A010774 Decimal expansion of 12th root of 2.

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

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

Index entries for sequences based on music

Index entries for algebraic numbers, degree 12

Formula

Equals Product_{k>=0} (1 + (-1)^k/(12*k + 11)). - Amiram Eldar, Jul 29 2020

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

Cf. A103922.

Cf. A214832, A254531.

Sequence in context: A129956 A305865 A342204 * A272610 A350760 A340216

Adjacent sequences: A010771 A010772 A010773 * A010775 A010776 A010777

Keyword

nonn,cons

Author

N. J. A. Sloane

Status

approved