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%I #27 May 24 2022 01:44:52
%S 1,8,4,3,2,3,8,1,4,2,3,1,3,4,1,2,1,3,1,3,2,1,1,1,3,1,3,1,1,1,1,3,1,3,
%T 1,1,1,1,3,1,3,1,1,1,1,3,1,3,1,1,1,1,3,1,3,1,1,1,1,3,1,3,1,1,1,1,3,1,
%U 3,1,1,1,1,3,1,3,1,1,1,1,3,1,3,1,1,1,1,3,1,3,1,1,1,1,3,1,3,1,1,1,1,3,1,3,1
%N Frequency ratios for notes of C-major scale starting at c = 1 (denominators).
%H <a href="/index/Mu#music">OEIS index entry for music</a>.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,1).
%F a(n+7) = a(n) for n >= 21; (1,1,1,3,1,3,1 repeats). - _Rick L. Shepherd_, Apr 06 2006
%F G.f.: (x^27 + x^22 + 2*x^20 + x^16 + 2*x^15 + 4*x^13 + x^11 + 2*x^9 + 4*x^8 - 8*x^6 - 3*x^5 - 2*x^4 - 3*x^3 - 4*x^2 - 8*x - 1) / ((x - 1)*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)). - _Colin Barker_, Feb 14 2014
%e The ratios are 1 (c), 9/8 (d), 5/4 (e), 4/3 (f), 3/2 (g), 5/3 (a), 15/8 (b); followed by these 7 numbers multiplied by successive powers of 2.
%t Denominator[2^Floor[#/7]Rationalize[2^((-1+Floor[12(1+Mod[#,7])/7])/12),2^-6]]&/@Range[0,70] (* _Federico Provvedi_, Feb 14 2014 *)
%t PadRight[{1,8,4,3,2,3,8,1,4,2,3,1,3,4,1,2,1,3,1,3,2},120,{1,1,1,3,1,3,1}] (* _Harvey P. Dale_, Nov 16 2020 *)
%o (PARI) r=[1,9/8,5/4,4/3,3/2,5/3,15/8]; for(n=0,20, a=2^n*r; for(m=1,7, print1(denominator(a[m]),","))) \\ _Rick L. Shepherd_, Apr 06 2006
%o (PARI) A071832(n)=denominator([1,9/8,5/4,4/3,3/2,5/3,15/8][n%7+1]*2^(n\7)) \\ _M. F. Hasler_, Jun 13 2012
%Y Cf. A071831, A071833.
%K nonn,frac,easy,nice
%O 0,2
%A _N. J. A. Sloane_, Jun 10 2002
%E More terms from _Rick L. Shepherd_, Apr 06 2006
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