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
Vincenzo Librandi, Table of n, a(n) for n = 1..5000
Étienne Ghys, Musique..., Images des Mathématiques, CNRS, Mar 15 2020.
Wikipedia, Twelfth root of two
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
AUTHOR
STATUS
approved