cp's OEIS Frontend

A010774 Decimal expansion of 12th root of 2.

%I A010774 #57 Oct 19 2024 15:57:32
%S A010774 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,
%T A010774 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,
%U A010774 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
%N A010774 Decimal expansion of 12th root of 2.
%C A010774 This number figures in our standard 12-tone tuning of music today.
%C A010774 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
%D A010774 D. Coulter, Digital Audio Processing. Berkeley, California: Focal Press (2000) p. 30
%D A010774 Ian Stewart, Professor Stewart's Incredible Numbers, London, Profile Books, 2015, pp. 217-228.
%H A010774 Vincenzo Librandi, <a href="/A010774/b010774.txt">Table of n, a(n) for n = 1..5000</a>
%H A010774 Étienne Ghys, <a href="http://images-archive.math.cnrs.fr/spip.php?page=image&amp;id_document=15039">Musique...</a>, Images des Mathématiques, CNRS, Mar 15 2020.
%H A010774 Wikipedia, <a href="http://en.wikipedia.org/wiki/Twelfth_root_of_two">Twelfth root of two</a>
%H A010774 <a href="/index/Mu#music">Index entries for sequences based on music</a>
%H A010774 <a href="/index/Al#algebraic_12">Index entries for algebraic numbers, degree 12</a>
%F A010774 Equals Product_{k>=0} (1 + (-1)^k/(12*k + 11)). - _Amiram Eldar_, Jul 29 2020
%F A010774 Equals sqrt(A010768). - _Hugo Pfoertner_, May 31 2024
%e A010774 2^(1/12) = 1.059463094359295264561825294946341700779204317494...
%t A010774 RealDigits[N[2^(1/12), 100]][[1]] (* _Alonso del Arte_, Jan 06 2011 *)
%o A010774 (PARI) sqrtn(2,12) \\ _Charles R Greathouse IV_, Apr 14 2014
%Y A010774 Cf. A103922, A010768.
%Y A010774 Cf. A214832, A254531.
%K A010774 nonn,cons
%O A010774 1,3
%A A010774 _N. J. A. Sloane_