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A071833 Frequency ratios for notes of C-major scale starting at c = 24. 6
24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 64, 72, 80, 90, 96, 108, 120, 128, 144, 160, 180, 192, 216, 240, 256, 288, 320, 360, 384, 432, 480, 512, 576, 640, 720, 768, 864, 960, 1024, 1152, 1280, 1440, 1536, 1728, 1920, 2048, 2304, 2560, 2880 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..48.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,2).

FORMULA

2^int(n / 7) * ( 3 * ( 91 + (-1)^(n mod 7) ) + 42*(n mod 7) + 8*sqrt(3) * sin( pi*( 1+(n mod 7) )/3 ))/12. - Federico Provvedi, Aug 28 2012

G.f.: -(45*x^6+40*x^5+36*x^4+32*x^3+30*x^2+27*x+24) / (2*x^7-1). - Colin Barker, Feb 14 2014

EXAMPLE

The ratios are 24 times 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

Table[ 2^Floor[n/7] ( 3*(91 + (-1)^Mod[n, 7] ) + 42 Mod[n, 7] + 8 Sqrt[3] Sin[Pi(1 + Mod[n, 7])/3] ) / 12,  {n, 0, 70}] (* Federico Provvedi, Aug 28 2012 *)

3*2^(3+Floor[#/7])*Rationalize[2^((-1+Floor[12(1+Mod[#, 7])/7])/12), 2^-6]&/@Range[0, 70] (* Federico Provvedi, Oct 13 2013 *)

LinearRecurrence[{0, 0, 0, 0, 0, 0, 2}, {24, 27, 30, 32, 36, 40, 45}, 50] (* Harvey P. Dale, May 23 2016 *)

CROSSREFS

Cf. A071831, A071832.

Sequence in context: A286130 A279427 A116203 * A064159 A141632 A308603

Adjacent sequences:  A071830 A071831 A071832 * A071834 A071835 A071836

KEYWORD

nonn,frac,easy,nice

AUTHOR

N. J. A. Sloane, Jun 10 2002

EXTENSIONS

More terms from Kerri Sullivan (ksulliva(AT)ashland.edu), Oct 31 2005

STATUS

approved

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Last modified October 14 07:00 EDT 2019. Contains 327995 sequences. (Running on oeis4.)