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A010774
Decimal expansion of 12th root of 2.
15
1, 0, 5, 9, 4, 6, 3, 0, 9, 4, 3, 5, 9, 2, 9, 5, 2, 6, 4, 5, 6, 1, 8, 2, 5, 2, 9, 4, 9, 4, 6, 3, 4, 1, 7, 0, 0, 7, 7, 9, 2, 0, 4, 3, 1, 7, 4, 9, 4, 1, 8, 5, 6, 2, 8, 5, 5, 9, 2, 0, 8, 4, 3, 1, 4, 5, 8, 7, 6, 1, 6, 4, 6, 0, 6, 3, 2, 5, 5, 7, 2, 2, 3, 8, 3, 7, 6, 8, 3, 7, 6, 8, 6, 3, 9, 4, 5, 5, 6
OFFSET
1,3
COMMENTS
This number figures in our standard 12-tone tuning of music today.
It represents the frequency ratio of a semitone in equal temperament. The equal-tempered chromatic scale divides the octave, which has a ratio of 2:1, into twelve parts of equal ratio: [2^(n/12), 2^((n+1)/12)), 0 <= n <= 11. - Daniel Forgues, Feb 28 2013
REFERENCES
D. Coulter, Digital Audio Processing. Berkeley, California: Focal Press (2000) p. 30
Ian Stewart, Professor Stewart's Incredible Numbers, London, Profile Books, 2015, pp. 217-228.
LINKS
Étienne Ghys, Musique..., Images des Mathématiques, CNRS, Mar 15 2020.
FORMULA
Equals Product_{k>=0} (1 + (-1)^k/(12*k + 11)). - Amiram Eldar, Jul 29 2020
Equals sqrt(A010768). - Hugo Pfoertner, May 31 2024
EXAMPLE
2^(1/12) = 1.059463094359295264561825294946341700779204317494...
MATHEMATICA
RealDigits[N[2^(1/12), 100]][[1]] (* Alonso del Arte, Jan 06 2011 *)
PROG
(PARI) sqrtn(2, 12) \\ Charles R Greathouse IV, Apr 14 2014
CROSSREFS
KEYWORD
nonn,cons,changed
STATUS
approved