Twelfth Root of Two: Algebraic Number, Irrational Number, Frequency, Ratio, Note, Chromatic Scale - Softcover

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The twelfth root of two or sqrt[12]{2} is an algebraic irrational number. It is most important in music theory, where it represents the frequency ratio between any two consecutive notes of a modern chromatic scale in equal temperament; that is, the interval of a semitone.The twelfth root of two was first calculated accurately by the Chinese mathematician Prince Chu Tsai-Yu of the Ming Dynasty. In 1596, he published a work, Lülü Jingyi (A clear explanation of that which concerns the lu (musical pipes)"), which gave theoretical pipe lengths for 12-tone equal temperament correct to nine places. Prince Chu made note of the difference between his ideal mathematically-tuned lu and traditional pipes, which used a form of Pythagorean tuning. "

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