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The twelfth root of two or (or equivalently ) is an algebraic irrational number, approximately equal to 1.0594631. It is most important in Western music theory, where it represents the frequency ratio (musical interval) of a semitone in twelve-tone equal temperament. This number was proposed for the first time in relationship to musical tuning in the sixteenth and seventeenth centuries. It allows measurement and comparison of different intervals (frequency ratios) as consisting of different numbers of a single interval, the equal tempered semitone (for example, a minor third is 3 semitones, a major third is 4 semitones, and perfect fifth is 7 semitones). A semitone itself is divided into 100 cents (1 cent = ).

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  • Raíz duodécima de dos (es)
  • 열두제곱근 2 (ko)
  • 2の12乗根 (ja)
  • Twelfth root of two (en)
  • Корінь дванадцятого степеня з двійки (uk)
  • Tolfte roten ur 2 (sv)
  • 2的12次方根 (zh)
rdfs:comment
  • La raíz duodécima de dos o es un número irracional algebraico. Es relevante en teoría de la música, donde representa la relación de frecuencia de un semitono en el temperamento igual. (es)
  • The twelfth root of two or (or equivalently ) is an algebraic irrational number, approximately equal to 1.0594631. It is most important in Western music theory, where it represents the frequency ratio (musical interval) of a semitone in twelve-tone equal temperament. This number was proposed for the first time in relationship to musical tuning in the sixteenth and seventeenth centuries. It allows measurement and comparison of different intervals (frequency ratios) as consisting of different numbers of a single interval, the equal tempered semitone (for example, a minor third is 3 semitones, a major third is 4 semitones, and perfect fifth is 7 semitones). A semitone itself is divided into 100 cents (1 cent = ). (en)
  • 열두제곱근 2, 는 열두제곱하여 2가 되는 양의 실수로, 대수적 무리수이다. 음악 이론에서 중요한 수로, 12평균율에서 반음 사이의 진동수 비에 해당한다. (ko)
  • 2の12乗根(2の12じょうこん) は、代数的無理数である。音楽理論において非常に重要であり、十二平均律における半音の周波数比を表す。歴史的にこの数はシモン・ステヴィンによって1580年(草稿、1610年に書き直し)に調律との関連で初めて提唱された。 (ja)
  • Tolfte roten ur 2, betecknat , är ett algebraiskt irrationellt tal. Det används inom musikteori, där det representerar frekvens-förhållandet av en halvton i liksvävande temperatur. (sv)
  • Корінь дванадцятого степеня з двійки або 12√2 — алгебраїчне ірраціональне число. Воно є важливим у теорії музики, де воно задає співвідношення частоти півтонів рівномірно-темперованого строю з дванадцяти тонів. Уперше це число було запропоноване для задання музичного строю в 1580 (вперше описано, переписано в 1610) Сімоном Стевіном. (uk)
  • 2的12次方根是一個代數無理數,計為或,是方程式的正實根。它是音樂理論中的一個重要常數,它代表了十二平均律中半音的頻率比。 (zh)
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  • http://commons.wikimedia.org/wiki/Special:FilePath/Pitch_class_space_star.svg
  • http://commons.wikimedia.org/wiki/Special:FilePath/Monochord_ET.png
  • http://commons.wikimedia.org/wiki/Special:FilePath/4Octaves.and.Frequencies.Ears.svg
  • http://commons.wikimedia.org/wiki/Special:FilePath/4Octaves.and.Frequencies.svg
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