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A329220 Decimal expansion of 2^(11/12).

%I A329220 #23 Apr 28 2024 16:25:08
%S A329220 1,8,8,7,7,4,8,6,2,5,3,6,3,3,8,6,9,9,3,2,8,3,8,2,6,3,1,3,3,3,5,0,6,8,
%T A329220 7,5,2,0,1,5,1,3,6,6,0,6,6,7,7,4,8,5,6,2,7,4,8,4,2,5,0,2,8,4,6,3,6,5,
%U A329220 7,2,9,7,5,4,7,7,4,1,3,4,0,6,0,9,0,3,9,6,9,0,9
%N A329220 Decimal expansion of 2^(11/12).
%C A329220 2^(11/12) is the ratio of the frequencies of the pitches in a major seventh (e.g., D4-C#5) in 12-tone equal temperament.
%H A329220 Wikipedia, <a href="https://en.wikipedia.org/wiki/Equal_temperament#Comparison_with_Just_Intonation">Equal temperament</a>
%H A329220 Wikipedia, <a href="https://en.wikipedia.org/wiki/Twelfth_root_of_two">Twelfth root of two</a>
%H A329220 <a href="/index/Mu#music">Index entries for sequences based on music</a>
%F A329220 Equals 2/A010774.
%F A329220 Equals Product_{k>=0} (1 + (-1)^k/(12*k + 1)). - _Amiram Eldar_, Jul 29 2020
%t A329220 First[RealDigits[2^(11/12), 10, 100]] (* _Paolo Xausa_, Apr 28 2024 *)
%o A329220 (PARI) default(realprecision, 100); 2^(11/12)
%Y A329220 Frequency ratios of musical intervals:
%Y A329220 Perfect unison:   2^(0/12) = 1.0000000000
%Y A329220 Minor second:     2^(1/12) = 1.0594630943...  (A010774)
%Y A329220 Major second:     2^(2/12) = 1.1224620483...  (A010768)
%Y A329220 Minor third:      2^(3/12) = 1.1892071150...  (A010767)
%Y A329220 Major third:      2^(4/12) = 1.2599210498...  (A002580)
%Y A329220 Perfect fourth:   2^(5/12) = 1.3348398541...  (A329216)
%Y A329220 Aug. fourth/
%Y A329220 Dim. fifth:       2^(6/12) = 1.4142135623...  (A002193)
%Y A329220 Perfect fifth:    2^(7/12) = 1.4983070768...  (A328229)
%Y A329220 Minor sixth:      2^(8/12) = 1.5874010519...  (A005480)
%Y A329220 Major sixth:      2^(9/12) = 1.6817928305...  (A011006)
%Y A329220 Minor seventh:   2^(10/12) = 1.7817974362...  (A329219)
%Y A329220 Major seventh:   2^(11/12) = 1.8877486253...  (this sequence)
%Y A329220 Perfect octave:  2^(12/12) = 2.0000000000
%K A329220 nonn,easy,cons
%O A329220 1,2
%A A329220 _Jianing Song_, Nov 08 2019