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A329219 Decimal expansion of 2^(10/12) = 2^(5/6).

%I A329219 #22 Apr 27 2024 18:09:46
%S A329219 1,7,8,1,7,9,7,4,3,6,2,8,0,6,7,8,6,0,9,4,8,0,4,5,2,4,1,1,1,8,1,0,2,5,
%T A329219 0,1,5,9,7,4,4,2,5,2,3,1,7,5,6,3,2,0,8,0,6,7,6,7,5,1,3,9,8,4,5,0,3,8,
%U A329219 6,1,6,0,6,6,3,1,5,2,4,9,8,5,2,7,5,0,5,1,5,3,4
%N A329219 Decimal expansion of 2^(10/12) = 2^(5/6).
%C A329219 2^(10/12) is the ratio of the frequencies of the pitches in a minor seventh (e.g., D4-C5) in 12-tone equal temperament.
%H A329219 Wikipedia, <a href="https://en.wikipedia.org/wiki/Equal_temperament#Comparison_with_Just_Intonation">Equal temperament</a>
%H A329219 Wikipedia, <a href="https://en.wikipedia.org/wiki/Twelfth_root_of_two">Twelfth root of two</a>
%H A329219 <a href="/index/Mu#music">Index entries for sequences based on music</a>
%F A329219 Equals 2/A010768.
%F A329219 Equals Product_{k>=0} (1 + (-1)^k/(6*k + 1)). - _Amiram Eldar_, Jul 25 2020
%e A329219 1.78179743...
%t A329219 First[RealDigits[2^(5/6), 10, 100]] (* _Paolo Xausa_, Apr 27 2024 *)
%o A329219 (PARI) default(realprecision, 100); 2^(10/12)
%Y A329219 Frequency ratios of musical intervals:
%Y A329219 Perfect unison:   2^(0/12) = 1.0000000000
%Y A329219 Minor second:     2^(1/12) = 1.0594630943...  (A010774)
%Y A329219 Major second:     2^(2/12) = 1.1224620483...  (A010768)
%Y A329219 Minor third:      2^(3/12) = 1.1892071150...  (A010767)
%Y A329219 Major third:      2^(4/12) = 1.2599210498...  (A002580)
%Y A329219 Perfect fourth:   2^(5/12) = 1.3348398541...  (A329216)
%Y A329219 Aug. fourth/
%Y A329219 Dim. fifth:       2^(6/12) = 1.4142135623...  (A002193)
%Y A329219 Perfect fifth:    2^(7/12) = 1.4983070768...  (A328229)
%Y A329219 Minor sixth:      2^(8/12) = 1.5874010519...  (A005480)
%Y A329219 Major sixth:      2^(9/12) = 1.6817928305...  (A011006)
%Y A329219 Minor seventh:   2^(10/12) = 1.7817974362...  (this sequence)
%Y A329219 Major seventh:   2^(11/12) = 1.8877486253...  (A329220)
%Y A329219 Perfect octave:  2^(12/12) = 2.0000000000
%K A329219 nonn,easy,cons
%O A329219 1,2
%A A329219 _Jianing Song_, Nov 08 2019