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

Author

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

Keywords

• cofr
• nice
• nonn

Comments

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

Links

• Michael Rubinstein, University of Waterloo, The Conspiracy of Equal Temperament
• Eric Weisstein's World of Mathematics, Continued Fractions
• Wikipedia, Equal Temperament

Crossrefs

Cf. A010774, A341113.

Programs

Mathematica

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

PARI

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