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A071832 Frequency ratios for notes of C-major scale starting at c = 1 (denominators). 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..104.

OEIS index entry for music.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,1).

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

EXAMPLE

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.

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 *)

PROG

(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

CROSSREFS

Cf. A071831, A071833.

Sequence in context: A050135 A109595 A256782 * A327121 A091475 A197482

Adjacent sequences:  A071829 A071830 A071831 * A071833 A071834 A071835

KEYWORD

nonn,frac,easy,nice

AUTHOR

N. J. A. Sloane, Jun 10 2002

EXTENSIONS

More terms from Rick L. Shepherd, Apr 06 2006

STATUS

approved

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Last modified October 14 00:32 EDT 2019. Contains 327991 sequences. (Running on oeis4.)