A103922 - OEIS

%I #19 Feb 16 2025 08:32:56

%S 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,

%T 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,

%U 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

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

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

%H Michael Rubinstein, University of Waterloo, <a href="http://www.math.uwaterloo.ca/~mrubinst/tuning/tuning.html">The Conspiracy of Equal Temperament</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ContinuedFraction.html">Continued Fractions</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Equal_temperament">Equal Temperament</a>

%t ContinuedFraction[2^(1/12), 100]

%t ContinuedFraction[Surd[2,12],120] (* _Harvey P. Dale_, Jan 02 2019 *)

%o (PARI) default(realprecision, 120); contfrac(2^(1/12)) \\ _Seiichi Manyama_, Feb 05 2021

%Y Cf. A010774, A341113.

%K cofr,nice,nonn

%O 0,2

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