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The temperament of neutral intervals in temperament

The emergence of neutral intervals can be traced back to ancient Greece. In the accompaniment of singing, the Greeks sometimes changed the natural four-note sequence to form an "altered four-tone sequence"; later Achytas proposed reducing the semitones in the four-tone sequence to approximately 1/3, and then further narrowed it. , insert another tone between the two tones that are a semitone apart. It is about 1/4 tone away from the left and right tones and is in a neutral position, forming a "quarter tone four-note sequence".

The Arabs inherited ancient Greek civilization in the Middle Ages. They tuned the lute-style plucked string instrument Oud in a pure fourth relationship and used four tones. The middle finger on the oud is a third minor note higher than the open string, but its pitch wanders. It is customary to call the lower one the "ancient middle finger" and the higher one the "Persian middle finger". Due to the traditional hearing requirements of the ancient Bedouin people, they often move to higher phonemes. In the 8th century, the famous Oud player Zarzhar (? ~ 791) determined this requirement as a new middle finger hoop position between the minor third and the major third, which was called "Zarzal middle finger". Later, A.N. Farabi in the 9th to 10th centuries and Ibn Sina in the 11th century made stipulations on this phonetic theory respectively. The theoretical explanation proposed by the former had a greater influence.

The existence of Zalzal’s middle finger position makes the Arabic scale musically characterized by including neutral intervals. The interval between the major and minor thirds is called the “middle third”, and the interval between The interval between the major and minor sixths is called the "middle sixth". However, this practical temperament is inconsistent with the theoretical temperament established based on the traditional fourth-degree law, both in pitch and mathematics; even in the 13th century, the Persian music theorist Safi al-Din set the temperament based on the fourth-degree law. After the number was increased to 17, the differences and conflicts between the two could not be eliminated. The result of incorporating the unique Arabic modes into the 17-temperament system was to cut corners and inhibit the development of the unique style of Arabic music. It was not until 1888 that the Arab musician and mathematician M. Musaga proposed using 24 equal temperament intervals to simulate the neutral interval, which allowed the neutral interval to break free from the shackles imposed on it by the law of fifths and the pure temperament and display its style and expression. feature.