Temperament - Onritsu

A scale is a standard that defines the relationship between the pitches of each note in a musical scale. The process of actually determining the pitch of an instrument according to a scale is called tuning.

The Chinese and Japanese tuning system is the twelve-tone system. The interval is determined by the ratio of the vibration frequencies of two tones, and when perfect fifths with a vibration ratio of 3:2 are stacked in order, the 12th tone almost coincides with the reference tone. This is why the twelve-tone system, which defines 12 tones within an octave, is the same as the Western Pythagorean tuning system. The method is the third-minute gain and loss method, which alternately adds and subtracts one-third of the length of the tube, and there are records of 60 and 360 tones being found. The twelve-tone equal temperament system was discovered by Zhu Zaiyao of the Ming Dynasty earlier than in the West, but it had already been calculated in the Southern Song Dynasty (420-479), and in Japan, the Japanese mathematician Nakane Genkei attempted it in his book Ritsu Gen Kaihatsu in 1692 (Genroku 5). However, these were all just theories, and in reality, tuning was done with 12 tubes. In India, they use a tuning system called shruti, which is made by dividing half of the string into 9 equal parts and the other half into 13 equal parts, and in Thailand they use 7 temperament. In Arabia, which is characterized by the use of 3/4 tones, 9 or 7 temperament was used in the past, and currently 24-tone equal temperament invented by Meshaqa is used. In Indonesia, there are five-tone and seven-tone tuning systems such as the Slendro scale (Laras) and Pero scale, but they are not unified and instead the subtle differences between each ensemble are valued.

The theory of temperament in Western music originates from the ancient Greek Pythagorean tuning. The method of determining the 12th note is the same as that of the twelve-tone tuning, but the 12th note is strictly a step below the standard note.

The difference between the two is called the "Pythagorean comma." Later, with the development of organum, dissonances of major thirds and major sixths became an issue, and the just temperament system was devised, in which major triads are in harmony within a single key system. In mean tone temperament, the mean tone is an average of the greater tone and the lesser tone, expanding the consonance to closely related keys, making modulation easier. However, as modulation to distant keys progressed, this also shifted to twelve-tone equal temperament, which consists of 12 equal semitones. This equal temperament allowed complete freedom in modulation, and led to the rise of Western music, from late Romanticism to impressionism and twelve-tone music.

[Yoko Hashimoto]

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

音階中の各音の音程関係を規程する基準。音律に応じて実際に楽器の音高を決定することを調律という。

　中国、日本の音律は十二律である。音程は2音の振動数の比で決まるが、振動比3：2の完全5度を順に重ねると12番目の音がほぼ基準音と一致する。このことからオクターブ内に12の音を定めたのが十二律で、西洋のピタゴラス音律と同一である。方法は、管長の3分の1を交互に加減する三分(さんぶん)損益法であり、60律、360律まで求めた記録もある。十二平均律は西洋より早く明(みん)の朱載堉(しゅさいいく)が発見したが、すでに南朝宋(そう)（420～479）で試算されており、日本でも和算家中根元圭(げんけい)が1692年（元禄5）の『律原発揮』のなかで試みている。しかしこれらはすべて理論にとどまり、実際には12の律管で調律した。そのほかインドではシュルティと称し、弦の半分を9等分し、残りの半分を13等分して得られる22律が使われ、タイでは7律が、3/4音の使用を特徴とするアラビアでは、古くは9律や7律、現在ではメシャーカの考案した二十四平均律が使われる。インドネシアにはスレンドロ音階(ララス)、ペロ音階など5音、7音の調律体系があるが、統一的ではなく、逆に合奏楽器ごとの微妙な差異が尊ばれている。

　西洋音楽の音律理論は古代ギリシアのピタゴラス音律に始まる。求め方は十二律と同じだが、12番目の音は厳密には基準音より

高く、その差を「ピタゴラスのコンマ」という。のちオルガヌムの発達とともに長3度、長6度の不協和が問題となり、一つの調体系のなかで主要三和音が協和する純正律が考案された。また中全音律では、大全音と小全音を平均した中全音（ミーン・トーン）により協和関係を近親調まで広げ、転調が容易にされた。しかしこれも、遠隔調への転調が進むにつれ、12の等しい半音からなる十二平均律に移行する。この平均律では転調が完全に自由となり、後期ロマン派から印象主義、十二音音楽に至る西洋音楽の隆盛がもたらされた。

［橋本曜子］

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