cp's OEIS Frontend

A071831 Frequency ratios for notes of C-major scale starting at c = 1 (numerators).

%I A071831 #28 Apr 28 2025 07:03:17
%S A071831 1,9,5,4,3,5,15,2,9,5,8,3,10,15,4,9,5,16,6,20,15,8,9,10,32,12,40,15,
%T A071831 16,18,20,64,24,80,30,32,36,40,128,48,160,60,64,72,80,256,96,320,120,
%U A071831 128,144,160,512,192,640,240,256,288,320,1024,384,1280,480,512,576,640,2048
%N A071831 Frequency ratios for notes of C-major scale starting at c = 1 (numerators).
%H A071831 <a href="/index/Mu#music">OEIS index entry for music</a>.
%H A071831 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,2).
%F A071831 a(n+7) = 2*a(n) for n >= 21. - _Rick L. Shepherd_, Apr 06 2006
%F A071831 G.f.: (15*x^27 + 9*x^22 + 15*x^20 + 5*x^16 + 9*x^15 + 15*x^13 + 3*x^11 + 5*x^9 + 9*x^8 - 15*x^6 - 5*x^5 - 3*x^4 - 4*x^3 - 5*x^2 - 9*x - 1) / (2*x^7 - 1). - _Colin Barker_, Feb 14 2014
%e A071831 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 A071831 Numerator[2^Floor[#/7]Rationalize[2^((-1+Floor[12(1+Mod[#,7])/7])/12),2^-6]]&/@Range[0,70] (* _Federico Provvedi_, Feb 14 2014 *)
%o A071831 (PARI) r=[1,9/8,5/4,4/3,3/2,5/3,15/8]; for(n=0,10, a=2^n*r; for(m=1,7, print1(numerator(a[m])", "))) \\ _Rick L. Shepherd_, Apr 06 2006
%o A071831 (PARI) A071831(n)=numerator([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 A071831 Cf. A071832, A071833.
%K A071831 nonn,frac,easy,nice
%O A071831 0,2
%A A071831 _N. J. A. Sloane_, Jun 10 2002
%E A071831 More terms from _Rick L. Shepherd_, Apr 06 2006