Sanfen Sunyi (Subtract and Add a Third)
The ancient method of generating the twelve pitches by subtracting or adding one third of a length
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Sanfen sunyi is the ancient Chinese method of generating pitches: take the length of a pitch pipe or string, subtract one third (sun) to reach the fifth above, add one third (yi) to reach the fourth below, and repeat the alternation to produce the twelve lü in order.
It works on the same principle as Western Pythagorean tuning, but measures pipe and string lengths. After the twelve have been generated, the chain still fails to return to Huangzhong, leaving a comma; that gap is exactly what twelve-tone equal temperament later solved. Sanfen sunyi produces twelve pitches but not free modulation.
Read deeper → The Twelve Lü
Sources
- 三分损益的损一益一算法与十二律不闭合，参《中国音乐词典》与 The New Grove Dictionary of Music and Musicians, "China" 相关条目；本文为原创表述
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