A341113 -id:A341113 - cp's OEIS frontend

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

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

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

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

Cf. A010774, A341113.

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

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

A341114 Denominators of continued fraction convergents to 2^(1/12).

Original entry on oeis.org

0, 1, 16, 17, 84, 185, 1379, 1564, 2943, 7450, 17843, 132351, 547247, 679598, 1906443, 2586041, 157068903, 159654944, 636033735, 795688679, 2227411093, 18614977423, 95302298208, 113917275631, 323136849470, 437054125101, 760190974571, 1197245099672

Offset: 0

Seiichi Manyama, Feb 05 2021

Eric Weisstein's World of Mathematics, Continued Fraction
Wikipedia, Twelfth root of two
Index entries for sequences based on music

For numerators see A341113.

Cf. A002351, A010774, A103922.

Join[{0}, Denominator[Convergents[2^(1/12), 27]]] (* Amiram Eldar, Feb 05 2021 *)

a(0) = 0, a(1) = 1, a(n) = A103922(n-1) * a(n-1) + a(n-2) for n > 1.

cp's OEIS Frontend

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

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