A328228 - OEIS

%I #41 Oct 30 2019 13:28:27

%S 1,2,147,5,1,3,5,4,4,1,1,159,6,1,1,1,4,1,2,1,2,3,1,8,15,47,1,103,1,1,

%T 1,1,2,1,1,1,1,1,1,2,1,10,3,1,2,1,2,4,1,1,1,9,28,2,4,2,2,5,1,3,1,1,2,

%U 1,1,1,52,6,2,6,1,5,94,3,6,26,1,6,5,1,3,109

%N Simple continued fraction expansion of 2^(7/12).

%C 2^(7/12) is the multiplier with respect to a base frequency to produce a perfect fifth interval in an equal tempered chromatic scale.

%C This constant is of interest because it is close to the just intonation perfect fifth coefficient of 1.5 (continued fraction [1, 2]). It is the closest to just intonation of the chromatic scale divisions other than the octaves (2*frequency), and unison (1*frequency). The perfect fifth is the most consonant division of the chromatic scale.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Twelfth_root_of_two">Twelfth root of two</a>

%H <a href="/index/Mu#music">Index entries for sequences based on music</a>

%p convert(2^(7/12), confrac,100); # _Robert Israel_, Oct 24 2019

%t ContinuedFraction[2^(7/12), 82] (* _Michael De Vlieger_, Oct 25 2019 *)

%o (PARI) contfrac(sqrtn(2^7, 12)) \\ _Michel Marcus_, Oct 09 2019

%Y Cf. A005664, A103922, A328229.

%K nonn,cofr

%O 0,2

%A _Daniel Hoyt_, Oct 08 2019