (Master Lv's Spring and Autumn Annals)
◎大抵不用三分損益，而用勾股之術(shù)及開立方之法求之所得也。是以隔八隔六，循環(huán)無端，上下相生，首尾一貫，以證往而不返之說為非。是蓋二千余年所未有，實(shí)自我朝始耳。（朱載堉《律歷融通·附錄·音義》）
大體上不用三分損益的方法，而是用勾股定理和開立方計(jì)算可得到音律的高低。因此每相隔八個(gè)律或者六個(gè)律，就可以無限循環(huán)，前后相生，首尾連貫，這可以證明音律不能循環(huán)的說法是錯(cuò)誤的。這大概是兩千多年來從未有過的發(fā)現(xiàn)，確實(shí)是從我朝才有的理論。
In general, instead of using the method of finding a pitch by mathematical calculation based on the proportional relationship between the length of the wind or string and the pitch of the sound, the Pythagorean theorem and the extraction of a cubic root are used to calculate the level of the temperament. This way, every eight or six temperament interval could be cycled infinitely, with the last and first temperament intervals being produced in succession, proving that the saying that temperament intervals cannot be cycled is wrong. This is probably a discovery that had never been made in the past two thousand years and more, and is a theory conceived in our own dynasty. (Zhu Zaiyu: On the Relationship Between Temperament, Astronomy and Calendars)
推薦：教育部 國家語委
供稿：北京外國語大學(xué) 外語教學(xué)與研究出版社
責(zé)任編輯：錢耐安
