A071832 Frequency ratios for notes of C-major scale starting at c = 1 (denominators).

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, 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, 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

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 (0,0,0,0,0,0,1).

Crossrefs

Cf. A071831, A071833.

Programs

Mathematica

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

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

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

Formula

a(n+7) = a(n) for n >= 21; (1,1,1,3,1,3,1 repeats). - Rick L. Shepherd, Apr 06 2006

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

Extensions

More terms from Rick L. Shepherd, Apr 06 2006