| Twelfth Root Of Two |
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Its Decimal value is approximately 1.0594630943593... (which can be rounded up to 1.06 with about 99.95% accuracy). This value can be computed using the Continued Fraction : : Since a musical interval is a ratio of frequencies, and the equal tempered chromatic scale is a way of dividing the equal parts, the semitone must be that ratio which when multiplied by itself twelve times will be equal to Two . Therefore it is the positive real solution for in the equation , or the twelfth Root of two. HISTORY 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, ''Lu lu ching i'' ("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 . This would be calculated again later in 1636 by the French mathematician Marin Mersenne , and as the techniques for calculating Logarithms became widely known, this calculation would eventually become trivial. SEE ALSO
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