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

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, 16, 18, 20, 64, 24, 80, 30, 32, 36, 40, 128, 48, 160, 60, 64, 72, 80, 256, 96, 320, 120, 128, 144, 160, 512, 192, 640, 240, 256, 288, 320, 1024, 384, 1280, 480, 512, 576, 640, 2048

Offset: 0

Author

N. J. A. Sloane, Jun 10 2002

Keywords

• nonn
• frac
• easy
• nice

Examples

			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.
		

Links

• OEIS index entry for music.
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,2).

Crossrefs

Cf. A071832, A071833.

Programs

Mathematica

Numerator[2^Floor[#/7]Rationalize[2^((-1+Floor[12(1+Mod[#,7])/7])/12),2^-6]]&/@Range[0,70] (* Federico Provvedi, Feb 14 2014 *)

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

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

Formula

a(n+7) = 2*a(n) for n >= 21. - Rick L. Shepherd, Apr 06 2006

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

Extensions

More terms from Rick L. Shepherd, Apr 06 2006