A103922 Continued fraction expansion of the twelfth root of two, 2^(1/12).

1, 16, 1, 4, 2, 7, 1, 1, 2, 2, 7, 4, 1, 2, 1, 60, 1, 3, 1, 2, 8, 5, 1, 2, 1, 1, 1, 5, 1, 1, 3, 5, 1, 1, 1, 2, 3, 1, 1, 1, 73, 3, 5, 1, 1, 1, 2, 26, 2, 1, 1, 2, 7, 2, 1, 1, 2, 3, 1, 1, 1, 14, 1, 2, 1, 4, 1, 19, 8, 3, 6, 5, 1, 2, 1, 1, 1, 5, 1, 4, 1, 1, 3, 10, 1, 1, 4, 4, 9, 4, 4, 1, 1, 1, 4, 1, 19, 16, 13

Offset

0,2

Comments

Successive note frequencies in the twelve-tone equal temperament chromatic scale are 2^(1/12) higher than their predecessor.

Links

Table of n, a(n) for n=0..98.

Michael Rubinstein, University of Waterloo, The Conspiracy of Equal Temperament

Eric Weisstein's World of Mathematics, Continued Fractions

Wikipedia, Equal Temperament

Mathematica

ContinuedFraction[2^(1/12), 100]
ContinuedFraction[Surd[2, 12], 120] (* Harvey P. Dale, Jan 02 2019 *)

Prog

(PARI) default(realprecision, 120); contfrac(2^(1/12)) \\ Seiichi Manyama, Feb 05 2021

Crossrefs

Cf. A010774, A341113.

Sequence in context: A040265 A040264 A040266 * A040267 A363917 A040268

Adjacent sequences: A103919 A103920 A103921 * A103923 A103924 A103925

Keyword

cofr,nice,nonn

Author

Nicholas A Kooij (nickkooij(AT)hotmail.com), May 02 2005

Status

approved